# Should a minority win a majority of seats in PR if it more intensely prefers its candidates?

Consensus PR makes it possible for a minority to win a majority of seats simply because it gave its candidates 5/5s, while the majority gave its candidates a 4/5. This seems to make consensus PR more gameable (without complex solutions), but could potentially be better. Thoughts? How might this affect the viability of consensus PR relative to more proportional forms of PR, either cardinal or ranked?

Can we please have some simulations?

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Did you mean examples? Hereâ€™s one:
3 seats, 100 voters, Hare Quota is 100 x 5/3 = 166.67 points
Party A: 51 voters scoring their candidates 4/5
Party B: 49 voters scoring their candidates 5/5
Under Sequentially Subtracted Score, the first round results are:
Party A candidates 204
P. B candidates 245
B1 wins, and 166.67/245 = 68.02% of B votersâ€™ ballots is subtracted.
Second round:
A candidates 204
B candidates 78.33
A1 wins, and 166.67/204 = 81.7% of A votersâ€™ ballots is subtracted.
Third round:
A candidates 37.33
B candidates 78.33
B2 wins.

Final result is 2 B to 1 A.

The object lesson in your example appears to be that bullet voters beat nuanced, judicious voters of the type score is supposed to prefer.

The example also raises the question of why, in a multimember election, we even want to have cardinal or ordinal methods and why not just go for straight old fashioned PR, with the voters simply having one vote to cast for a given party?

Presumably independents can run but then theyâ€™d hit a paradox if they were so popular as to get more than one seat, similar to the dilemmas facing parties contesting Single Non-transferable Vote (that is, there are N multibody positions to fill but every voter only gets one vote for one candidate).

Presumably in this simple example each of the two parties A and B run three candidates, and I presume each voter can score them 0-5 individually?

So it is a single body with three members, presumably some sort of city or county council or perhaps some kind of more or less Swiss collegial executive board? (Say a council of 9, three members elected every cycle with terms 3 times the cycle, staggered).

So now, as a check, do it the old fashioned way as in Denmark, straight party PR, party lists, the works and no innovations to allow voters to control the party list ranking or some such. A voters just cast 51 ballots for A, B voters 49 for B. Iterative Jefferson goes A, B, A. Hamilton says we have 3 x 0.51 and 3 x 0.49 respectively, so A has raw share 1.53 and B 1.47; each gets a quota seat and the greatest remainder is A so A gets the last seat just as in Jefferson.

â€śProportionalityâ€ť here means a very lopsided outcome, but with just three seats we expect that a lotâ€“the alternatives are a 2:1 council majority for one of two parties or for one to get such an overwhelming majority they get all of them.

Note that happens with Jefferson when x/(1+2)>(1-x) or to do the algebra, x>3-3x=>x>3/4. As long as B manages to retain over a quarter of the electorate their outcomes are the same as if they retain 49 out of 100 in other words. In Hamilton the raw share of party A as the superdominant majority must be over 5/6, so if we value inclusion of minority voices we ought to prefer Hamilton IMHO, also if we value inclusion of the maximum possible share of voters on the body.

Now let us pretend instead that the 100 voters are apportioned into three districts:

1&2 with 33 voters
3 with 34

and that there is a spectrum of preference with A being strongest in 1 and weakest in 3, and vice versa for B. 51 as it happens divides neatly by 3 so say we have
20 A in 1,
17 A in 2, and
14 A in 3.
Then we must have
13 B in 1,
16 B in 2, and
20 B in 3.
First look at what happens if they vote FPTP (which with 2 parties always gives a majority if not a tie) so we have A wins 1, and 2, and B wins 3.

Applying my top off notion having found the simple proportional distribution which is the same, the top off is zero and our council is fairly founded as is.

If we wanted to get fancy, we could make the council 5 member, find proportionality from the raw partisan voteâ€“Jefferson A, B, A, B, Aâ€“Hamilton 2.55 compared to 2.18 so again 3 to 2, now A has 2 FPTP and B has 1 so each one gets to elevate one of their unelected majority-race losers.

We could say it is the highest one left on the party list, which might be 2 candidates for each party that did not run at all; my approach says pick the leading district losers, anyway A has only one candidate left anyhow; all 3 of Aâ€™s district candidates win, and B gets its candidate in district 2 to join its majority winner in district 3, leaving only Bâ€™s forlorn candidate in District 1 to sit on the sidelines kibitzing unofficially.

But you want this to be a score election?

Note if we can assume the single highest score on each ballot equals a Prime Choice single vote, and in fact all 100 voters pick one party or the other, the proportionality figured that way remains 2 to 1 in Aâ€™s favor (we are back to 3 council members here).

So the procedure you were following seems terrible in this case. Why use score at all if we have an integrated multimember race? Youâ€™d have to mix your example enough considerably to explain where score â€śproportionalâ€ť whatever that means is better than just having each voter pick their favorite and let the chips fall where they may.

One reason might be that you want the voters to control who the delegations from each party are as well as how many, which is reasonable.

