Open Question :

Can anybody come up with ANY party-agnostic rated deterministic non-delegated optimal proportional voting method that is not Thiele-based and passes:

  1. Independence of Irrelevant Alternatives

  2. Independence of Irrelevant Ballots (if a ballot rates all candidates equally, that ballot is irrelevant and adding/removing irrelevant ballots should not change who wins and who loses)

  3. (if possible) Monotonicity

The definition of proportionality this open question will be using: Whenever a group of voters gives max support their favored candidates and min support to every other candidate, at least one seat less than the portion of seats in that district corresponding to the portion of seats that that group makes up (or how many of those candidates exist if there exists less then this amount) is expected to be won by those candidates.

I have trouble defining optimal and non-Thiele-based individually, so here is the combined definitions of Independence of Irrelevant Alternatives, optimal, and non-Thiele-based this open question will be using: The voting method must be defined via a quality function that takes only a set of candidates and ratings the voters give to each of the candidates in that set as inputs and outputs a quality value of that election result. The voting method must pick the set of candidates with a size equal to the number of winners that maximizes this quality function. In the approval ballot case of the voting method, the voting method can NOT be simplified to simply picking a set of candidates with a size equal to the number of winners that maximizes a quality function equal to a sum among all voters f(the number of candidates in that set that that voter approved of) where f(x) is a function.

What makes this extremely difficult is the Independence of Irrelevant Ballots, which seems to be a property that only Thiele-based voting methods (or methods that violate IIA by simply discarding all ballots that give all candidates the same rating) have. However IIB seems like a very reasonable criterion (why should a ballot that does not care about which candidates win be used to influence which candidates win???) which is why I am interested in finding other voting methods that pass it.

Just curious, is it possible to have them count as a “Vote of Indifference” where each candidate has the points symbolically added onto their tally after the process has elected them? I’m guessing you also want a method where a ballot treating some candidates equally is irrelevant in changing which of those candidates wins, while the ballot still counts when determining which of the candidates it differentiates between should win.

Yes. I only care about inputs and outputs where the outputs are who wins and loses. If I add an irreverent ballot, quality values of each set of candidates can all increase or decrease together but who wins and who loses should not be altered by such ballots.

I thought of one, but it’s stupid.

Consider the “Loser Independent PR” criterion I posted in the committee doc:

The winner set must be proportional even if some losing candidates were disqualified and/or scores for some losing candidates were reduced. That is, if at least n quotas of ballots approve the same set of candidates, but there is partial disagreement on unelected candidates outside of that set, then at least n candidates in the set must be elected. (If 2 quotas approve ABCD, 2 approve ABCDE, and E is not elected, the standard PR criterion would require 2 of ABCD to be elected, whereas this criterion would require 4 of ABCD to be elected.)

  1. Find the smallest quota size for which it is possible to choose a winner set that passes this criterion. (We know that it must be between 0 and a Droop quota, assuming there are more candidates than seats).

  2. Find the winner set(s) that would pass the Loser Independent PR criterion for this quota size.

  3. Elect that winner set. If there is more than one such set, consider the election outcome to be a tie between those sets.

I’m not actually sure that this passes IIA. Instead: the score of a given winner set is the largest quota size for which it would be required to be elected by the PR criterion if all candidates outside the set were ignored. (We know that this must be between 0 and a Hare quota.) Elect the highest scoring winner set.

Does my optimal extension of vote unitarity not work for this? It is clealry Monroe based but I do not think it is monotonic. The general class of these methods which use what Warren calls the “corner trick” could have other similar models.

Nop. As we have previously discussed on the wolf committee, it fails IIB.

Almost everything that’s proportional fails IIB, so as a starting point try to pass that and then move on to the other properties.

So as an equation of what the quality (Q) of a two winner election result would be in terms of the % of voters that approve of only the first candidate (va) the % of voters that approve of only the second (vb) and the % of voters that approve of both (vab), Qab = max(vab/2, min(va, vb))? Is this what you mean? Because if so, it doesn’t pass IIB because you can add enough voters that approve of all candidates such that the PR criterion will only ever force groups of candidates to be elected because it can do so with a quota that is to high to elect candidates via their individual supporters.

