A Simplified Simple Approach to Partisan Proportional Representation, motivated by desire to prevent spurious body majority--Two versions

A: Overhang Resolution (OR) Preventing Spurious Majority

  1. District Winner phase
    a) SIngle Seat FPTP districts, with expanded options:
    i)Vote with a single vote for the office of district representative for a single candidate running in the district as USAians are accustomed.
    ii)But as an option, a voter who chooses to abstain from influencing the identity of this district representative may instead cast their vote for a party, or individual candidate running in another district in the race; this is the only difference in the mechanics of voting from typical FPTP single winner in single district races. (The accommodation of the out-of-district or party only options can be done as simply as providing a write in line, especially aided by the voter being able to look up and write in a code for a party or candidate, to prevent ambiguity. Note that this means a person can vote for a party while withholding voting for the candidate who might be running in that party in their district, but cannot vote for a person without also voting for the party the candidate they select is affiliated with). All votes always specify a party.

Note “party” is defined by the electoral machinery in an inclusive way that avoids dependency on formal party machinery. For instance an independent with no affiliations is treated as a party of one. This definition starts from a fundamental basis of all races being between persons as individual candidates, but the priority here is to get representation the voter can best count on to meet their goals. As historic practice shows, most voters value party existing toward this end, and the approach is designed to give voters maximum options in getting one they closely align with–by whatever values they deem important.

  1. Proportional phase
    a) Determining overhang magnitude:
    i) Each vote has necessarily recorded a partisan choice; these partisan votes are now added up across the entire system. Using Hamilton’s method of Greatest Remainders, proportional shares of the standard legislature size are computed. (Reasons for favoring Hamilton will be presented with examples).
    ii) Grouping the individual district winners also by their registered partisan affiliation, the totals for each party from the district votes are counted and compared to proportional shares.
    iii) If any party has more than their proportional shares, the differences in each case are added together for total overhang. This number is doubled, and added to the standard seat number of the body being elected, and the proportional shares for each party again computed based on the larger seat count thus generated. (If this fails to fully raise any overhanging party, that could be a partner in a multi-party coalition controlling a majority of seats, which coalition however falls short of a majority in its combined popular vote share (this is what I mean by “spurious majority”), another iteration of overhang top off as above must be done–small parties might retain an overhang, but this can remain if the excess cannot enable a spurious majority.

  2. Top off using the district candidates who did not win plurality district seats:
    a) Using the proportional shares computed with the smallest expansion after the first pass needed to adequately resolve overhangs to prevent spurious majorities as above, we now subtract the district wins from each party’s proportional share.
    b)Then we rank the list of each party’s votes in each district where they did not win the district race. For each party having N seats above their plurality win count remaining, take the top N ranked candidates to become the top off delegation to complete the party delegation.
    c) Special case of party shares greater than candidates contesting for that party: It may be that a party wins more seat shares than it ran candidates, so a procedure to choose extra representatives who did not stand for election would then be required. (Party lists are not satisfactory aside from other objections to them, since not all entities treated here as a party are actually parties. I have a suggested general procedure in mind, but note in this version of the basic proportionally by top off approach, this will happen mainly because of parties not choosing to contest all races but proving popular anyway).

  3. As an option the system may consider seeking to maximize representation of all voters by an asset voting procedure to fill another iteration of top off additions providing opportunity for parties failing to get any direct representation, in numbers proportional to the share of unrepresented voters taken together.

B: Fixed Top Off Seats (as in MMP).

Here, instead of the number of top off seats floating based on plurality discrepancies, we have a fixed house size larger than the number of districts. I think in terms of a doubled size, or doubled plus one to maintain an odd number for tie breaking if that is valued. Thus, the US House of Representatives (method might not be fully Constitutional to apply as is, variations will be offered in another topic) would be raised to 871 members, but states will be apportioned 435 districts for single seat plurality races. (Approach might be modified to allow for other modes of choosing the single seat district reps, provided an acceptable way of determining proportionality is possible–this holds for OR top-off approach too of course).

  1. the same as for OR, the voter has the same voting experience, essentially identical to current prevailing US practice but with added choices as described above.

  2. Here the proportionality is computed for the full size house, not the district number. Overhangs ought to be rare and small but can still happen and if they do the same principles as in OR apply–one guaranteed round of overhang compensation if any overhangs occur, followed by elimination of those which involve parties that can create a spurious majority in coalition. But generally we can hope overhangs will not occur at all, though scenarios to cause them are easy to describe.

  3. The top off seats are filled as in OR by identifying the top vote winning candidates not elected in phase 1. The possibility a party has not run enough candidates to fill their share is much more likely here, and is sure to happen if any party gets a majority of popular votes–as voters spread their choices around more, that might happen rarely in practice, but with almost twice as many seats the likelihood of a party failing to contest enough seats for their total share rises generally anyway. I mean to describe an option to fill those seats meant to both keep voter choice meaningful and relevant, and enable non-party independents and coalitions of them to be exactly as capable of realizing their claim. I am aware in some MMP systems as in New Zealand this is not done, but this is not an MMP system though there are resemblances, or if it is it is a special kind, and the philosophy of the system serving voter interests is the reason to insist all parties be able to fill their full share somehow.

  4. again as an advanced option to explore, provision can be made for maximal possible representation of all voters with some indirection via an asset voting plan to fill a final, small, set of seats based on the number of voters as yet still unrepresented by any elected members.

Posts on theory and philosophy may follow soon, but first I would like to offer at least one example; I have many others I have worked on over the past few years. These are mostly entirely based on real world election returns–one reason that while I am interested in exploring options to improve the system with perhaps better ways to do the district wins, such as AV, Score voting etc, I want people to bear in mind the system as conceived is grounded on simple single choice voting with no further elaborations for the voter.

The idea is, if the voter knows their vote will not be wasted and will result in a proportional share for their prime choice, that is sufficient because other benefits of other systems will occur in legislature operational dynamics. It becomes important to reform those institutions too of course, but we should be doing that anyway! The mechanics of the vanilla top off model are those of plurality single district FPTP races, but the outcomes should differ significantly as do the options for the voter.

Therefore the choices voters make will presumably, and we rather hope, change from those they make with FPTP, but we can always conceive these examples as showing what could happen even with current voting patterns, and as instances where the unfamiliar new system is met with conservatism by the voters initially, before they learn their way around.

I am open to criticism that points out pitfalls, but optimistic that these will overall be far less harmful than the reality we in the USA generally currently live with, and trust that on that, we can at least all agree!

That may be unconstitutional. A “do not transfer” option on the ballot should be sufficient to remove that issue.

For examples, let us start with the state of Michigan State House Election of 2012, as this case has been made pretty notorious among election reform communities across the nation, notably by FAIRVOTE.

Basic facts: the State House of Michigan has 110 members elected from 110 single member districts. In addition to Democratic and Republican parties, the Libertarian, Green, and US Taxpayer party regularly contest though they have not to my knowledge elected any candidates, and other candidates run in various ways which I have lumped together as NPC, no party candidates.

Data is from the Michigan state Secretary of State’s election reports, though much collated by hand. I believe I can paste in a detailed district by district table and this would be needed to fully explore phase 3, but let us begin with statewide totals:

Michigan State House			
    2012			                                DEM	     REP	    LIB	    GRN	    UST	    NPA		
    110		              State race total								
    Totals		              4478331	            2387756  2040126	28842	4820	3351	13436		
    Contested districts249	                        108	     110	    17	    5	    4	    5	*Note 1	
    FPTP district wins 110	                        51	     59						
    Processed for Hamilton Greatest Remainder proportions										
    Maximum district vote			                43993	 32466	    4843	1415	1362	6882		
    Total/districts (quota)40712.1								
    Fraction			                            0.5332	 0.4556	    0.0064	0.0011	0.0007	0.0030	*Note 2	
    Raw seat share			                       58.6498  50.1110	    0.7084	0.1184	0.0823	0.1690		
    Hamilton seats  			                   59	    50	        1					
    Excess plurality seats?			               -8	     9	       -1					
    2*positive excess		18								
    Expanded House membership		128								
    New quota		34986.96094								
    Raw seat share			                       68.2470  58.3110	    0.8244	0.1378	0.0958	0.1690		
    Hamilton seat quota			                   68	    59	        1					
    Make up seats over plurality		           17	     0	        1     *Note 3	
    No further top offs needed as the Republican share rises to match their plurality wins. 										
    Alternative approach: 220 seat House as standard										
    Double raw seat shares vs 110 seats as above			
                                                  117.2996   100.2221	1.4169	0.2368	0.1646	0.3381		
    Hamilton seat quota		       117	           100	        2			                        1	*Note 4	
    Expand party list to examine viability of largest indepenent										
    State total		4478331								
    Quota for 220		20356.05	
                                  DEM	        REP	           LIB	   GRN	UST	    Bing Goei, District 76	NPA	
    Totals			  2387756	2040126   28842	   4820	3351   5484	                                7952	
    Maximum		      43993	    32466      4843	   1415	1362   5484	                                3784	
    Raw seat share	     117.29100.2221 1.4169	 0.2368	0.1646 0.2694	                     0.1859*Note 5
    Hamilton seats     118	        100	           2					
    Make up seats 	      67	          41	           2	*Note 6	

Dear God, that was difficult! Apparently there are limits to how well the system will parse a paste from a spreadsheet; I lost control over the last lines.