Note that one way to accomplish that (I have not studied the various PR open list methods other than STV, so donâ€™t shoot me for reinventing a bad wheel here, I donâ€™t actually advocate it) is to tell voters they may score the candidates in one party list, but marking another party list would be a spoiled ballotâ€“either that or the officials take the list with more scores on it as the real partisan preference, and discard the scoring of less numerously scored other party candidates completely.

Another would be if you want to have a mixed district system with some approach to global proportionality.
Going back to my proposed distribution in three districts, and sticking to your restrained, apparently subjectively 80 percent but not 100 percent satisfied A voters, we have in
District 1 80 score points for A and 65, for B
so A still wins there; we donâ€™t have to even bother with the math in 3, B wins it clearlyâ€“in
District 2, we have 174=68 and 145=70, so district 2 is flipped vs FPTP.

Your â€śproportionalâ€ť cardinal method applied globally gives the same answer as if we did this district thingâ€“which is what AV was invented for.

We have here an example then why I was rather negative when first exposed to CES on Facebook and why I have been urging attention to the values we want to promote.

The question is exactly as you titled the topic thenâ€¦if AV or Score voting is meant to favor candidates with broader appeal, is this result perverse or not? I felt the CES elevator speech on the main public site often speaks normatively about the superiority of middle of the road candidates inherently, and this made me nervous since I think the recent pop analysis of recent problems blaming â€śextremism on both sidesâ€ť of the duopoly is facile at best, and downright dangerous if it masks one-sided culpability, and worse still if it smooths the already precipitous slippery slope of one side domination when that side is IMHO entirely the wrong side.

We would need to know more about who A and B, voters and candidates, are. Perhaps A has lukewarm support for reasons? Or are A voters failing to counter Bâ€™s max-out strategy with their own because they know they are the majority and are complacent? B might be objectively better and Aâ€™s weakened support reflects fatigue with an unsatisfactory program.

But that need not be true for B to win!

Suppose we insisted on voters marking a Prime preference and forming the 3-seat proportional balance based on that. Then with an anti-overhang top off procedure, after the score vote above winning B both 2 and 3 districts, B has an overhang of one, so we have to add two to get a 5 seat council, we already know the outcome of thatâ€¦A gets both top off seats, B has to be happy with its two district wins.

The question of pressing on with the votes you gave and the system of iterative quasi-proportionality you are using does not come up in overhang top off with both cardinal methods being used, because you show how the global evaluation comes to 1 A, 2 B and that is exactly the district outcome.

However suppose we noted that Aâ€™s score votes can average to 4 if we figure they vote on a spectrumâ€“17 vote 5 for A, 17 vote 4, 17 vote 3. If the higher ratings for A are in the numerical stronghold of district 1, with 3 dissidents there voting just 3 (because there are only 14 A voters in district 3 and only 17 A voters will vote a score of 5) it makes no difference, nor is district 3 different, the scores are just more skewed in each district but on the same side.

What if it is the other way round?
17 A voters in the stronghold are somewhat disaffected, and only rate A 3 (but still donâ€™t cross party lines and cast any nonzero scores for B). Just three of the 20 are A loyalists who rate it 5.

So we have 51+15 A scores=66 there, while 13 B voters almost win with 65 score! If we mixed it up a bit and moved two of those loyalists to District 2, or rather those two dropped their score to the average 4 sharing in the malaise, A drops to 64 and B wins District 1!

Having energized two A voters in District 2 to higher loyalty, can A now win District 2â€“letâ€™s see, 15 x 4 = 60+2 x 5=70, while 16*5=80, so no, weâ€™d need lots of upswing of A voters, enough to raise the average considerably above 4.

Now the combination of Bâ€™s fanatical max-out strategy and Aâ€™s disgruntlement, not enough to make them cross party lines but enough to basically sit out the election by lowered score instead of simply staying home, allows B to win two districts where they are outnumbered.

Can the upswing of ratings by A voters in district 3, possibly in polarized reaction to Bâ€™s dominance there, turn the tables completely and give both parties victories where they are weakest? There are 14 A voters all scoring A with a 5 there, that is 70, and 20 B voters still rating B 5, 100, so no. B totally sweeps all three districts.

But if your iterative calculation is unchanged by A polarizing into equal numbers of 3 and 5 scores maintaining the average of 4, we already know this quasi-proportional method for multimember races gives B only two and A one, so in that case, we again have an overhang, now it is B with too many seats and we have to iterate to 5 seats instead of 3.

Unless I misunderstand because breaking A into 3 bunches rating 3, 4, and 5 points changes the procedure (and I canâ€™t see how or why it should), following your steps, we have
Hare Quota is 100*5/5=100 points
B still wins the first round, and 100/245 =20/49 are subtracted, leaving 29 x 5=145 for Bâ€™s Sequentially Subtracted Score.

Now A wins one, and if average score holds, we have 100/204=25/51 are subtracted, leaving
26 x 4=104 score for A.

B2 wins third seat, and as before we subtract 20 from the remainder leaving just 9 B seats for score of 45.
Now A again leads and wins the fourth seat, and again 25 from 26 leaves just one
B beats it for a third seatâ€“which means top off has succeeded.