Yup, you are right. Sorry

It might be possible to prove that all Monroe (quota) systems fail IIB. This would be because adding relevant ballots would change the quotas and thus the winners. This would mean there is no such system which meets your criteria.

The determinism clause is also very important or something like this might get you there.

Would using “Winner Independent Proportionality” instead of the standard PR criterion fix this? In the doc, I described it as:

The winner set must be proportional even if scores for some winning candidates were increased. That is, if at least n quotas of ballots approve the same set of candidates, but there is partial disagreement on m elected candidates outside of that set, then at least n-m candidates in the set must be elected. (If 2 quotas approve ABCD, 2 quotas approve ABCDE, and E is elected, the standard PR criterion would require 2 of ABCD to be elected, whereas this criterion would require 3 of ABCD to be elected.)

What if, before running any Monroe algorithm, you calculate the Hare Quota based only off ballots that didn’t identically score all on-ballot candidates? That might cause problems when a write-in candidate gets a significant number of points though.

I think I’ve also found one more situation which merits a criterion: if a set of ballots, when their scores are totaled up, equally rates all candidates, they shouldn’t influence who wins.

The first paragraph’s idea doesn’t make Monroe methods pass this new criterion.

Edit: This actually turned out to be a nonsensical criterion. An example of how it fails:

That’s an interesting claim to me. I am generally in a fog on all this recondite terminology, so let me see if I understand it at all correctly.

IIB, with IIA seeming to be another way of writing the exact same concept, means that when a method has arrived at an outcome, some of the input data, as in say scoring candidates who did not get elected, should have no bearing at all on the outcome even if it were changed.

Immediate reflection suggests that the changes to be considered have to be constrained somehow or it becomes impossible to satisfy in all cases–for instance, if simple Score ballots of a given number of districts determine the whole body, then IIB means in this case that the maximum alternate score in an alternate reality vote any non-winning candidate in each district could have would be limited to be no greater than the winning score in reality. As this is entirely arbitrary and varies from district to district, does it follow such a simple straight implementation of Score voting fails IIB?

But that is not a proportional method by any means, so let me turn to the simplest proportional method I know of; straight party list, everyone has a single choice for supporting a given party, and then we apply a standard proportionality formula to get the integer outcomes to the total of seats under election. Jefferson, which seems to be embedded in Thiele, is at one extreme of those methods, shifting seats won to the largest factions by raw vote share, and Hamilton as far as I know at the other extreme, maximizing the seats going to the smallest factions and thus also maximizing the share of total votes included on some scale in the body. Other methods such as Webster and Huntington-Hill (which can have an open form allowing it to be applied to all parties, not just those winning a simple quota) fall in between in that respect.

So say we apply either Jefferson or Hamilton’s method to a given vote distribution, it will happen that in addition to voters who get at least one seat elected for their faction, others will fail to. As every voter has only one choice, the only “irrelevant” choices are those of this bloc of non-winning voters.

It is plain on the face of it to me that indeed this fails IIB if I understand what that is supposed to mean generally. For it makes a difference in either Jefferson or Hamilton evaluations, even if we stipulate the constraint that the exact vote shares of all candidates who historically won a seat at least are unchanged, and that the total of all votes cast also stays unchanged which means the number of loser voters also remains the same in total, whether the “others” whose votes failed to capture even a single seat in fact grouped themselves together behind one failed party, versus scattering their votes across a wide spectrum of failed candidacies going down to single voters writing themselves in (or even having properly registered themselves in advance to have properly appeared on the ballot).

Under any integer proportionality apportionment, some single party is at the bottom, winning a single seat by the slimmest margin, and the next faction down the ranked by vote count list is the first of many who win nothing, and therefore the strongest among them must have won fewer votes than the Omega-winner, the one who got that last seat by the slimmest margin. If #1 and #2 in the list of also rans were to have consolidated and all voters for one instead voted for the other alongside that one’s historical supporters, they might or might not outnumber the Omega party that barely won a seat, and thus pole vault if they did outnumber Omega to take their place, dumping Omega into the heap of failed parties.