This was the first of the so far four races in Michigan under the 2010 Census based redistricting, which is quite infamous in the news of late. FairVote jumped on this for their poster example of unfair effects of gerrymandering and has put up a number of proposals to reform MI’s system.

As one can I hope see at a glance, if the fixed width font formatting holds for everyone’s browsers, Democratic candidates won 53.32% of all State House race votes, the Republicans on;y 45.56%. The balance went to several third party contenders, mostly to the Libertarians who contested 17 districts.

As is infamous at least among us electoral reform wonks, the FPTP upshot quite literally reverses the Democratic-Republican balance to give the Republicans precisely the share of the 110 seats proportion would give the Democrats, giving them control over the House by a margin of 9 seats.

I trust, assuming the formatting of columns does not get all borked again, that the Hamilton method is clear–all parties get the whole number part of their raw fraction, here 58 Democrats and 50 Republicans, leaving two seats unassigned; these go to the two parties with highest remainder, here the decimal fraction–that is the Libertarians with over 70 percent of a seat quota get the first one, then the Democrats with nearly the same excess are raised to 59.

Leveling is done by noting the Republicans alone exceed their share, by 9 seats, so on the theory that an extra seat gained by one party is one denied to another, we add 18 to 110, for 128 total seats. (The additions always being even automatically preserves the choice of either having even or odd numbers of seats too–most state legislatures I have seen do not bother with the tie breaking odd number as the US House of Representatives does). Refiguring the proportions, the Democratic share rises to 68, the Republicans are leveled up to match their plurality won share of 59, and the Libertarian single win holds to make the balance of 128. 65 seats are needed to control the body, the Democrats hold that and more by 3 seats, as they should if they got the majority of PV. The process of choosing the makeup seats is explained in the notes, which I had better provide now!

  1. No Party Affiliation candidates contested in 5 districts, but at least one of them and perhaps more were contested by more than one independent, so there were actually at least 6 independents.

  2. To compute independent, unspecified Other or write in potential for inclusion, we can, instead of looking at the total of all of them, look at the largest and divide it by the quota to get raw share for that single candidate alone. (As it happened, here this was a district with 2 NPA independents running, so it is further necessary to check this kind of thing and break them out before concluding one won a seat). If the Hamilton evaluation gives the strongest independent a seat, we need to make them a new column, and remove them from the combined NPA column, and proceed in this way with the next largest until we don’t get them winning seats. It is necessary to treat a potential winning NPA/independent as though they were a party in their own right, to get the total evaluation to be correct. Accordingly here on the chart, the fraction is the fraction of the whole group of NPA but the vote share is based on the maximum district.

  3. at this point on the chart we have 17 make up Democrats and one Libertarian to elect from the also-rans who lost the plurality vote. These are the top 17 Democrats who did not win in their district and we would have to refer to the district totals line by line to find them–it is easily done with the spreadsheet Rank function of course. These all lost to Republicans so we know that those 17 districts all become two member, with one each Republican and Democrat, and we will see if we look these are all strongly contested districts, with the electorate divided, so it seems right to represent them with both major parties. The Libertarian is the strongest performing single Libertarian candidate, one Michael J Perry of the 88th District in Ottawa County (near Muskegon on the Lake Michigan shore, IIRC) with 4843 votes–as it happens, this was one of two districts the Democrats did not contest at all, so this district too gets two members, one Republican, one Libertarian.

  4. Following the alternative track of apportioning 220 seats fixed to the various parties, before we can conclude the other three parties have the shares the initial line indicates, we need to determine if the NPA top district total merits a seat or not. As it happened, there were two independents running in that district, so we have to expand out District 76’s Bing Goei’s 5884 votes separately (and check no other district exceeded that in NPA–none does) and leave the remainder for the other guy in the NPA column.

  5. When we do this, it turns out Goei does not quite have one of the largest two remainders, and thus is not elected. The expanded raw seat shares clearly show the Democrats get the last seat, for a total outcome of 118 D, 100 R, 2 L.

  6. Thus, as above, we need to seat 67 Democrats beyond the 51 who won plurality races, 41 additional Republicans, and 2 Libertarians. We know one of those Libertarians already. The Democratic total of 118 is eight more than they could possibly have run with only 110 districts, because they won the minority–the New Zealand MMP “solution” of dropping the excess wins would thus automatically prevent any party that wins a majority of PV from ever having a majority in the house, clearly wrong in this system. As it happens the Democrats also did not contest two districts, so actually they need ten more than they ran. I mean to discuss a system for choosing the non-candidates who fill out the list, but suffice it to say now it is not true that only parties can do this–one system I have in mind works the same for independents should one win two seats share, as is entirely possible if not extremely likely. No party lists need apply! We know then that every Democrat who put their hat in the ring now takes office, along with ten more who did not run. Meanwhile that is not quite true of the Republicans–they ran 110, in every district, but their bottom ten among the 51 defeated in the districts by Democrats do not win, though the other 41 do. The second Libertarian has much lower numbers than the first, and comes from a district contested by both major parties, and so that district will have 3 representatives–but hey, it is a district where three parties contended strongly! Meanwhile another district was not contested by either Democrats or Libertarians, leaving a Republican to run unopposed–it is impossible for that district to have more than that one Republican (unless the Republicans won more than 110, and this unopposed fellow was among the top Republicans to clone for a spare representative. But they didn’t, so that district can have only one rep, along with 10 others where the Republicans lost with the lowest numbers. Thus we have 11 districts with one rep, 108 with two (one of these being R-L not R-D) and one R-D-L district.

This method may need some graphics to explain for voters. I’d like to see it trialed with a small group.
The biggest issue with this is that you can’t support multiple independents if any one of them has no chance. I still don’t understand your opposition to Approval being used normally here, since in the worst case everyone can just vote for their one favorite, and in the best case, they vote for multiple, and their ballot gets exhausted once someone they picked is elected. This allows for more independent-only voting.

On what grounds? I am not saying I am sure you have to be wrong, by any means, but offhand, what sort of rights protection issue do you think this violates? It is an action the voter has to take a little bit of trouble to take, and that alone is plenty of evidence that this is the result they aim at.

The purpose of allowing a voter to vote for a party not running at all in their own district is to enable people in small minorities who have different priorities than the winning majorities in their district to express their own judgement and concern. (You might have noticed I evolved it in my thinking with the struggles of the Civil Rights movement very much at the front of my mind, from comments I made on that subject. It can be a very important failsafe in this system!)

If the system supports counting a vote for a candidate running elsewhere in the race for the same category of office but in another district, why require a person who approves a party in general, but not its particular candidate who happens to be running as the face of that party in their home district, to specify another candidate of the same party in another district, why not just allow them to write in a party code for the party they like (even if it is already on the ballot) to thus pointedly exclude supporting that candidate as a person?

There is no logical contradiction in holding that a party in general deserves support but a particular candidate of it does not.

I forget if it was you or someone else who referred me to PLACE voting. I found that while the machinery of PLACE is quite different than mine, the philosophy of the person expounding on it at Electowiki made many points I agreed with very much. PLACE certainly provides a route to do exactly what I propose here with this special provision, and off hand I cannot see a reason why anyone would object.

Except to be obstructionist of course! I don’t think anyone here has been obstructionist although I get badly misunderstood a lot, but we all know there are plenty of people who will offer disingenuous objections, and not boggle at blandly contradicting themselves on the purported principle later when it suits them on another point. Obstructionism is most definitely a thing.

But a bad way to do it in context.

Right or wrong, the whole philosophy of this approach is “partisan” in the sense that even anti-party people in a sense use party identity of a kind all the time, and relies on party, in the broad sense, to register what it is people want.

One can support a party of one, an independent, and sometime I mean to make a whole topic about “anti-party party,” taking the Ray v Blair SCOTUS decision of 1952 and the subsequent existence in Alabama and Mississippi for at least two election cycles after, '56 and '60, of “unpledged electors” winning MS and Alabama electoral college seats on that explicit platform.

It is no prejudice or exclusion or burden then on persons who are strongly averse to party generally to be required to register some kind of party choice here–bearing in mind that can be an “anti-party” independent or even coalition–or organized party for that matter!