A gets the two seats where Aâ€™s score was highest as make up â€śminorityâ€ť seats.

Letâ€™s check if it matters what sequence we deduct Aâ€™s seats in.
As I understand it the philosophy is to take the highest scoring ballots first, then work your way down.
100 score points are twenty 5-scores, but there are only 17 5-scores, so we come up 15 short, which then come from 4 score votes, requiring 4 and leaving 1/4 of the last one presumably. Now there are 13 and 1/4 4 score votes left to A, worth 53 score points, and 17 x 3 for 51, or 104 left. Thatâ€™s enough for one more leaving 1 1/3 3 score voters unsatisfied.

If any of them had voted for second parties weâ€™d reserve them for last, exhausting all the bullet voters of whatever score first.

The order does not matter.

We therefore did not have to do this iterativelyâ€“but I suppose if third and Nth parties came into the picture, with anyone from A or B scoring any of them, that would mess up the ability we clearly have to just say A got 204, B got 245, out of 449 1/3 is 149 2/3â€“it is easier to just multiply by three actually and say each quota is 449, so we have 621 versus 735, subtracting 449 from each we have 172 versus 286 for remainders, so B gets the third seat.

We could also instead use Jeffersonâ€™s rule, and say first B gets one, since Bâ€™s score is clearly less than twice Aâ€™s A gets the next, and that leaves A and B 's scores in the same ratio again.

Note that the subtractions you have been doing are in fact a form of Hamiltonâ€™s method therefore. And as in my single vote for single party approach, here Jefferson and Hamilton give the same answer again because there are only 3 seats in play.

Similarly if we go to 5 seats we can do this directly, now for Hamilton we multiply A and B scores by the number of seats to get 1020 and 1225 respectively, now twice 449 is 898 so clearly both have 2 quotas and remainders are 122 and 327 and again B wins the final seat, or by Jefferson the two iterate to get one and one, then two and two and again B wins the balance.

Now at last, let us suppose instead of just looking at raw scores, we consider that one person one vote means that if average scores for A are 4, versus 5 for B, we simply divide Aâ€™s score, 204, by 4, and Bâ€™s 245 by 5. This of course is simply a roundabout way of arriving back at each partyâ€™s number of ballots! But wait, there are three different versions of Aâ€¦but that does not matter, in this case, where all voters bullet vote (with variable scores, but that does not matter at this point) they all recover the number of voters who cast these ballots. This is because no voter crosses party lines, all their choices being for one party each.

Of course that simply returns us to my approach where voters explicitly indicate one Prime choice of party separately from their cardinal vote for district office. We already know that with these votes globally over the whole system then, A should have 2 seats and B just one.

But B has three seats by the score system in each district, so we have overhang of 2, and thus need to raise the number of seats total to 7.

In Hamilton terms, this means we compare 357 for A with 343 for B and subtract 100 for each seatâ€“or dividing by 100 we get the close but clearly decisive 4 seats for A, three seats for Bâ€“B has already won 3 seats so A gets four (!) make up, top-off seats.

Note A had no opportunity to run four candidates nor did any voters get to vote on any fourth candidates, so what is to be done now?

I say we clone the top scoring A district score winner, who wasâ€“a tie with score of 70 in both 2 and 3, but the number of A voters is greater in 2 so that breaks the tie, so the party, or just the A candidate in district 2 personally, names someone from District 2 who is deemed suitable and qualifies for the office.

I have a cloning mechanism in mind but this post is too discursive already, so I have to put it in a new topic.

Speaking of breaks, it is now time I think to draw some conclusions:

1. as noted, the choice to use a cardinal method is presumably guided by other values than attempting to form a proportional body, so it should not be too surprising if trying to implement a â€śproportionalâ€ť outcome from a form of voting that haphazardly if at all records voter first preferences gives notably different outcomes.

2. in this example, the alternative to one-choice proportionality seems pretty perverse, and even worse considering how it is actually possible for a 49 percent minority party to sweep all the officesâ€“adding a quasi-proportional step to straight district votes does give the majority party a foot in the door but not anything like restoring their majority status.

3. therefore, it is not too instructive to take an exercise like this to evaluate the proposed Hamilton-like quasiproportional procedure. The point of Approval or Score voting is supposed to be to accomplish a bunch of benign benefits alleged for it, and one thing promoters tout is the ability of third parties to be better recognized; another is allegedly building consensus by moderate candidates presumed to be in the happy medium being favored with support from both currently polarized factions in recent US history. We therefore need a better example that mixes things up a bit with such featuresâ€“third parties should be showing their faces, and at least some third candidates should be presenting themselves as voices of consensual reason â€śbetweenâ€ť the dominant parties. Then if we can model how such additional players might vote and then follow analogous procedures to find both district and global victory patterns, we can better judge whether we gain something in flipping majority seat control from A to B. Clearly we are not maintaining â€śproportionalityâ€ť in the usual sense that is understood, the question is whether the shift represents some kind of notable improvement offsetting the loss of proportionality. Remember, if we suppose voters will start to actually use the power to score multiple candidates and parties, we will no longer be able to tell for sure which were which in terms of party allegiance from the ballots castâ€“at best, we might guess top scores correspond to that, but what if some voters give the same top rankings to more than one party?