So clearly it matters in this classic version of proportionality how consolidated versus how scattered voter choices are; the more scattered the voters, the larger the unsatisfied on any scale voter bloc is, and that bloc is liable empirically to be considerably larger than Omega’s quota. The more seats there are, the smaller that bloc is, but until we raise the seat count to a level where the whole bloc falls below the share of votes of Omega, how the losing voters could have reorganized themselves remains relevant.

So having parsed it that way, I need to ask–why should we worry about IIB as a criterion at all? Voters know going in to the election how the mechanics work and are aware of the consequences of their choices. The failure to be elected of some parties is part of the rules, why is it bad to have the final list be immune to possible alternatives? We could use this standard as a yardstick to evaluate how many seats should exist, but I suspect trying this with even the most inclusive proportionality method leads to an open ended spiral requiring us to seat each and every faction! Keeping it proportional then would require a body size of tremendous proportions, that fluctuating very unpredictably, and tending to spiral to ever larger sizes as voter blocs realize they can fragment more and still win something, leading ultimately to every voter simply writing in themselves and going to direct democracy of the whole.

If we insist that voters ought not to have any reason whatsoever to factor in how they think other voters will vote, what kind of voting system other than sheer lottery can satisfy that?

If IIB means something else, please say what!

As I understand it, IIB means that if someone entered the voting booth and gave every single candidate a 2/5 score, their vote shouldn’t change who wins and loses. It is really a criterion that only makes sense with methods where you can show equal preference between multiple candidates when casting your vote, though your idea to let people Approval Vote and have the vote split up equally between the various parties they voted for (which is called “cumulative voting”) would make those methods fail IIB (giving 0.01 votes to 100 candidates changes the result because you are factored into the calculation of the quota, even though you equally supported all of the candidates.)

So if as a critical criterion it cannot be generalized to non-cardinal methods, how can it be relevant to comparing a cardinal and non-cardinal method? You seem to be saying it cannot be, it only applies in evaluating different cardinal methods.

I cannot see at all how anything I wrote here could be interpreted as suggesting that!

Well, not here–elsewhere I was suggesting maybe it could allow some kind of definition of something usefully analogous to proportionality, both as a touchstone for comparing district by district outcomes to a global overall target for each faction we could meaningfully infer and thus adjust via top off to enable the most “disproportionate” faction’s district wins to be brought into line with this quasiproportionality, and perhaps pointing to a quick mathematical way of parsing the global vote to arrive directly at the same quasi-proportional outcome iterative methods deemed reasonable would in one direct global mathematical procedure shorter than iterative. Your suggestion I was in fact reinventing Cumulative Voting there (and certainly Lani Guinier, as the short-time Clinton nominee for the Equal Rights Enforcement dept head, before being torpedoed by a combination of viciously inaccurate mudslinging and Clinton’s spineless “moderation” in surrendering to it, one of many instances where I question the general value of defining moderation as “appealing to all sides” and its normative elevation, did propose that and it did seem admirable enough to be quite an improvement on our current FPTP norms)) seems to stand up pretty well to my looking up that, and so far “panacharge” voting too perhaps.

But all this is relevant on the topic I brought it up on, which might be several but not this one! So further remarks are deleted.

Now then, I confined myself to comparison with a single choice system. It is not clear to me whether the common, near-universal single choice approach, which dominates both US and Anglosphere generally dominant single district FPTP (and also multiple member FPTP, which is definitely a thing, and to my knowledge continues in West Virginia, having been banned for US Congress after being practiced for these races by various states in various forms by the Civil Rights era combination of court rulings and Congressional Voting Rights Act legislation) and also traditionally conceived PR where single choices are for a party, analytically would be categorized as ordinal or cardinal, or properly a third category we don’t seem to name much.

But that is what the analog was in terms of. You seem to be saying there is no analogy. Reading up on IIA in Wikipedia, it seems plain you are mistaken about that.

In voting systems, independence from irrelevant alternatives is often interpreted as, if one candidate ( X ) would win an election, and if a new candidate ( Y ) were added to the ballot, then either X or Y would win the election.