When I moved to Humboldt County California in 1992, I was incensed that after registering as a Green and thus screwing myself out of the Democratic primary, the Green party held no primary… when I asked someone who claimed to be a Green why there was no primary he said something along the lines of “Um, dude, like aren’t we Greens, like, the party of people who don’t think there should be parties?” I did not argue the point, just went and registered Democratic at the first opportunity. No, reading Petra Kelly on the German Greens, that is not at all what I thought we would be about! Haven’t seriously been involved with the Greens since.

So it is optional to vote for a person, but essential to register support for one party, bearing in mind that is a broad open category.

If someone says “the system must be for voting for persons and not parties generically,” the straightforward workaround is to provide for voting for a candidate out of district as PLACE also does, and for the disgruntled person wanting to pointedly exclude supporting their local candidate to write in their favorite candidate the party runs they do like–and that actually helps that admired if distant candidate advance to office if they lose the plurality race (out of district support does not count in that race, as the district outcome is the business of district residents properly) but are advanced up the ladder of votes won by this expatriate support.

The option of voting for a party not embodied by a local candidate was mainly envisioned not for some such disgruntled person who wants to vote Libertarian say, but not for this Libertarian, but mainly for people whose favored party is simply not present in the district at all. So, in the British Westminster Parliament, such a reform allows someone to vote say for Scottish National while not a resident of Scotland, or Plaid Cymru while living far away from Wales, or vote Tory in a district where absolutely everyone else votes Labour. So the idea of allowing a vote for party but not specifying any person in particular to benefit from that vote was mainly for convenience. The ballot can just print all the parties on the bottom, or selectively just those that don’t have a candidate in the local race, and the voter can just mark it, one and done, no need to scribble or type in a name and code number for some candidate on the other side of the country.

If some pettifogging argument (or weighty, serious concern that if I understood it might wreck this whole scheme perhaps) forbids decoupled party votes as an option, then of course the purpose is best achieved by requiring the voter to name a specific candidate running elsewhere. After all there is no meaningful way to vote for a party that has no candidates whatsoever! I’ve always said the complete party list is of parties running someone, somewhere.

Please re-read the portion I quoted. I was talking about the part where voting for a person explicitly counts as a vote for their party if that person can’t win. The right to association (1st Amendment) may mean that a voter should be allowed to have their vote staying only with who they want. Even the creator of PLACE had at one point considering putting “do not transfer” in their system, though I don’t know why or for sure if they removed it.

That is not my strong suit particularly, though if I took some trouble and time I might be able to kludge out something. My freehand drawing is about preschool level of competence. I can use software to make diagrams, but they won’t exactly pop, nor do I own any good software to speak of.

And I have a lot of trouble imagining what should be shown in pictures anyway.

The verbal description seems straightforward, just vote the way USAians are used to, pick one, and as with PLACE the system does the donkey work for you–your one counts three ways to come as close as reasonable, considering whether one is in line with a large majority where one lives or some weird outlier, to deliver a legislature you have influenced to a maximal degree, one person one vote. The mechanics are for wonky people, but they are simplicity itself compared to say cranking out STV or the nightmarish iterative tangled process in the “The Excess Method.”

Pictures comparing Hamilton’s rule versus Jefferson’s (those are the ends of the spectrum, other PR fraction to integer mapping methods lie between them in outcome) might come in handy, but only in arguing with someone who already knows what Jefferson’s method is.

Um, how does that work? It is a pitfall of my approach that one has to pick one–if one picks a person one has picked their party too; if one has the option of not picking a person but only a party, that party is one’s only choice. So if there are multiple independents, I would be voting for one of them only if they were my honest preference, if I felt “damn, this person would kick ass in the Assembly and for all the right causes, so much better than anyone running in any of the parties!” Then I would hope other people also saw this person’s merits and voted for them too. But I can’t simultaneously hold off the Greater Evil big party by throwing the Lesser Evil Big Party an electoral bone, no. I have to decide, kickass super great independent, or line up with a party that is pretty good. Frankly, the odds of such a paragon independent appealing to me and not running under some party banner strike me as near zero; part of being a kickass super candidate is knowing one needs to have an alliance.

Talking about how the “party” system is clean-sheeted, by building conceptually from individual candidates to compacts of independents to chartered parties, is meant for another if related topic. But it seems to be a major conceptual barrier that when I talk about parties, I am talking about a spectrum that includes independents as a party of one–and have shown how one almost could have been elected in Michigan 2012, which is a terrible example–when I get to examples like US House of Representatives in 2012, 14, 16 and 18 it will be pretty amazing how many independents can be elected despite their being unable to form alliances, in fact about as many independents typically win as third parties (not third party delegations, but separate parties getting anyone elected). All that is with people voting as they do now, afraid for good reasons to step out of the duopoly box.

So the system provides in fact for a person to vote for several independents simultaneously, just not in their own district. A group of independents with more or less compatible aims can form a compact (by unanimous mutual consent) and register it with the state, and then all votes each one gets group together just like a party, and if the compact wins one or more seats it goes to the one or more who got the most votes. Such an independent might run in my district and I might choose to cast my single vote for them, not some longer established party. My vote counts toward electing someone in that coalition and if the coalition does well, they might all be elected. But only one per district of course.

I think you mean, two or more in my district. Yep, the district will elect one person as district rep, and the top off process might or might not name a second or third candidate from my district to take office too. But the district race is to elect one, not to elect a bunch, so necessarily my vote in the district, whether we used AV, Score, IRV or what have you, Borda Counts or what not, will boil down to either supporting the one who does win, or not supporting them. So if there are two great independents who I think deserve to win–too bad, only one of them can. With AV I can support both, but this just punts the decision of which one will win, or some third person none of us likes, to other voters. With IRV I can agonize over which one to rank first, which second–and glumly fear that I better rank one of the big parties third, because neither of these will win and my low rank choice will be my first choice effectively.

In real life I have been voting since 1984, and I can’t recall a lot of mental wrestling and agonizing over choosing between two or more great candidates. It has always been a monotonous slog of “the great one has not got a snowball’s chance in hell.” Sometimes I slog along and back them anyway, knowing we are going down in flames but perhaps might do so nobly. But come November it is always a choice between Dumb and Dumberer, so Dumb gets my vote–otherwise the wrong lizard might get in you know. Sometimes I feel absolutely great about the one I was privileged to vote for, people like Lynn Woolsey, US Rep from California, or State Senator Wes Chesbro, or my current Assembly member, or my former state assembly woman in Sonoma county, Patty Berg. I like voting for social workers you see, or single moms who have been on Welfare. Sometime I should tell the Dan Hamburg story.

Other times, not so great. I put a ton of effort into getting Harry Reid reelected to the Senate in 2010 and it leaves a sour taste in my mouth, but absolutely I’d do it again (or not, if I were sure my slacking and just voting for him with a sigh would get him, and not the person running against him, elected in 2010). It was a grind and I felt kinda dirty. But nevertheless, given the binary choice we had, I absolutely did the right thing. I am sick of those binaries and want more flexibility.

But I follow Mark Twain’s maxim, “put all your eggs in one basket–and watch that basket!” Give me assurance my vote will not be wasted and I can turn away from the Harry Reids of the world to find their own friends, and shrug off the danger of the Sharron Angles getting in alongside the Reids, knowing at long last I can do my part to put one of the really good ones in, and hope they shine there and either the Reids trim their sails to follow the lead, or people desert them when they see what they are about.

So if they pick mainstream big party as one of their choices, it gets exhausted and their support for the indies is a placebo. If you cast your approval vote for two indies but neither of them musters enough support to win, your vote vanishes into the ether anyway.

Mine is the system where your vote can be guaranteed, or nearly so, to go somewhere and do something other than get grounded out in the duopoly. It can’t go two places at once, but neither can AV really.

So I am far less against AV than I was when someone Liked CES on FB a week ago which brought me here. I actually think it would be a cool way to settle the single seat district races.

What I am worried about, if everyone casts AV just in one district race only, is that there is no way to define a coherent inference of what each person’s favorite was, so that these favorites can be granted seats in proportion to the numbers of those whose honest first choice was them. Nor would Score voting leave that any clearer, if anything I think it muddies the waters even more. The only good thing about RCV in my view is that I do think you can count the first choice as a sincere indication of what each voter actually wants, and count them up to get proportional targets to guarantee hitting. I’m told this is an error but darn it, if I rank someone number one, and someone else number two, number two is not my sincere first choice! Let alone 3,4,5, etc. So we could have IRV in the districts, if in fact people knew that they were not risking anything at all in being sincere in their first choice, because a make up would guarantee their first choice winning proportionally, and then it does not matter what weird shenanigans go on locally, that just churns up the need for more top off seats at worst.

So what I don’t understand is people opposing the idea that we can have AV but should have a separate indication of which of the approved choices is one’s Prime choice. That’s all I ask.