I think now is a good time to break off and get cracking on an elaborated example based on yours but with more parties to mix things up a bit.

OK, so what happens if we mix it up a little? I think Iâ€™ve shown the utility of sticking to a three district model, where we attempt to aggregate these to get a proportional or quasi-proportional outcome, compare with straight district results to see if top off expansion of the body is warranted, then recompute proportional or quasi-proportion again, and pick the top off seats.

Introducing three new parties to the 100 votes seen so far, adding 15, 21, and 15 respectively and with 5, 7, and 5 voters in each district.

Party â€śMâ€ť is what I understand the normative values the CES site touts says an approval or score voting system should promote for the greater goodâ€“namely a party of people who see themselves â€śin the middle,â€ť seeing the point of view of â€śboth sides,â€ť though there will be more â€śsidesâ€ť than just two to consider here. I declare they are 21 voters in number, with a candidate running in each district (as the other two parties will too) and spread evenly, 7 votes in each district.

Party â€śSâ€ť is to the left of Party A, as moderately or extremely as you like to imagine. They think that A is too compromised with unacceptable extremes B is guilty of, and it would be better to break left. They number 15, but are skewed a bit, stronger by one in Aâ€™s traditional stronghold (distribution of A and B party voters are as in the modified example in the previous post) so there are 6 of them in District 1, 5 in District 2 and 4 in District 3.

Party â€śZâ€ť is the mirror image of S; on the right of B, similarly rejecting, or anyway criticizing strongly, the misguided notions of A that they think B has compromised too much with (and therefore, as with S voters, are not inclined to support M either). They too number 15, and have the opposite skewing to S with only 4 in District 1 and 6 in District 3, again with 5 in middle district 2.

Now consider first the pattern that will emerge under single vote for single district winner FPTP enhanced by proportional figuring of the whole leading to top-off make up seats perhaps.

The plurality votes in all three districts are exactly as in the example in the post above, because all three new parties add 17 to each but are split up so that the pluralities still go to A and B as they did in the simpler system. Thus we get A winning in the first 2 districts and B holding D3 as its stronghold.

Here the symmetry between Hamilton and Jeffersonâ€™s rules in the 2-party examples breaks down however. We now have not 100 but 151 voters, and so a quota for 1 seat is 50.33333. When we divide all parties by that, we find that A has a quota but only a tiny remainder, B falls just short of a quota and M, the largest of the two new parties, has a remainder around 40 percent. Under Hamilton then we get A, B, M with one seat each as the outcome. Note that this results in pretty much the dynamic that CES urges us to hope would emerge under Approval Votingâ€“M is now in the catbird seat, able to implement their policy of supporting what they judge to be the good ideas of each major party and veto the bad ones.

But with Jeffersonâ€™s rule, A gets the first seat, which makes its reduced weight 25.5, so B gets the second seatâ€“but M has only 21 weight, so A gets the third seat too. In this case, as was the case with either rule in the 2-party version, there is no â€śneedâ€ť for overhang correction; the distribution of seats by party matches the outcome of FPTP. But note the huge differenceâ€“A represented a slim but actual majority in the 2 party example, but here it is little more than 1/3 the total vote, yet it dominates B 2 to one and all three other parties, taken together quite as large as A, are frozen out completely! Again, in the context of proportional rules; Hamilton fan here!

With Hamilton, the plurality district versus proportional outcomes are not a match; A overhangs by one so we have to reevaluate with 5 seats. Dividing 151 by 5 we get 30.2, so both A and B win quota seats, but then Aâ€™s remainder is 20.8, Bâ€™s is 18.8, and there are three seats outstanding still. M wins one with its 21 as the greatest remainder, then A and B each ace out both S and Z which remain frozen outâ€“but put together they are just a bit under 20 percent of the whole; versus typical FPTP this is more positive representation. Note of course this particular outcome is the contrived result of my picking certain numbers; in real life S might be larger than either of the other two new parties, or Z might be; M might be the smallest actually instead of the largest. This is voter sovereignty at work.

With those chosen numbers though, A retains its two district wins as its share, B picks up a seat from its second strongest district, 2â€“thus 2 is represented by 2 parties, the dominant two. I neglected to skew Mâ€™s vote so we need some kind of tie breaking to decide which district Mâ€™s sole member of the council body comes from, but whichever one it does, the dynamic is preservedâ€“unless either the delegates of A or B split and one joins with the other bloc to bypass M, M must approve all council majority decisions.

Now what would happen if we introduce Score voting? If we do it with Prime choice indications, we know the two possible outcomes of a 3 member proportional division; the question is, if we can determine and define proportionality that way, how will Score change the district outcomes?