In this definition, clearly if we have a single choice option, and we simply imagine running the same election with the same candidates on a closed ballot, with the same voters pursuing the same strategic versus honest-preference balancing, but in one universe we have only A and B candidates, but in the other add C, with the same voters any votes for C have to come from either those who voted for A or for B in the other world. We could instead assume C pulls in new voters, leaving A and B total votes identical since they have done the strategic math and made their single choices as their best overall balanced utility choice, so C does not tempt them–if C gets any votes it must be then from first-universe non-voters. Either is plausible in the USA, we have huge margins of people who just sit out elections who could register and vote. In the first case, clearly enough voters switching to C more strongly from one of the first two than the other could cause the two-choice world winner, A let us say, to lose to B as long as any votes B loses to C do not cause B to fall below C’s own level. Only if we stipulate none of A or B’s voters would be tempted to switch to C can we maintain this system passes IIA, but clearly that is a voter choice, and both their prime utility and strategic minimax utilities could be upset by C’s running. Classically in fact, if C appeals to A voters more, we have the well known spoiler effect at work, a clear violation of IIA. Which is a little bit suggestive of why anyone is even worried about IIA as a criterion–we want to avoid spoiler effect if we can. But actually there are other considerations affecting whether C is a “spoiler” or not, in terms of ultimate victory.

I did not use the example of classic single winner FPTP though, but the classic single choice proportional system, looking at the fact that some voters always are left in a residual nonwinner category that summed up ignoring the fact their votes are much split among each other, would merit by a given proportional apportionment one or more seats but do not get any because they are divided. Again it seems plain, adding a candidate C to the loser pool could well siphon off some votes from any party winning seats without C in the race, and if we have this happening to party Omega who is last on the list of seat winners, it could as showed flip C up to replace Omega. Well, that is OK per IIA compliance by the Wikipedia commonly given definition! But can votes siphoned off to C from Omega, or even a somewhat larger party, result in both demoting Omega to nonwinner and allowing another party than C to rise to take its place from the non-winner pool? I think clearly this is conceivable! Suppose C rises from zero as we transfer voters formerly supporting Omega to it, until Omega drops below vote share of the largest party that failed to win anything before, but this share is larger than C has won at this point? Then Omega is replaced by that party, and that party was included in the other universe that did not include C in the race, and indeed does not need its alternate world vote share raised one bit to here defeat Omega.

So I think we can say single choice voting systems do not “satisfy” IIA, not in the full range of conceivable changes adding a new party can cause. Again if all first-universe votes are fixed and unaffected by C’s alternate-universe candidacy, then C can win only by drawing in new votes, and in pretty well defined numbers too–in FPTP single winner races, only by drawing one more vote than the plurality winner without C, which typically would imply raising the total vote by over 50 percent–but even that is not inconceivable in real world situations, and in the PR case involves merely drawing in more votes than Omega wins, which plainly can be quite a modest addition to the whole.

Again, the question remains, should we be worried if a voting system does not satisfy IIA? Clearly the classic spoiler effect is a pretty deplorable form of violation!

However, what does it take for cardinal methods not to violate IIA?

Approval voting, range voting, and majority judgment satisfy the IIA criterion if it is assumed that voters rate candidates individually and independently of knowing the available alternatives in the election, using their own absolute scale. This assumption implies that some voters having meaningful preferences in an election with only two alternatives will necessarily cast a vote which has little or no voting power, or necessarily abstain.

Am I crazy to say that seems like a lot of “if” to assume? Wikipedia continues:

If it is assumed to be at least possible that any voter having preferences might not abstain, or vote their favorite and least favorite candidates at the top and bottom ratings respectively, then these systems fail IIA. Allowing either of these conditions alone causes failure. Another cardinal system, cumulative voting, does not satisfy the criterion regardless of either assumption.

So all it takes is one bullet voter, and the system fails IIA.

What is the real world significance then of IIA compliance versus failure?

Further quoting Wikipedia

An anecdote that illustrates a violation of IIA has been attributed to Sidney Morgenbesser:

After finishing dinner, Sidney Morgenbesser decides to order dessert. The waitress tells him he has two choices: apple pie and blueberry pie. Sidney orders the apple pie. After a few minutes the waitress returns and says that they also have cherry pie at which point Morgenbesser says “In that case I’ll have the blueberry pie.”