That’s better odds than only one. And what if the coalition the independents form isn’t the way a voter wants?

Not if you look at who was most preferred in a Hare Quota, or check who got the highest score on the ballot. See Apportioned Score Voting.

Possible additions:
Each party’s legislators get a weight of Total Party Vote / Party Seats Won. (Or at least the party vote weights average that, the system could be done in a way that guarantees district winners a weight no less than the number of votes they received.) Then each candidate from a party with no seats can transfer their votes to a party or legislator in an Asset phase.

To make the Asset phase more palatable to the public, it could be required that only the top X candidates among the unelected can win with Asset votes.

I’ve had a look at the chart and it is interesting. What it does for me is take me back to the question, “what is proportion that we are mindful of it?” The basic concept I put out here is that we have a system first of all allowing people to vote in local districts for any benefit that gets us, which might be upon consideration great or negligible–but as noted, I am thinking grounded in the project of getting a system applicable to the USA, and we are a huge country. I don’t think we are actually all that diverse, our monoculture is pretty pervasive, and if we were somehow forced to use a vanilla party list PR system we’d get along well enough, probably way better than we do now. But supposing local districts with single winners (or small numbers of multiple) are vital somehow, how then to neutralize the terrible effects of making the entire governing body entirely a composite of dozens of balkanized, separated local district runs? That is a huge part of why more nuanced political positions have trouble being expressed–if you have to pick just one, it is necessary that one has very broad appeal, so that there is no opportunity for more obscure positions to get any expression, save virtual, whatsoever. That clearly locks a significant part of the electorate out, and there is just a legion of other serious problems–total exclusion of ethnic minorities for instance, or partisan gerrymandering–that are best attacked at the roots, by cutting off the leverage that makes them effective.

So let’s think of that chart a second. It reminds me of a way to think of what we are doing when we figure “proportional” outcomes based on just single votes, say as in European party list global elections–cast one vote for your favored party and that is all, no districts or being allowed to fiddle with the party list to be elected or anything like that.

Say then we elected ten seats, to a city council or something, based on a party vote of that kind. And we had the outcome 43% A, 35% B, 16% C, 3% D and a bunch of weird outliers (figuring the ballot is very liberal about inclusion, so anyone can write in any party they care to pretend exists and the votes count as unspoiled if the registrar can identify some organization running under that name–say rather as in my system, the registrar has to just record the applications of a group and give them a code number so voters can identify them unambiguously, and most of the voters do that, only a small part the last 3 percent are spoiled or joke or flaky ego self-write ins with no identifiable support. Note though that once my application of the basic system I propose here had an unidentifiable write-in in Virginia teetering right on the edge of being elected–and I had no way to determine if those votes were even for a single person, let alone find out who that person might have been!)

Raw seat shares under Hamilton would be 4.3, 3.5, 1.6, 0.3 and perhaps the Greatest Remainder paradigm means someone in the last 3 percent can win a seat, but let’s take a look…we have 8 quotas right there, so there are just 2 seats in play, remainders rank 0.6, 0.5, two different 0.3–for tie breaking say the small party has just a hair more votes than A’s remainder…by basic Hamilton we are done when we award a spare seat each to B and C, in the opposite order in fact, so the outcome is

4 4 2

Ha, that worked, apparently I need to stay under a certain size limit (anyone who understands how posting charts from spreadsheets here works is begged to chime in!)

Now following the chart, say the electorate were just 100 people so we had 43, 35, 16, 3 and 3 others voting for themselves or something. Mindlessly following the flowchart without taking easy and just as accurate math shortcuts, We’d go "who scores highest–why A does, with 43 votes, so A gets a seat, now A has 33 and B scores highest so B gets a seat, now B has 25 so A gets the next seat and has 23, now B wins and has 15, now C gets one and has 6 left. Going on like that, when we have seated 8 of the 10 seats, we get to a level where no one has a quota, and this means further seats awarded presumably on the principle of the next one going to whoever has the most left, result in the awardee–B for their 4th and C for their second as it happens–not having 10 but only respectively 6 and 5 being deducted. D and the three individualists have nothing on the council, but comprise 6 votes out of 100 that never accomplished anything, and A still has 3 left unsatisfied, for a total of 9 left out.

So what do we think of the last two seats being won for cheap, just six votes for the 9th and 5, half price, for the second? This is how it goes with Hamilton’s rule; the last few seats are won below quota, either by some big party with a remnant or a little one (or several) at the top of the list of subquota parties; the big parties have essentially random, anyway chaotic (that is, deterministic but extremely hard to predict) fractions of a quota left over–here all the party contingents in the ones place are that fraction, so we could see in advance that the remainders would be for C, 6, for B, 5, for A and D, 3 and the three individualists are each a remainder of one. So we can see at a glance also by adding up the tens places that there would be eight quota seats and know that therefore C and B must pick up the last two.

Is this some kind of artifact of using Hamilton? Well consider the conceptual approach that matches using Jefferson’s rule–that is, a divisor method where we are running a round robin, sort of auction like, where we give the first seat to the biggest party then discount that party (for Jefferson-D’Hondt, dividing by 1 plus the seats already won, for Webster-Sainte Legue, by 1 plus double the seats won) and alternate like that until all ten are gone and call that good. Note there are other approaches to computing either divisor method–we can for instance just line up all the parties, divide by the same basic quota we use for Hamilton (that is, divide voter count by seats) and then if the whole number parts of the results do not add up to the total, we can fiddle around–usually described as varying the divisor, but that is the same thing as varying a common multiplier of all the numbers, until the whole number parts rise or drop to the target numbers. That’s Jefferson; for Webster we first round the raw shares according to the normal rounding rule, but we might wind up with the wrong total that way and again have to fiddle with a common multiplier. Yet another tack we can take, bearing the equivalency of this spreadsheet approach to the iterative one, is use the fixed quota divisor to get us the first draft whole numbers, then iterate from there until we hit our target of seats. Anyway that works for Jefferson, if Webster gave us an excess on the first crack we can’t exactly run the iteration backwards so we have to go back to fiddling with a multiplier below one–but we could, if our first shot at estimating the multiplier took us low, iterate from there.

So conceptually, we again start with the raw shares we get by taking the ratio of each party to the total vote and multiplying by seat total, so we get to 8 seats distributed A 4, B 3, C 1, and then the Jefferson procedure would be to compare 43/5, 35/4 and 16/2–not by coincidence these are all in the ballpark of between 8 and 9. All are well above D’s “bid” as it were (I keep thinking of this exercise as an auction and the votes as money!) of 3, as yet discounted and it seems quite likely never to be. C is out for the moment, being clearly 8 and the lowest, we can compare A and B by cross multiplying, A becoming 172/20 and B, 175/20, so B gets the 9th seat, and its index becomes 35/5 or 7, while A remains nearly 9 and so gets the last seat. We get A 5, B4, C1 and everyone else is just frozen out, 6 of 100 votes winning nothing. In that metric it is the same as Hamilton which gave us the same three parties winning seats, but there it was meaningful to consider the deviation of satisfaction–if a seat is worth ten votes, A still had 3 left over, B was 5 ahead, and C 4 ahead, and not by accident A’s dissatisfaction with 3 of its 43 votes not winning anything, added to the frozen out 6 of D-G, add up exactly to the surplus B and C enjoy. But with Jefferson, while B is just the same, C loses a seat vs Hamilton, and thus is dissatisfied and shortchanged 6 votes, while A is two ahead, the eight surplus units of power concentrated in 2 parties at the top, while all below B are shortchanged, for a total of 12 voters effectively frozen out, though half of those voted for a party that did get one seat.

Again, not a big fan of Jefferson! In this case, Party A controls half the seats with Jefferson–which is still not a majority, so actually in terms of either controlling the body unilaterally or having to make some deals with someone in B or C, A is not better off, except that maybe with C reduced to one lousy seat, they are desperate enough to come over to A’s Dark Side and eat the cookies of a majority coalition, while with Hamilton, it is indifferent whether C chooses to ally with A or B. All C can accomplish under Jefferson with this outcome is to deadlock the body; they are under some pressure to join with A, and A can try to partner with B instead and make C completely irrelevant. If a coalition between A and B is in the cards, it matters little whether A has 5 or 4 seats because either way C is steamrollered and having two seats would not help. With Hamilton, C can dicker with either A or B, presumably actually negotiating with both, or if one of those is repugnant, marry the other one, and the council is run 6 to 4 by either.