Note we need Prime party affiliation indications, because with 17 A voters dropping their own party ratings down to 3 in a funk, I would have to drop Aâ€™s support for S down to a rating of 2 to maintain the clear distinction allowing us to suppose the highest rated party is the prime choice of that voter; I donâ€™t want to go that low, but it would mean that there would be no way to tell that votes rating both S and A at 3 would all be A prime votes. Weâ€™d have to adopt a rule splitting votes where two or more parties have the same top rating between those parties in the proportional phase. Of course there is some justification for saying a voter who rates S and A equally really is indifferent between them and their votes should be split 50/50 in the proportional phase.

In fact I see no reason for the supposition that Aâ€™s ratings average 4 for itself; if a voter identifies with A primarily, why not give their own party a maximum rating of 5 every time? That would be the strategic thing to do after allâ€“if the voter is not so alienated from A as to say â€śIâ€™m not an A voter any more, A is dead to me!â€ť In that case, why support A at all? Perhaps for reasons of ideological strategy, fearing B or even Z will triumph? But why not vote for S? If all former A voters voted for S, S wins in a landslide; if only a few do, presumably the ones who donâ€™t still prefer A warts and all, and therefore, even if willing to give S some support, should max out their rating of A the way B voters are doing. Having offered an example then, you, @AssetVotingAdvocacy , should offer an explanation for this lukewarm performance by A voters. This is yet another reason I like the simplicity of one choice in the vote, for the party you actually like; let others who subjectively like another one you like but not the most vote for that one, see how it sorts out, and then if the party you like is compatible with your own mentality presumably the representatives you help elect will work with those the party you want to give some support to in the bodyâ€“if none get elected there it is because not enough people liked them that much. It is nice to be able to throw the people you have some admiration for a bone, but not so nice if they wind up beating your first choice because you did not prioritize it yourself!

But the scenario is, A averages only a score of 4 from its own voters for reasons you ought to explain.

We need some assumptions here. How will the members of the 5 parties cast votes? The point of this exercise is to explore what happens with some cross-party voting. So some voters in all 5 will in fact do that.

M, being the party of professed moderation and balance and â€śboth sides have good and bad points,â€ť will have no truck (for now anyway) with the â€śextremistsâ€ť of S and Z. All three new parties will vote themselves a 5, the moderates being no exception in thisâ€“all three are crusading and have the zeal of a new way at this time. But M will give approval to A and B to some extent; they know they are in a minority and wish to tip the duopoly balance some. They lean against whichever party dominates a district, on the theory that something is wrong with the existing order or it would not be necessary to move past the old duopoly. And in each district, one voter for M will support both mainstream partiesâ€“there are thus exactly three three party voters in the whole system. But in district 1, 4 will approve B but not A, while two approve A but not B. One approving A will give A only a 3 rating, while the other will give it 4. 4 will give B ratings of 4.

S will somewhat approve A, but only half of them will, and in district 1 they rate A just 3. Z is the mirror image but in D1, half plus one will approve B with 4 ratings.

The two big parties will not be so symmetrical; as noted I infer A is in some disarray and B is in ascendency, presumably after a period when A dominated with some comfortable margin. So some A voters, about 1/4, will vote for S as well, and in D1 those who vote only 3 for their own party will also give S the same rating; those voting 4 for A itself will not vote for S nor will the one voting 5. Meanwhile about 1/3 of all A voters, not the same voters as consider supporting S, will give a rating of 3 or one less than their own self-rating, whichever is greater, to M. As there are 20 A voters in D1, there are thus 5 casting score votes of 3 for S, and 7 casting votes for M. Party B on the other hand, feeling their oats, are more reluctant to aid some other guys, just 3 will cast scores of 4 for Z, while 4 will cast ratings of 3 to M.

Moving down the ladder, S voters will slightly increase their support of A as underdog; A voters will slightly increase their support of S, and maintain 1/3 share of their total for M; M will shift to favor A more due to it becoming the underdog party. B will hold its level of support of M, and boldly increase its support of Z. Z however observing A being stingy with support will ramp back their support of B a little bit.

Drawing up a chart for this is a pretty complicated exercise! Actually tallying the real ballots would not be so bad, depending on the rules; if we have Prime votes marked on the ballot we just tally them separately in each district as we go along and pass the totals on to the central registrar, while also totalling up the scores in each district within the district and reporting those tallies too; there is no need for the central registrar to muck around with the original ballots. If we donâ€™t have Prime votes marked, we can still generally infer the single highest score on each ballot is that voterâ€™s choice, split the ones who insist on marking two or more parties with the same highest score into fractions for each, and report that as a virtual Prime tally along with the score totals. Indeed the only reason the central registrar even needs the district score totals is to figure out where make-up seats come from which is a simple matter of looking at each partyâ€™s score in the various districts and picking the highest ones.

But if instead we have nothing but the score votes and we donâ€™t decide to pretend we can infer peopleâ€™s Prime party affiliation, we have a rather grinding exercise in careful bookkeeping ahead of us for figuring quasi-proportion.