As often the case with these kinds of anecdotal examples, it seems rhetorically to make a strong point–what kind of crazy system veers like that? But consider substituting a political model for a choice of pies–Morgenbesser will vote Democratic if the choice is Democrat versus Republican, but if there is a Green candidate he might switch to vote Republican instead. If Morgenbesser is in fact a centrist, and worries that a Green might draw in lots of lefties with what he regards as a dangerously irresponsible agenda, and that a Democrat who wins only against a Republican can be counted on to leave supporting such policies off the agenda but the same Democrat, observing a large number of Green votes that perhaps come close to challenging their own victory and might rise to unseat them in future, veers left and adopts at least some of the “wrong” policies and perhaps even pushes them through. Therefore Morgenbesser is moved to shift his vote rightward to try to compensate–this might undermine the more moderate Democrats and thus leave the Greens relatively stronger but he might reckon that the Greens are too extremist to succeed in pushing any of their program on their own without moderate Democrats giving them the cover of gravitas. Therefore the harm he does his no-Green-candidate preference is more than offset by the damage control he might do by shoring up the conservative Republican.

Note this logic holds whether the election is FPTP for a single candidate in his district, where his shift tends to help either a Green or Republican win depending on the numbers of Green voters, and applies whether all the Green votes are new or whether any of them come from the Democrat or even from the Republican bloc, and applies also in a proportional race where his shift assuredly both weakens the Democrats collectively and strengthens the Republicans.

Thus IIA is violated, but the nature of the perturbation of the overall outcomes by addition of a new candidate is in line with voter preference rational calculation. It might seem perverse in FPTP, and the likelihood that more Democratic voters would shift to the Greens instead of the Republicans thus producing classic spoiler effect underscores the craziness of it in common sense terms.

Unless, I note, one holds as my partisan rather than pie-choosing Morgenbesser example does, and frankly as it seems the values often expressed to extol cardinal methods do as well, that the center holding is an aim of our voting system–clone spoilers, and spoilers who are not clones but represent a significant differentiation from the mainstream party they threaten to take the most voters from, are quite distinct, and our system has been good at largely preventing the former from running, but not the latter. But under FPTP single representative system, there is no distinguishing them in immediate effect. Under other systems there could be a quite effective operational distinction.

Under positively representative PR, which I have offered a straightforward single choice vote system preserving districts and the option of preferring local and individualist priorities to voters who value them and doing away with party lists to enable, true clones representing two clone parties certainly split the vote for whichever of these existed first, but collectively they do no harm if they split the older party’s electorate 50 50 because they collectively command the same share of delegates as the single party formerly did, and presumably, being clones, can cooperate closely and may in fact tend to re-merge. Indeed, if there is some small differentiation between them, the respective camps of voters who gravitate to one or other presumably feel happier with their representation, and there is scope for each to annex new voters who formerly would not consider supporting the old party, so that taken together the new two party configuration commands more share of the legislature than the old single party did–by being more inclusively representative and spanning a larger total share of the electorate. In this model, the other kind of “spoiler,” attacking a moderately left leaning party from the left or right leaning from the right, is on a continuum actually; the farther left the leftist challenger is, presumably the fewer of the old party’s voters it “poaches” and as above, the outcome is two parties each with voters better satisfied, and each able to more or less work with the other on those issues they share common ground in. Thus IIA seems pretty irrelevant.

Especially considering, again per Wikipedia:

In other words, whether A or B is selected should not be affected by a change in the vote for an unavailable X , which is irrelevant to the choice between A and B
…{to repeat from an above quotation} voters rate candidates individually and independently of knowing the available alternatives in the election…

Reflecting we are talking about politics, about electing officials who will wield social power purportedly on behalf of the democratic community, deliberating about different interpretations of the general welfare, why the heck ought we assume that evaluation of one candidate “should” be independent of knowing the available alternatives?

In fact politics is not a case of choosing what kind of dessert we privately prefer from a limited list of options available at the moment. It is about choosing people we hope we can trust to act on our behalf, in global situations not under their control, in reaction to events that are more or less unpredictable. Our choice of which persons to trust most assuredly does depend on which persons are credibly able to put themselves forward to address this unpredictable future on our behalf! We need to weigh both the probability they will in fact maintain our interests as priority versus some interest that might be antagonistic, and the values they bring to a wide range of possible situations, and their competence to handle any of these possibilities that might arise. Certainly their ability to work creatively with others of different inclinations is one important value, one of many to be weighed. Persons are not static quantities defined by a set of statistics; our judgement as to what a person will do depends on our notion of who they are, based in party on what they have done in the past, and on which persons they associate with, as well as whatever values they verbally claim to hold. We judge the credibility of the latter against the former real world evidence (insofar as we can and choose to limn out what their actual track record and associations were really; this relates in part to the weight we give various information sources and the effort we make to ferret out more information, and evaluate its quality, beyond whatever happens to be dragged in front of our eyes without our particularly willing it).