What about spurious majority? The popular vote any of 3 possible coalitions of the 2 parties embody is the same no matter which PR formula we use, the latter just affects whether it amounts to a body majority or not. Under Hamilton with these numbers there are 4 combinations giving a body majority, including of course the unanimous total coalition of all together. The smallest of these is B and C, which give a decisive 6 to 4 body majority. And this embodies 35 + 16 members, which is clearly a majority of voters, though just barely–especially significant with 6 voters not counting to any party in the body! Under Jefferson there are only 3 including the grand coalition of all, and both involve A and someone else–these have a more solid majority of the whole electorate since B and C is excluded as being one short of majority–though it can deadlock A alone, and that seems fair considering it does in fact embody the (smallest possible!) majority of the whole electorate. However I just pulled these numbers out of the air, not doing any kind of figuring in advance, and it would be possible for B or C to be smaller and still combine to 6 seats under Hamilton.

How small can C be and still get a second seat? We have to transfer some people to other parties, but we have plenty of room for them to shift over to the bottom 4 without any of those coming close to getting a seat. C had the highest remainder and one quota seat, so as long as we don’t change the quotas of the three major parties, and C retains the second highest remainder, we can shrink it down. Another limit is not losing the quota seat so right away we see C can’t lose more than 6. It can lose two and fall to a remainder of 4 and still be the second in remainder order, but if it falls to 13 then A,C, and D are tied for the last remainder unless we also trim down A and D. Let’s bump C down to 14 then. This can be done by shifting two voters to support say E and F, one each. If we shift B down a vote, its remainder will tie with C’s, but maybe that is OK, now E to G are tied with two each. We can then trim off 3 from A, if they all go evenly to E-G, now D-G are all tied at 3.

So we have A=40, B=34, C=14, and D-G all with 3. Per Hamilton, we still get 4, 4, 2 for the top parties, and the coalition of B-C embodies 48 voters while having 60 percent of the vote in the body. That’s a spurious majority!

I will say this is bit of a far fetched extreme, with me shifting the votes just so; clearly it can happen naturally, but I don’t think it highly likely, whereas Jefferson’s method shifts support up the ladder, as seen here in taking a seat from C and giving it to A, consistently.

This exercise is making me think harder about spurious majority. Is it something we can prevent by any contrivance of electoral rules? I’m thinking, no it is not!

But perhaps we can make rules for how the legislature operates, in combination with top-off rules to mitigate it a bit perhaps. I certainly have to go back and change the rule that mandates further overhang iterations because if any overhang whatsoever is tolerated, clearly including that party in a coalition will almost certainly enable a spurious majority. Rather than junk the extra iteration rule completely, I can reduce it to apply only to a party that gets a spurious majority in itself via the overhang. Can I show that under Hamilton, no single party can have a spurious majority in itself?

Well, what if B and C were combined into one party, call it Alpha, with the trimmed figures above–that is we have Alpha with 48 voters, A with 40, D-G all with 3. Now we see per Hamilton the quota part of seat assignment jumps straight to 4 and 4 for the top two parties, and we get Alpha with 5, A with 4 and the last seat goes to D–and we need a tie breaking rule (asset voting among the 4 bottom parties comes to mind!) Now we have 9 unrepresented, but with tie breaking two or more of the bottom 4 parties must combine to elevate one to the third party role. The smallest possible majority coalition is now guaranteed to have a majority.

But can Alpha win 6 seats with fewer than 51 members? If Alpha were raised to 50 members it would win 5 seats by quota, but then have no remainder at all. So no, no configuration of other parties could result in Alpha picking up that sixth seat.

But what about in general? Can a party have half the votes minus epsilon, where epsilon is some small number greater than zero, and win a decisive majority of seats? If we have S seats, Rounddown(S/2) + 1 is the majority, if S is even then we have just S/2 + 1, if it is odd we have (S-1)/2+1. Can a party get these numbers Nmaj while having half or less the total popular vote?

If the popular vote is P, the quota is P/S, and so to get Nmaj the party must get quota P/S times either S/2 for even S or (S-1)/2 votes, plus enough more to be included in the greatest remainders for the final seat. For even S, we see that the party must get at least P/2 and so any extra votes to be in the remainders list will raise the party into the popular vote majority. “Epsilon” cannot exist then for even S.

Odd S however seems to open the door pretty wide! Now we have P*((S-1)/S) plus some number enough to get it onto the greatest remainder list. In theory the remainder list can go very low, but going below half of P/S makes the chances of getting a remainder seat pretty remote! From all the practical work I have done, I think a party with as much as a fifth of the quota is going to be practically ruled out in all but the most extreme cases, and typically it needs a lot more than that.

But a large enough remainder will push the party over the majority line in any case–specifically, 1-((S-1)/S) =1/S. So for very small bodies, say a 3 member body, getting a single member with a majority (that is, 2 votes) without that party having gotten over 50 percent might happen fairly often, but make it as small as say 7 members, and the range between the maximum that remains at just 3 seats and an actual P/2+1 vote count will be very narrow, and when we go to say 39 it will be practically impossible.

So for practical purposes we can say we exclude the danger of a spurious majority of the largest party if we guarantee it has no overhang.

But still that might leave smaller parties with remaining overhang.

I think though we can maybe deal with that by making rules in the legislature operations.

I will post this and then post some thoughts this provokes about another way to fill out a multi-member body, using asset voting to complete it!

OK, the question of whether we should attempt a final round to complete a body with asset voting, so that we can meaningfully say that even factions that were simply too small to earn a seat in their own right at least participated significantly in trying to influence the identity of some seats, raises the question, perhaps we should simply use quota to fill the majority of seats, and then use asset voting to handle the entire remainder?

Again recall my pulled out of the air example

A 41
B 33
C 16
D 4
E 3
F 2
G 1

So here I changed it, to break the tie of the bottom parties, taking two votes each from A and B.

For 10 seats, clearly the quota is 10, and as before with a Hamilton–or Jefferson, or any PR rule whatsoever–we have 8 pure quota seats going to the three top parties like this

A 4
B 3
C 1

So now instead of applying any math rule at this point, what if we just declare the asset voting phase of the race open, for two final seats? With the eight Quota seats settled as above, we have, subtracting 10 for every quota seat won 7 parties with the following remainders amounting to 20 votes among them:

6 4 3 3 2 1 1

The election officials just announce the assignment of the 8 votes, publish this list of remainders, and declare an open period in which all seven parties can bargain among themselves.

What should the rules of this competition be? Note I have not made any effort to separate out or handicap the three parties already with some seats; everyone knows who they are, and they are in contention along with the others.

The basic rule should I suppose be that when there are N seats remaining, the top N vote combinations at the end of bargaining take the seats, with another rule providing that if any of the higher totals are greater than or equal to a multiple of any whole number greater than one of the lowest on the initial N list, the big one gets that multiple and the smallest ones are dropped to make the total N. So if say the biggest one were 9 and the smallest 4, the party with 9 gets two and the smallest on the initial list of N, with 4, is dropped. Any ties are to be broken by noting the initial shortfall of satisfaction, in the list presented just above, and breaking it in favor of the one with a higher shortfall (that is, a tie between C and D favors C, a tie between F and A favors F, etc) and when we have a tie in final accumulated votes between two with the same dissatisfaction as above, we favor first the one that has no seats yet, and then the one with more initial votes. In real life exact ties are quite unlikely anyway!

So by these rules, if none of the parties does anything to change it, C and D win the last 2 seats.

I think we can leave it up to Democracy! Or since it is precisely your point that this is the action not of the people voting, but of others trusted with their votes, explain that whatever wheeling and dealing these seven candidates do now, they remain accountable to the people who voted for them, bearing in mind there will eventually be another election and what they do now might well be used against them in the campaigns–or of course used in their favor. If not Democracy in action, anyway Republicanism. With a small r of course.

So, no rules really. I was going to suggest that the bigger parties cannot transfer their votes to a smaller one, on the grounds that the people who voted for them trusted them to represent them, and they don’t want their votes used as so much currency. But actually, at this point in the process, all the unambiguously entitled seats have been assigned, and now the time has come to bargain. This is the session’s first exercise of republican power, the first action voters can judge the true character of their favored candidates on, with the chips down. The gates of Hell are open, it is Walpurgisnacht, and the sausage factory is open for business!

This is what asset voting means.