I am in the middle of preparing the chart enabling me to figure the district scores, and the distribution of votes between bullet party votes, two party combinations, and three party combinations (that is going to be just 3 ballots, one from each district, from M voters voting for both mainstream established parties along with their own, all other voters consider only supporting someone immediately to the left or right, and veering in only one of those two directions). We have to keep each distinct combination separate in tallying, because the quasi-proportional process of discerning party shares globally will I think no longer have the simple â€śpotential fieldâ€ť form it does when party votes are separated by the system or by the votersâ€™ choices; it will be a tangly â€śvector fieldâ€ť as it were, and it will make a big difference how we discount semi-satisfied voters and anal voter groups we strike from further consideration while grinding through round after round iteratively. There will be no convenient process analogous to just dividing the ballots for each party by a quota and glancing at the whole and remainder parts for each party, and we must keep track of which blocs of voters voted for just one party to exhaust them before moving on to those who split their vote between two, and in turn look at the ballots with higher score there for the party winning a seat. The closest thing to a simple integrated act of division I can think of is to discount each ballot by the total sum of all scores, add up weighted scores from that (which simply reduced to the allegiance of each voter to A or B in your example and thus standard proportionality applied) and suppose the weighted totals have some meaning. The purpose of this exercise of mine is to see how that works, but I have little hope it will be anything resembling a real proportion with any meaning.

So I am posting all this now and hoping to get the chart drawn up of the score votes.

It is rather unrealistic, but suppose A had averaged something like 4.8 to Bâ€™s 5. That still gives 2 seats to B, because the final round of Sequentially Subtracted Score would yield (roughly) A 78.13 B 78.33.

This may happen because some A voters gave one of the A candidates a 5/5 and the other one a 4/5. It might also be because a few A voters are just honest and want to send a message to party leadership (â€śchange to suit me or Iâ€™ll threaten your re-election chances.â€ť) This is probably the strength of a cardinal method, that it doesnâ€™t require any new competitors for a voter to influence the candidates.

Forgive me but I think new competitors is exactly what the system in the USA needs!

Again, I came to this board agitated that the cardinal approach would in practice amount to little more than a placebo much as IRV does, for essentially the same reasonsâ€“essentially that the real key to voters having positive representation is to consolidate the whole systemwide electorate, so that small factions can indeed amass a proportional share of the whole without having to â€śqualifyâ€ť by pleasing some large threshold percentage of the whole population.

It does not follow from that the only legitimate multi-body outcome is a finely graded rainbow of dozen or more boutique parties and a scattering of another dozen independents; in fact, if the sort of â€śconsider me because I have somewhere else to go if you take me for grantedâ€ť dynamic is really available to any group large enough to win a seat or two, odds are that a few broad gauge big tent parties can indeed do the mediation and reconciliation and brainstorming win-win options to largely offer between them satisfactory programs.

What I question is, can voters indeed walk away in a cardinal-vote based system at all?

Note that we donâ€™t have to achieve properly proportional representationâ€“indeed if there is a certain degree of chaos in the outcome, so that small groups might have power far out of proportion in one election but capriciously vanish into insignificance in the next, despite essentially the same people casting nearly identical votes, with subtle interactions between fine balances of guessed at degrees of â€śsafetyâ€ť in expressing multiple choices causing essentially unpredictable results, then that too is a powerful inducement to big broad party leaders to attempt, if not to be all things to all voters, then at least to pick a good broad swathe of them and focus hard on pleasing the whole lot of them.

But mere chaos in outcomes, while indeed raising sobering considerations that literally anyone could have sudden, arbitrarily amplification of their political power for a two year session or two, only to vanish again with the next election, cannot have any greatly reassuring effect on the credibility of our systemâ€™s broad legitimacy.

So, I regard the rise of many new actors more or less here to stay as a major feature and not a bug of any useful reform; if it fails to do this it cannot be too effective or be taken too seriously.

In Britain there are lots of fine gauged parties to choose from already and it would be more about giving them fair shares of power.

Dunno about Canada and Australia and NZ, but while the electoral systems of all could do with reform (even NZâ€™s MMP system seems flawed to me, the least bad of this major Commonwealth nation lot though) they are day to the USAâ€™s night in terms of existing options.

I could say far more, and probably should move it to a topic under general electoral theory or even off topic.

These are both possible with cardinal. But it encourages some placation of voters outside the quota because they might throw a point or two your way, and doesnâ€™t require as many new competitors as other PR systems to give voters significant influence.

I know I have been distracted from systematically laying out the dozen or so very specific examples in detail I have meant to, but I think by now I have put it out there that if US House of Representatives elections could be positively representative and proportional, then given the historic balances of actual votes cast, at least twice in the 2010s decade the House would teeter in the balance with neither major party having a majority of PV and therefore ought not have a majority of seats, forcing them to seek ideological allies. Specifically, under straightforward application of Hamiltonâ€™s rule, the Democrats in 2012 would have to persuade every possible ally elected to just barely enable a single seat coalition majorityâ€“it would have to involve two Greens and an independent named Terry Phillips from Fresno, California to just reach 218 seats (or rather the higher minimum majority after topoff, or to get to 436 seats in a doubled house. Historically of course the Republicans, who fell short of the Democratic popular vote, got 234 FPTP seats in flat defiance of two layers of weighty reason why they should not have been able to do that. FPTP for the lose, obviously. With very similar district win numbers, in 2016 the Republicans did pull ahead of the Democrats (or rather, given their quite genuine though again exaggerated PV majority in 2014, fell down to just barely keeping ahead of them) but even so their entitlement on proportional basis to House seats should have kept them at least half a dozen seats short of 218. They could govern, and the Democrats could not, because most of the parties outside the duopoly who should have gotten some seats proportionally were in fact right wing parties, mainly the Libertarians, who alone would hold considerably more than the balance of missing seats to get a Republican led coalition to and past the magic 218 number. Also there would be several others the Republicans could recruit too.