So people are not slices of different flavors of pie. Political choices made ought to be expected to hinge on options available. Perhaps I should examine the examples offered in the thread in light of these reflections and see if I can make some narrative with verisimilitude that shows how specific voting systems yield outcomes perverse as far as the voter is concerned–and whether a simple alternative election system of single choice voting in the context of the whole system aiming at faithful positive representation would be better, worse or indifferent.

I was talking about IIB, not IIA. Cardinal systems do “practically” fail IIA, but the point of saying that they technically pass IIA is largely just to say that they don’t have a spoiler effect (that’s forced onto the voters, anyways.)

Divisor methods are embedded in Thiele, but Webster could just as easily be used as Jefferson. With PAV, the weight of each ballot would be 1/(1/2+w), where w is the number of approved winners.

There’s Asset. (Though it depends on the rules.)

Well, this remark opened a great big can of worms of musing that probably belongs elsewhere, here I am trying to focus on @parker_friedland 's original post issues, and limn out why we should worry about IIA and IIB at all; I believe we have discussed Monotonicity elsewhere. Also the OP definition of “proportional”

seems remarkably of little use to me–it pretty much assumes that voters, handed a cardinal voting system, turn it into a single choice system by bullet voting. Certainly that tells us if a proposed system fails to be proportional but it does not tell us anything about whether such a system remains meaningfully proportional in any sense if voters use it as intended!

Regarding different divisor methods, I think I can say yeah, of course, but I still find that kind of limiting, since one divisor method that comes closer to Hamilton than the others (Huntington Hill) can be given an open form allowing it to be used in a single-table form that cranks out all the seat shares for all parties in one step (when we fiddle with a common multiplier of raw shares to land on the correct total of seats, just as we do in Jefferson or Webster single table process approaches) evaluating all parties, not just those with a full quota or more for a seat at the start of evaluation. My goal for any iterative method would be to find such a corresponding combined solution method, and we can’t do Huntington Hill iteratively without knowing in advance which parties will in fact get at least one seat fairly. (A kludge might be to use Hamilton to find the set of those winning by greatest remainder, and then see whether a common multiplier including the smallest party winning that way yields the right number of seats or too many, and successively drop the smallest parties remaining until it closes. But frankly that requires a valid Hamilton process to be run first, why not just stick with that one’s outcomes?)

Anyway I suppose all this off topic here so I will truncate it at that for now.

All right, apologies to @AssetVotingAdvocacy and @parker_friedland for badly misreading the former’s response to me and their own upthread contributions on IIB, and failing to note the distinction with IIA are in order. Emily Litella Award for sloppy reading to me.

But I don’t think I should be saying just “never mind!”

The question of whether IIB is anything to fash ourselves over remains, and I think we can reasonably disregard it, and consider saturation votes in Score or Approval to be meaningful and intentional, and a system that permits them to change the outcomes valid.

Consider a two-party approval vote race between A and B. In one version, all voters bullet vote A or B, and the outcome is say 601 out of 1000 ballots for A, 399 out of 1000 for B. If this were a district race in say 100 districts, we’d have to construct some kind of model of where these bullet votes were distributed. But let us say it is instead a multi-body race for 10 seats all in one merged systemwide at large vote, on a party list basis.

Clearly with the race degenerating into a single choice referendum all proportional counting methods would make it 60 seats for A, 40 for B–plainly so for Hamilton, and I just verified it for Jefferson.

But now suppose another 1000 voters weigh in, and these are centrist-moderate “unity” voters who value reducing party extremism by means of supporting both. They add 1000 score points to both, and in a district race would make no difference, except for “nursery effect” variation signaling to both parties that extremism is not appreciated and if they want to keep getting elected are on notice half the expanded electorate will punish the ones each sees as more extremist by withdrawing approval and thus favoring the one seen as less immoderate.