Now the optics of asset voting are certainly open to question. On the subject of how to elect the President of the USA, I think Andrew Jackson took us down a wrong turning, or rather we have let him lead us there, when he denounced the outcome of the House of Representatives settling the Presidential election of 1824 as a “corrupt bargain.” The truth was, the choice of who to give the power of chief executive to is inherently political. The outcome of 1824 was to solidify the current custom (for that is what it is) of states setting up their discretion to choose Electors for the President any way they like (there are some Constitutional constraints, such as not being able to elect a Federal government official as an Elector, and it might seem like common sense the Electors should be citizens of their states (that’s not written in the Constitution including the 12th Amendment though). I hold that plainly the states can bind Electors to vote as they might have pledged (but the immediate reaction in some Southern states to the ruling of Ray v Blair in 1952 was to take the majority opinion remark that persons could after all run for Elector independently of a party as explicitly declared Unpledged Electors by doing exactly that, and winning in Alabama and Mississippi, several times, which is a major reason I think any person or even court that says states can’t bind the Electors is seriously mistaken) to enable the people to vote on the Electors, and even without attempts of state law to hold the Electors bound to their pledges many factors work in favor of that practically–I worry about that coming unglued nowadays to be sure. Winner take all (and even Maine and Nebraska do that, it is just that they break up the venues a bit, but each elector subject to a CD as well as the statewide vote for the two is being chosen the same way as all the electors of the other 48 states). This is how the American people worked their way as close as they could, under the current Constitution, to direct election of the President in the same manner as we elect our governors or mayors or any unitary office. In fact, except for plain instances of illegal manipulations in four cases now, since the 1830s every election has produced an EV majority, and every EV majority except cases of plain fraud (1876, 1888, 2000 and 2016–honestly I still am not sure there is a smoking gun unambiguously exposed in the same sense as in the other 3 for 2016, but certainly it was an extremely hinky election!) has always corresponded to the plurality in the popular vote.

That’s Jackson’s legacy, starting with his successful campaign in 1828, and I think it is an ambiguous one at best. On the whole I think the de facto plurality election of the President has generally worked out OK, but it is perfectly clear the office is only growing more powerful generation after generation, and the world it operates in is more complex and nuanced, and we would do well to have some kind of grounding of supreme unitary power in accountability to some sort of council of those who ran for the office–the way I envision it, the President would have discretion not to include all their rivals, but would pay a price for leaving any out and get benefits for bringing more in, and by creating auxiliary, countervailing powers of some kind for those the President chooses not to include, a package of incentives for inclusive foundations meaningfully tying an administration to a broad mandate with many persons involved in checking the President closely would seem important in the modern world. And it would open the way for a more nuanced selection process for the office!

The point here being, one serious current I am running against is Jackson’s legacy denouncing the legitimacy of wheeling and dealing for public office using votes as currency. Honestly I think this exactly what we need more of, and so we should fight to justify asset voting as an option instead of trying to sneak around it. Andrew Jackson was wrong about a lot of stuff, and this is one of them; there were good reasons they didn’t give him the office in 1824. It was not corrupt, it was republican government at work. Jackson drove it into another direction and God knows I am not recommending the House should routinely elect Presidents–God willing, we can close that possibility off for good with a better method.

So back to wheeling and dealing…

6 4 3 3 2 1 1

To repeat the chart, since it is buried pretty high up there now.
If no one does anything, C and D win one each with half of the total of 20 votes on the table; that is really not so bad. In fact bearing in mind the seats already distributed, that would mean only the bottom three (in the absolute vote ranking before seat assignment, not the remainders list) parties are left with no seats, and they hold 6 among them, so no worse than the baseline Hamilton distribution in that metric.

But beyond what the default winners hold, there are 10 votes in play, and that is more than enough to elevate any of the other five. In fact it is even possible, with much cooperation, to drive C off the list. the bottom 5 only need to gather together half of the votes in play among them to boot D out. To drive C off the list with two different parties getting the seats, someone must have 7 votes and someone else 7. There are just enough votes to do this, but note that involves D cooperating and most likely D will insist they be put back as one of the pair. But another way the 14 votes in play outside of C’s six can bump C out is for 12 votes to go to any other party, that way that party has twice as many votes as C and takes both seats! C might retaliate by persuading one or both of the other two votes in play to be vested in C, if C gets just one, it becomes impossible to bump C out at all. So anyone can win, anyone can lose, depending on how the parties choose to cooperate.

We should look at it in the big picture though, so regrouping back into the main vote order:

raw votes 41 33 16 4 3 2 1
Seats won by quota 4 3 1
Votes in play 1 3 6 4 3 2 1
Maximum seats theoreticaly available 6 5 3 2 2 2 2

Only A can hope to hold a majority on the council, but to do it A, the weakest (along with G, but tie breaking rules favor G) in the Asset Voting round, must persuade 12 votes beyond their own to join, which is all of them but one, and would require D to give up the seat, the only seat D can hope to win, D would get by default. D might respond to any overtures from A to give A 2 seats with the reply, no, you help us get the two seats and we will vote with you in the council. Meanwhile B along with E has 3 votes in play, which does not look like much but it makes B and E the 3rd and 4th strongest in the AV race, and getting an extra sea would make B equal to A in the council, and with any ally that has 2 or more seats B can run the council instead with that coalition. To get one seat B needs to outrank D which means 5 votes, so any party that can give B two votes will earn B’s gratitude (and maybe something more concrete, read on). If B can prevent anyone from bumping C off, C will have 2 seats and so B and C can control the body.

We might then see something like a factional campaign with A and D allied against B and C, vying for the six votes among the weaker 3 parties. Suppose all 3 of E-G agree to support A and D, what can they do? not much actually, mainly just guarantee D is not bumped out. All six doubling down on D, will suck the oxygen out of any plots to knock out D, but leave the A-D coalition with just 5 votes. A might want to get two seats for themselves, but the votes are not there; getting one by knocking out D is not much better than just sitting pat with 4 and keeping D happy, either way it is just 5 seats all up, which prevents the other guys from having a majority. The power in that coalition though goes to D who can switch sides any time.

If all six small votes go into aiding B and C in a coordinated strategy, two of the six put B up above D, and the other four going two and two to B and C raise them to 7 and 8. That would leave just 5 between A and D. If G will not play along, leaving B and C 7 and 7, that is still enough for B and C to hold. If F also refuses with 2 votes, now B and C are at 6 each, and 8 votes are in play to favor either A or D, but that just leads to gridlock in the council.

It is impossible to be more specific about who would support whom, that relates to values and ideology and program. If B and C are deadly rivals for instance this plot to rule via the asset seats won is moot.

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Your idea of “party list but give the remainder using Asset” is basically Asset, albeit with similar candidates “merged” into the party label.

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Yeah, but with some of the dealmaking clearly stated in advance via the party affiliation, perhaps it will be more palatable to the public.

I took some time to divert to a simplified half-assed approach to looking at what Approval might look like in a real election. I did not at all attempt to look at the individual district votes, but did look at a model of the 2012 US House race, in which I supposed certain empirical seat of the pants small fractions of each “party” vote I have recorded from sources would cast additional approval votes in various numbers, across the nation, to alternative parties.

What this means is that I, as omniscient little man behind the curtain, know what I have taken to calling the “prime” votes of each voter–the same as the real world party choices everyone actually made in 2012.

In a real election with just asset votes and no extra layer, such as a single vote only “Prime” vote indication (which would not by its nature actually be a Score vote, though perhaps analysis would reveal it always can be seen as one, I think though I will be able to demonstrate the outcomes of pretending it is versus counting it separately will show it makes a difference which way we treat it) there would be no way to know, as I do, which approval votes come from voters primarily identifying with what party. What we would know, if we took the trouble to keep track, is how many approval votes are associated with combinations of a given number of approved totals,

Intuitively, I think if we were, after the district round which is simply vanilla approval vote (counting only those votes cast that are votes for a candidate running in the district–including write ins who are not registered candidates, but these would tend to be negligible; in the grand anti-spurious majority anti-overhang system, the voters should be able to vote for people or parties off the local ballot as well, but we simply ignore those in the district phase) we simply divided the votes in groups of two or more by the number of votes in the group–so, an approval vote for A and D, or one for A and party X (no candidate named) would be recorded as (A:1/2, D:1/2) or (A:1/2, Xp:1/2), and if either of these were included in a group of 10 AV they would be recorded A/10, etc–then certainly the total number of all votes examined when we sum them up for each party and then totaled would equal the number of voters who voted. Intuitively, that suggests maybe these party totals, composed of adding up votes suitably discounted–so a party’s bullet voters have their one vote counted in full, those splitting that party with another (again, no way to tell how many of those preferred the other party more) get recorded half and half, etc, would be reasonable to hold as party shares of the whole. Generally these would be different shares than we would compute by knowing the “Prime” choice of each voter I would think. But perhaps the manner in which they deviate from the Prime proportionality is reflective of useful and beneficial properties of AV?