But while from my point of view this would make little difference on many key issues I worry about, the Libertarians would in fact have considerable leverage despite numbering in the single digits. Why should voters vote Libertarian and not Republican? There are issues on which they have made themselves distinct and on those issues, the Libertarian caucus would be under some pressure to demonstrate ability to get the Republicans to go along with them. Decriminalization of drug use for instance; by no means is this the most important, high priority thing, but considering the massive incarceration rates and associated vast public expenses involved in trying to enforce a punitive approach, even an only partial and incremental relaxation of current draconian practices, especially if associated with retroactive releases and clearing of criminal records, would make quite tremendous and largely if not entirely beneficial impacts on the lives of many tens of millions of Americans, and even on global events. As someone who never voted Libertarian and never wanted to (well, maybe back in high school when I read some L Neil Smith novels) Iâ€™d be conflicted about whether to hope the Libertarians lived up to their IMHO dangerous â€śprinciplesâ€ť or didnâ€™t, but if they come out of this alternate 2016-18 House session proving the waggish claim that â€śa Libertarian is a Republican who wants to smoke dope,â€ť with little to show for it to distinguish them and demonstrate their influence, it would probably be disastrous for their party brand.

So I want to stress, this catbird seat they would be in is based entirely on the number of votes they actually won in the real 2016 election, and with no election reforms whatsoever beyond using the same polls as historic to get a proportional share of a modestly expanded House. Yet it seems to me they could be quite catalytic! Similarly in 2012, a pair of Greens and one moderate independent from Fresno would be the lifeline Democratic control of the House hangs fromâ€“presumably the three way dialogs this would catalyze could be quite transformative, and might have led to entirely different outcomes in 2016.

I think then you might underestimate how crucial even a handful of out of the box candidates being elected could be.

Allowing third parties to actually be competitive for Congressional seats, of course, would fundamentally change them, since they would have an incentive to broaden their appeal. If their current leadership canâ€™t handle such a change of direction, well, theyâ€™ll be removed from leadership or will lose support to newly formed third parties that can. The point is, itâ€™s hard to say what the Libertarians would look like under PropRep?

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I should let Libertarians speak for themselves of course! They donâ€™t know either though. As things are now, American third parties suffer from being an exercise in futility and so the parties can adopt any platform they like, say anything, nominate any candidate, and no practical consequence ever emerges, or one time in a hundred maybe and then they are all alone in the body, typically. Not always. Bernie Sanders of course served as Vermontâ€™s sole Representative in Congress for something like 16 years, 8 terms, and another two and counting as one of two Vermont US Senators, not registered or running in any party. Angus King of Maine also serves in the Senate not in a party; the legislature of the state of Maine has several independents serving in it. But I donâ€™t think the Libertarians ever elected a single Member of Congress.

If elected things change.

Thatâ€™s a reason I like the asset voting â€śroundâ€ť of the system under discussion here too. People can vote for some really out there low support candidate, and that candidate will have at least one real job to do to be judged on no matter what. It gives voters an opportunity to see what these people will actually do in a real situation.

The business of leaving them a role of sorts, in the form of being able to play games with shifting their asset support around during the session so as to affect the balance of power in the sitting body, gives them and their supporting voters more opportunity to demonstrate what they are really about. it is a kind of rolling â€śnursery effect.â€ť Some kids play nice in a nursery, others do not! Some voters have constructive intents, others might like disruptive trolling. But presumably serious candidates want to be taken seriously, and they will be constrained to use their limited but real power in a way that demonstrates ability to leverage their aims. Voters can observe this and factor it in for the next election, dropping support for someone who proves either flaky or following a different program than that voter likes, being attracted to someone doing the things they like better.

With current American voting habits, the Libertarian party will be the third ranked party in members, but on a grander scale than the possibly jittery behavior of asset voter also-ran candidates, they would initially be playing a similar role-far short of power to simply do things on their own, but with some influential leverage to get their feet in the doors of deliberation, and perhaps crucial in close votes.Thus they can find their footing and demonstrate what their vaunted principles mean in real practice.

From my own standpoint, I hope some other parties emerge and grow rapidly; I would not look forward to the Libertarians dethroning either of the established two partiesâ€“in some ways they might be improvements on one I wonâ€™t name, but other aspects of the Libertarian program as I understand it I would expect to be downright disastrous. It could be that if that party grows and finds its footing its character will change considerably, perhaps as I judge things for the better. But I still doubt I would ever make a Libertarian my prime preference!