Now we need some kind of multiseat procedure for Approval Voting. My own pseudopotential, which I thank @AssetVotingAdvocacy for pointing out is a version ofCumulative Voting–indeed FairVote’s archives name it exactly as Equal and Even Cumulative Voting, simply divides each combination of votes by the number of choices it endorses, so the bullet voters remain 60 and 40, being divided by one, but the unity votes are divided by two, then the fraction of their ballot count, 500, is awarded to both A and B. Thus, by this approach, we have for A 1101 and B 899 cumulative score out of 2000. A quota is 20, so we have 55.05 to 44.95 toward 100 seats, which by Hamilton clearly becomes 55 to 45, and by Jefferson we get the same outcome. We thus close the gap in representation between the two parties from 20 seats to 10.

In effect then, and despite a stronger A vote, the half of the electorate voting unity has moved the two parties closer together.

This might not seem to matter much with only two parties in play, one of which has a seat majority, but it does reflect a shift that might matter in a multiparty situation, where a third or Nth party might hold the balance, and their shares push the plurality party into minority. By spreading their votes evenly, the unity voters elevate the weaker parties closer to parity with the stronger, and shift seats downward; this leveling effect can change the dynamic of the body in operation.

And in this scenario, it is entirely reasonable that we interpret the “unity” voters vote as intending this very outcome!

This is entirely a meaningful choice toward a meaningful goal within the power of elements of the electorate to choose to drive toward.

To seek a method that satisfies IIB then strikes me as rather mindlessly carrying over what is perhaps an accidental and not too significant aspect of cardinal single candidate election systems; the fact that such a unity drive has zero effect in such elections would seem less a feature and more a bug of Approval or Score upon reflection!

If that is one cares about maximizing competitiveness of consensus candidates and goes about calling them “better.”

I remain committed to voter sovereignty and letting the chips fall where they may, trusting or anyway hoping that with positive representation and exponents of all factions showing up in the body in proportional numbers, voters will reevaluate their goals and expectations based not just on how abstractly stated goals sound in isolation, but how their appeal can translate into broadening support and practical implementation against opposition that has its own foundations in interests the body must balance and seek win-win options in order to act. They can judge the character of their chosen representatives and shift it away from those they deem whatever combination of faithless or ineffective they judge most important strikes against them, and toward those who on the whole give them the greatest self-judged combination of trustworthiness and hope for positive gains. So personally I don’t give a damn for stacking the deck in favor of the guy in the middle; insofar as the guy in the middle really is more open-minded, balanced and fair, they should win support on the merits of dynamically demonstrating these useful values, and demonstrating balanced consideration of opposed interests and finding positive resolutions, thus earning more support in their own rights, and not by virtue of being seen as a lesser evil by the most people. That is a valid and realistic attribute to credit a candidate with, but God forbid it be the only one, as often is the case with FPTP!

Thus the quest for IIB neutralizes positive expression of a value that actually I am pretty leery of myself, that of encouraging the most broad and presumptively moderate option and neutralizing the alleged evil of “center squeeze.”

Center squeeze is exactly what unity voters are opposing, albeit weakly, and can more actively oppose by approving positively only those candidates they deem most moderate.

It seems odd then to seek to abolish it from multimember versions, and thus seems, along with IIA, not an appropriate criterion to worry about “preserving.”

We might even want to revisit cardinal methods with positively giving “indifferent” vote-for-everyone votes more effectiveness rather than be happy they chance to be irrelevant, but that is not an ambition of mine! I value people making a choice and backing it, and having that behavior be reasonably and proportionally rewarded in a fair way.

We don’t have to necessarily stack the deck in favor of a compromise candidate, but the goal should be to allow such candidates to pick up bits and pieces of support from all voters without necessarily needing a group backing them outright. Of course, all of this takes place within the backdrop of a dynamic election campaign - if voters dislike compromise, they can pretty easily just zero out any compromisers. It’s fair to say most consensus PR methods do draw out some compromise forcibly from voters wanting to cast a fully effective ballots, but this seems a worthy price for allowing them to compromise without using up their entire vote. The ideal PR system would be one where you could choose whether you wanted your ballot to be processed in a way that maximally favored compromise or your own favorite candidates.