I should mention that one of several things starting me on this primrose path of amateur election reform was the debacle of Lani Guinier. I hope most of us here know about her, but if anyone has missed this, she was appointed to the office of the Civil Rights Division of the Justice Dept, or wherever else the administration is supposed to implement equal voting rights (I could look it up) by Bill Clinton immediately upon taking office in 1993, during the first month or so of appointments. Her resume by the way including having served just below that rank in the Bush administration previously, so she was no purely partisan appointment–and in the materials she wrote I later read, she did point out that “minorities” does not always mean “people of color.” A Republican living in a highly Democratic district (such as most any precinct of the District of Columbia for instance) might well want exactly the same kinds of protections African Americans or immigrants might need, and her mechanisms were meant to be fair to all. IIRC she stressed implementing a system whereby individuals would have as many votes as seats to fill on a multimember body, and the right to vote them wherever they liked, putting all down on one candidate or spreading them over as many candidates as there were seats. I can think of several flaws off the bat, but it would have been a big improvement over sticking with FPTP and then having to police the shapes of the districts. For, as she pointed out, a Republican in San Francisco or Boston, as much as for an African American in Birmingham, Alabama.

But upon being named, before being confirmed, some so-called journalists or opinion pieces attacked her as the “Quota Queen,” accusing her of recommending all sorts of nonsense she never proposed, and rather than defending his choice of her, Bill Clinton backed off and abandoned her.

In a sense, the ability of a voter to choose to asset vote at the price of discounting their votes at the proportionality determination phase (they sum up to one, but for each party they support are fractional) reminds me of Guinier’s suggestion; bullet voting is equivalent to putting all your votes down on one candidate (or rather in the proportional phase, party) while the more AV one casts, the more spread out one’s preference is assumed to be.

I realize now that therefore the investigation I undertook, involving intuitively assigning probabilities of prime voters of various parties to also cast approval votes for other parties and independents is inherently wrong, so it is not worth reporting the outcomes. What I ought to do I suppose is assume an exponential decay function, with each party having its own characteristic interval, governing the probability a voter with prime allegiance to that party would cast a vote for a given number of candidates–thus if the exponential function is base two, the probability they would vote for 2 is 1/2 that that they bullet vote, the probability of voting for 3 is 1/4 bullet voting, etc, and then weigh the various combinations, integrate and normalize, and fiddle with the interval to get reasonable AV totals from each party. Then it would be possible to tease out what portion of all AV a party gets come from 1, 2, 3 etc AV combinations, and discount, and that would give me a normalized transformed total number of effective AV for each party; looking at the Hamilton (and for comparison, Jefferson, but nothing is convincing me the virtues of Jefferson’s method in this type of application outweigh its vices, nor is Webster good enough) proportions for each versus what I know, from having set the exercise up, the “correct” balance is. Mind, I shouldn’t compare the raw “Prime” distribution with the transformed one, but to a transformation based on the willingness of each party to scatter its vote to other parties that are presumptive allies. In the bad exercise I did, the Democratic, and Republican, party numbers of course plummeted the more AV I assumed everyone would be willing to cast, but in fact if I summed up the Democrats plus the 3rd party wins I figured would be Democratic allies, the total seats remained in the same ballpark, even rising a bit. That is the presumptive Democratic led coalition would lead by the skin of its teeth. But of course I was assuming what I set out to prove there!

The Excess Method paper is essentially describing what a proper test would look like, except I think it can and should be transformed to a subtraction rather than divisor method–instead of dividing all combinations containing say Party C when C gains another seat by the Jefferson (1+n) divisor, one should simply subtract the quota of votes from all of them (proportionally, of course, to total up to a quota being satisfied.

The flow chart offered by @AssetVotingAdvocacy recommended a more sophisticated variation, where the quotas are not subtracted from all the combinations containing that party proportionally, but skewed to take them first from the combinations with the fewest other parties–that is to say, first take from the bullet votes, then from the party plus one other choice batch, and so on. I am not sure that closes properly though, and anyway to implement it with real data would be a PITA!

The point of the exercise I was doing with the made up body of 10 seats and 100 voters with 7 parties contending was to show that iterative subtraction, in the case of having single votes evaluated proportionally, is a matter of division by quota, instead of having to take step after step for each vote–in that case just fast forwarded to a distribution of 8 seats by quota, and then had to figure out how do fairly distribute the last two. With Hamilton, the answer just pops out of the slot if you set up a spreadsheet right. (To get the Jefferson distribution, I have to fiddle around with a multiplier).

So there are two goals here, one to see how the AV process transforms the presumed “prime” distribution, and also to see if a simple mathematical procedure analogous to dividing each party’s shares by a quota lets us fast forward directly to seeing how many seats each party should have, when unpredictable numbers of individual voters will cast unpredictable numbers of AV.

Without the latter, we are stuck with grinding through iteration after iteration.

{responding to me}

What I put up there was mixed, first whole number quotas, which are not subject to bargaining, on the grounds that the people who should be most considered are the voters, and if enough voters to amount to a simple quota of the whole electorate have voted for a party to get it a seat, that seat should be sacrosanct. Just as the plurality seats won in the two anti-spurious vote, anti-overhang procedures this topic is about are sacrosanct. Any proportionality method applied to a case of electing one equates to plurality wins; there is no democratic argument for a different candidate being a better choice of representative than the one who got the plurality. Therefore I don’t propose purging any of the excess plurality seats won, just riding with them and expanding the body until those high counts are indeed proportional.

Straight asset voting would be the voters vote, then the candidates all come to dicker over all the seats. This is Asset voting to resolve seats that must go to parties when no party has any full quotas of votes left, a thing that happens because the small parties sequester votes from the larger parties. I was arguing Hamilton over Jefferson, but realized that throwing it open to Asset haggling at that point automatically balanced the small and large factions against each other, pointing out how the priorities and interests of each party are only partially governed by how many (Hamilton!) remainders they have; each bargains in context of what getting another seat is worth to them or if they can afford to “altruistically” aid another party because no deal they could or would be likely to get can get them any benefit, whereas doing another party a favor creates a moral bond.

We should never lose sight of the fact that politics is at the end of the day only partially a function of mathematical laws. It is an interplay between math principles we are interested in that work “behind the backs” of persons, and personal decisions and judgements and values.

I have read a lot of “Prisoner’s Dilemma” type logic puzzles that try to explain morality and fairness and so on entirely in terms of such logics, but a lot of their conclusions seem to fly in the face of everyday experience. For instance, a Scientific American article many years ago I read set up a scenario where people eating at a restaurant agree to all simply split the bill equally, then one of them orders a light salad and another orders some fancy lobster dish that costs 4 times more–leaving the frugal one screwed. Well, yes, if they don’t speak up and say, hey, lets be fair here, or they do and some wiseacre says “fair is what you agreed to, you agreed to split the bill evenly, so shut up and pay your share!” then in that one transaction, they are screwed. But…people don’t always do things in one transaction. Human relationships factor in far more; arguably we can hit upon a logic that when fully integrated, predicts exactly what people will actually do, but I hold that such a logic will amount to a general science of everything, and involve computation effort comparable to just living your life and getting on with it, and that it will wind up affirming such grand and vague notions as “justice” and “fair play” and all that. The guy who ate the fancy meal is being a jerk, and ought to say something like “We’ll split the bill, but let me first put down $50 because my meal was so fancy, and then we’ll split the rest.” He might suggest his $50 includes his share already, or be generous again and stipulate it does not. Or, this little group might simply break up, and the free rider finds himself short of future dinner invitations, or that the ones he screwed later refuse to do him some other favor. And on the other hand, we all know that there are people who go around skimming like that all the time, some of them are essentially being con men and just move on from one set of chumps to the next, and others keep getting away with it because they are powerful or privileged in some way, and the fact is the people they screw cannot afford to refuse to do them favors later.

All this stuff is essentially “politics.” To paraphrase Aristotle in a less crassly sexist way than he put it, humans are political animals. (Because we are social, and achieve our economic survival via cooperation).

I loves me an elegant mathematical rule as much as the next person and probably a lot more. But at some point, we take the objective frame off and it comes down to people dealing with each other in concrete issues. I think if quotas take us to a certain point without raising conundrums, then when we get to that point where they start to get problematic, it might be time to switch over to letting politicians start earning their pay as politicians to settle the last bit.

I was going to go on to describe how any possible residual prospects of my dreaded “spurious majority” can be mitigated, if we institutionalize keeping track of which parties come out of the seat allocation process with a surplus of unsatisfied votes, versus those that have a deficit. Letting the parties all scramble to make deals to bid for the last seats will, when the dust (rather unpredictably, unless one knows all the actors and their situation pretty well) settles, involve some seats with surplus votes and some “bought at a bargain price” as it were. If we merge these into the quota seats (if any, in my model D with only 4 votes fell far short of a quota of 10) and figure the surplus or deficit being shared by all in that party alike (“All for one and one for all!”) and make a little footnote saying actually this party’s seat is worth a little more or less than standard, then in a specific case where it is all deficit seats just barely winning a bare majority, it might be the case that these votes (which might not be on straight party lines) all add up to representing less than 50 percent of the whole original popular vote. So if we have some bureaucrat keeping score, they can announce “actually this floor vote is a spurious majority” (or falls short of a supermajority when that is needed) and this gives the right of the other parties who dissented from the vote that passed to veto it. (The vetoing bloc should be large enough that anyone abstaining, if counted toward the ostensibly winning vote, does not cover the gap, as most likely it would).