This scenario can actually be broken to give B all 3 seats. If 50 A ballots and 40 B ballots are removed (these ballots in sum give: A 200 B 200, so they identically rate all on-ballot candidates, and so shouldnâ€™t impact who wins) then the example becomes (A 4 B 45), and the Hare Quota is 10*5/3 = 16.666. B wins 2 seats and it becomes A 4 B 11.666. No matter whether you run deficit handling, regular SSS or the capped-quota variant of A compromise between Vote Unitarity and Thiele PR methods, B wins the final seat.

This makes me wonder if removing identical ballots in sum is a good idea or not. In some cases, it seems to yield a better seat distribution, in others it makes it worse. So on net, considering its computational intensiveness, not removing identical ballots in sum (but possibly still identical ballots individually) seems better for public elections.

both caucus as Democrats, and one is running for the Democratic nomination for President.

And a major reason so many Democratic officials opposed Sanders despite his evident popularity was that he was not a regular Democrat. King has stated in the past he would consider switching sides.

Ultimately despite the many accommodations our Constitutional system has made with the existence of parties, fundamentally the elected Members of Congress are deemed to have been elected as individuals by their constituencies, and are perfectly free to declare themselves members of any party or none with no consequences other than politicalâ€“will they win reelection having betrayed the people who voted for them on the premise they were not affiliated with which ever party they just jumped in bed with? Or that they were of the identity that they have just repudiated? It is a calculation based on judgement that either sufficient loyal voters are shifting with them, or they are keeping up with the voters, or else that the ones they lose are outnumbered by the ones they gained.

You should recall a number of lifelong Southern Democrats dropping that affiliation and joining the Republicans in the 1990s, all were reelected I believe.

Sanders and King command very large majorities in their states; those voters understand the importance of their man forming alliances. Sandersâ€™s problems related to Democrats resenting an outsider intruding when he had not stuck with their party thick and thin, as they judged it.

Foolishly, in my opinion. It was a fact Sanders attracted in a lot of people who simply would not vote for a regular Democrat. As a Sanders supporter I believed and still believe he is compatible with the vision of what the Democratic party should be I hold; what amazed me about 2016 was how many other people I would have assumed would be more conservative agreed with my â€śmoonbeamâ€ť notions that have made me an admirer of Sanders for longer than I knew who the Clintons were, back in the late '80s when he was featured in a Progressive Magazine interview titled â€śGo Knock On Some Doors.â€ť Younger people today might simply assume Vermont is some kind of hippie utopia over the rainbow, but basically it remains a conservative backwater of New England and the progressiveness of the state is very largely down to Sandersâ€™s leadership there, and his willingness and energy in getting out there and learning what the people actually want to guide his own vision of what would be the general welfare. Thatâ€™s democracy! I gained considerable morale from the identity of many Sanders activists I metâ€“plenty of usual suspect fellow moonbeams and professional dissidents to be sure, but also lots of military veterans and small businesspeople. Such demographics gave me much confidence that a solid majority in favor of serious progress is possible in the USA.

And they should have been seen as a solid asset for the Democratic party. The fact that many of these people would not vote for most Democratic candidates is more of a criticism of the shortcomings of the mainstream Democratic vision than anything wrong with them.

In terms of mechanics, I assumed going into my Nevada precinct caucus that of course Clinton would get a clear majority of Democratic grassroots support and the Sanders campaign, like say Jesse Jacksonâ€™s in 1988 I actively supported, was mainly about leveraging the strength of the neglected left of the Democratic supporters to pull policy in a more progressive direction. Had the campaign been conducted in a way giving voters confidence it was fairly fought, and then Clinton had held out some serious olive branches of reconciliation and incorporation of this very important group in sheer numbers, such as picking Sanders for VP (which would also be an excellent anti-assassination insurance policy for her!) I believe many of the normally non-Democratic voters Sanders drew in would have in fact turned out for a Clinton-Sanders ticket, and it is also possible a significant number of people who did ultimately vote for Trump would have gone for the Democratic vote if they believed Sandersâ€™s endorsement and involvement in real policy making meant the Democrats would keep the promises they cared about (regarding jobs and so forth) better than they had in the past and better than Trump would. Enough of this in Pennsylvania, Michigan and Wisconsin and Trump would not be elected.

But the jealousy of some goofy outsider horning in , probably much driven by the fact that the Sanders program was in fact a sharp rebuke of positions many leading Democrats were entirely comfortable with, closed that door with the consequences with live with. I was despite my long experience naive enough to believe the Democratic leadership wanted to actually win and would recognize the opportunity Sanders was offering them to do so as positively as I did.

I donâ€™t think then that either King or Sanders are truly fused to the Democratic party, and if you are convinced otherwise, I wish youâ€™d convince the Democratic leadership of that.

King I think is on the opposite side of the Democratic spectrum and quite capable of joining with the Republicans. Maybe not if they are a moving target shifting even farther to the right, and especially not if Maine voters do not in the majority like that trend.