And that in turn suggested yet another dynamic to maximize the footprint of as many voters as possible. I proposed a scenario in which 6 votes held by three small parties E,F, G are donated to B and C, having the effect of blocking D from gaining an asset-vote-assigned seat and thus leaving D with nothing. So all 4 of the smallest parties get no direct representation. But suppose we hold that the 6 votes E-G gave B and C count toward their reckoning of surplus or deficit; this means that in addition to owing the bottom 3 candidates keeping or enhancing their seats for a 6 seat majority, they also on an ongoing basis owe these gone but not forgotten small candidates mitigation of the prospect of having one or all of their spurious majority votes vetoed–because with 6 more popular votes, B and C’s block is no longer a spurious majority! Meanwhile, the cheated party D, which would have taken a seat without these shenanigans, can either sulk off, or in retaliation join their 4 votes to the plurality, but also minority, party A; it remains a plurality but this raises the divisor of relevant votes on which the question of whether the B-C bloc comprises a majority or not is decided–with D retroactively casting its 4 PV to A anyway, though it gains neither D nor A any seats, the total value of the BC bloc PV is 33+15+6 =54/100. That’s a solid and not spurious majority, but if D were to go off in a huff instead, it would be 54/96, a bigger majority.

And it does not have to end there. A cannot veto BC bloc because with the 6 PV from the bottom three parties, it is assured a majority. But now suppose the 6 BC reps ram through something the three little bloc voters do not like at all. Their candidates are not in the council. But they might have a right to rescind their asset vote! It would probably be bad to force a replay of the Asset election, so until the next election, BC’s six reps are safe…but if the six votes of E,F, and G all walk, the council is now based on 94 votes, and BC have only 48 of them. Well gosh, that is still a non-spurious majority, isn’t it! But even if the walkout does not leave them vulnerable to a veto, it is an ominous sign.

And so suppose we provide that not only can the registered asset-vote wielding politicians yank their endorsement from BC, we grant they can declare they are supporting A? Now BC has 48 out of 100-that is a minority. They still have 6 seats, but if A holds unanimously they can veto anything the BC bloc tries to do. And D, E, F and G all now claiming to back A can walk again, if even just G decides to withdraw their proxy from A, A falls to 50, the seats are based on 99 votes, the necessary majority is now 50 votes–A still has only 4 of the ten seats and cannot pass anything with their new majority, because you need both PV and seat majorities to pass stuff without a veto, but BC is again paralyzed. Unless of course one or more rep in the A bloc crosses lines and supports BC actions.

So the tiny parties are not present on the floor, but being needed by the big ones to justify their majorities, they have leverage. At the same time, they cannot unilaterally shut down the government with their lousy 10 percent of the vote between them–because A and BC can still choose to cooperate; A can veto BC only if A chooses to exercise that option, otherwise the laws pass and the actions go forward. Or again a single rep from the A bloc can cross lines and support BC.

Thus everyone has to take into account everyone’s interests; there are going to be, depending on just how the voters vote, blocs that are immune to such shenanigans, but by and large, it behooves everyone to stay civil and keep their bargains, and even when making a deal with a bigger power to mutual advantage at the expense of the smallest works out fine in the short run, in the longer run the little people will remember being thrown under the bus.

It makes no difference to this if we have republican representation or direct democracy; issues will arise where decisions that have to be made screw someone, and what might upset and incense some voters might be completely necessary for the greater good. Hopefully sane people will learn to recognize that, but the dynamic of asset voting is simply that of republicanism writ small. The electorate in a democratic republic has to learn to be philosophical about not always winning and getting what you want not being always possible.

But no one should be asked to sell their interest off for cheap, and still less should anyone be deemed outside consideration at all.

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The big issue with trying to use Asset for only the non-quota-filled seats is that parties immediately have huge incentives to try to split the vote to avoid any of their candidates getting a Hare Quota, because it gives them more power in the negotiation process. Easier to corral 2 or 3 candidates than millions of voters :slight_smile:
Anyways, if you insist, I highly recommend @Abd’s writings for more explication on the best kind of Asset systems.

I guess I will be looking. Recall that on this topic, Asset Voting is a penciled in option, though I am wondering now if I shouldn’t double down more on it. I was thinking of it here mainly after some RCV advocacy some time ago caused me to reflect that the optics of that is “literally everyone’s vote is counted!” We all know what a crock that is here, of course. But it occurred to me that the baseline PR by single vote approach I liked so much would still leave a lot of people unrepresented at all–not nearly as many as under FPTP of course. But there has to be some people voting for candidates that are just getting too pathetically few votes to signify, and I wanted them to be able to have some say and hence some stake in the outcome, so my Step 4 penciled in is there. I found though that if we increase the total seat number to make space for the losers to scrape together a mandate for one or two seats, then if we refigure the proportionality of the body based on adding those seats, the duopoly parties, or more generally those on the high tend, gain entitlement to more seats too, and gobble up the seats ostensibly created to accommodate the outliers. Whereas if we say the duopoly, or bigger parties generally are locked out of that competition we’d see seats being won by parties which even counting their combined asset votes donated to them by other parties, are small compared to the remainders of the biggest parties.

So sticking with any of these linear non divisor methods seems to come with a lot of incentive to fission, as I had to acknowledge to @Marylander on your “Should CES advocate STV” topic.

I think though we can get some perspective. I am placing a lot of weight on voters becoming more engaged when they know their vote is not “thrown away” and actually to many of them boutique parties might seem quite nice, at least their own little ones. But if the whole thing seems to be spinning into wacky fragmentation for the hell of it, voters can observe this going on and start asking, shouldn’t we have more stability? Then they can vote for the parties that offer them stability as a priority. If lots of candidates are dickering a lot, members of the voting public are going to see how it is done and become more competent at judging party internal business and start demanding accountability. Meanwhile the lion’s share of seats will go to whichever parties manage not to split. The best laid plans of machine bosses could backfire–what if they aim for 98 percent of a quota but wind up with 101 percent?

Between general chaos, and the engagement of the voting public, I am not sure we should be too worried about fragmentation, not as an all bad thing anyway.

You can set a limit, say, only the candidates with the least votes who total to 20% of the nationwide vote are allowed to conduct the Asset negotiation, and only those candidates themselves (or the top X of them) can be elected through the negotiation, so as to prevent rogue candidates from electing a Hitler. This should solve the problem of candidates with too few votes to win while mostly preventing the bigger parties from wanting to split off too much.

I am tempted to run off in several directions with this. Let me just address the whole “Hitler” thing with the assertion that no particular electoral system was really responsible for Hitler taking power in Germany and that the breakdown there was something else, and that we seem to be quite vulnerable to the same basic thing happening with no proportionality in our system at all. The remedy against Hitler will not be found in any magic bullet constitutional system, I’d like to leave it at that on this topic. That’s me sitting on myself, anyone who wants to challenge anything here with showing how Hitler takes power in it is free to do so, that’s relevant. It’s just that if I start talking about what I think was to blame there in Weimar and what realistically threatens in the real modern world now, we’d be way off on many complicated and inflammatory things. Von Hayek can take a hike as far as I am concerned on this subject!

Since you are mainly concerned here with looking at what the ragtag fringe of least popular candidates looks like, let’s stick to the simplified sub-proportional approach, where the simple Hare quota of voters/seats is applied to the British Parliamentary election of 2017. I’ve never looked at it that way before by the way, I always applied Hamilton. Westminster is interesting and relevant here because the British vote diversely in their election despite the fact that riding/borough elections are FPTP too, and Parliament always has significant numbers of third party Members. It also has a duopoly despite that, almost always a majority of seats going to one of two leading parties, and it is about as rare (as in, just a couple instances in the better part of a hundred years) for the leading party in Parliament represent anything over 50 percent, much more common for it to be in the mid to low 40 percents, as it is for the plurality seat winner to fail to win a majority. The current Parliament, and the one two general elections back, were unusually coalitions (not counting the WWII era session under Churchill, that was a multiparty coalition by policy, using the same members elected in the pre-war last general election, which obviously delivered a majority of seats to the Tories).

So, I aim to look at that latest election through a lens I haven’t quite used before to highlight who the quota winners would be, then look at everyone not yet elected with at least one seat versus the remainder share of the quota winners, and take your suggestions from there, because frankly I have a little trouble visualizing what you are even saying the procedure would be and I think I need a concrete example to follow the instructions literally to see what they boil down to in practice. US elections aren’t much good for this since so few Americans step out of the two party box. Perhaps a cross check with the French Assembly would be in order too, based on the open first round votes.

Rather than leave this open all day I will post now and come back with actual results if my day permits.