I don’t see why we should not be taking that sentence and simply striking “such” from it. Let all candidates accumulate the share of support all voters care to give them. Why is this a value for compromise candidates only?

Concretely, I am moved by the site’s serious engagement with serious discussion to consider carefully the positive utility of cardinal methods, and am thinking in terms of limning out whether a purely cardinal single vote with multiple choice options can serve both as an Approval or Score vote in a single district and as an intelligible guide to global more or less, as I am saying now “quasiproportional” outcomes for the whole body, to be leveled up to the latter in MMP fashion, but ideally based still on the single vote to avoid the strategic gamesmanship noted in the other topic “Most Fatal Flaw of MMP.” By default in the absence of a suitably workable quasiproportional approach emerging from the cardinal district vote (suitably expanded to allow for out of district meaningful options–as by including all parties and permitting transfer of individual candidate support to out of district candidates) we can fall back on voters having a Prime option, but as you have noted this is somewhat confusing and complicating. Only moderately so! I would not insist that a quasiproportional system if we can hit on one–seeing Approval enabling a defined form of Cumulative Voting to be inferred from district votes seems mighty promising to me now–must match a hypothetical Prime Party vote in parallel outcome exactly, but certainly the larger dynamic should preserve positive representation in some form, albeit perhaps distorted. But effective, in the sense that no interest groups who can muster a quota of a body seat share of total ballots cannot be shut out, nor can minorities gain undue control of the body consistently without actually negotiating with others who joining with them make up something near a real majority, and the incentive is always to broaden rather than narrow appeal, by earning appeal rather than by trapping blocs with “nowhere to go.” Everyone should always have an escape hatch from any coalition; they pay a price to walk away to be sure, but so does the coalition in losing them. That seems essential for alliances to be credibly focused on seeking positive gains, rather than merely suppressing dissent.

Now of course my other quarrel with that sentence is that I don’t see why a stigma attaches to people supporting someone outright! I have offered a plain if somewhat far fetched motive for voters to saturation vote maximum scores for all candidates; but my honest judgement of such voters would be they are abdicating thinking about what it is they positively value and empowering a representative to positively advocate for it. Being specific and concrete seems more valuable than vague generalities about balance and moderation; put forth your values that they may be judged, while you judge others, and recognize that some kind of cooperation is the only way forward. If we know specifically what other people actually want, we can better devise appeals to gain their support and cooperation toward what we want.

So accumulating scattered support is exactly one way positive representation differs from FPTP single member (or multi-member, that is a historic thing in the USA and still practiced in West Virginia legislature elections, but the courts struck it down in House of Representatives races for reasons relating to squeezing out minority voices and the Voting Rights Act mandates single member district elections as part of the Civil Rights movement legacy). That’s how PR defeats gerrymandering and even gross malapportionment of some districts with much larger populations than others. I have been aiming at a system that gives voters flexibility to decide for themselves the salience of regional versus ideological concerns after all; in some communities a district approach, choose the best representative of a coherent community as a whole, might seem best, and would not want to make that difficult, but I still think any dissenters, whether few or many, from that consensus need their fair weight in the body too. Hence the concern for some meaningful integration of the whole electorate in arriving at the proper balance of the whole body, while still empowering strongly regional/communal interests to assert themselves organically if the people there have mind for that mostly.

Neither should come up short, therefore neither should be inflated.

I think this is also worth remarking on:

Good, but I am looking beyond the election campaign to the dynamism of the body in session. All through the session, the weight of all sectors should be considered in balance. The dynamism I referred to is the outcome not of promises and horsetrading during an election, but of voters observing the behavior of representatives when the chips are down and action must be taken, to judge on this concrete basis who these people are and which of them is best able and willing to give the best government. Words contrary to deeds will not weigh much; deals offered have to be credible–can the candidate deliver, and will they? Deeds are what is done during the session, and so it is important to me the actors all be present, not some predefined subset of them meeting qualifications subject to elite filtering.

I think I have offered that, by altering the traditional single choice system we are accustomed to to double as a proportional vote, a form of reconciling traditional district vote with global proportionality for positive representation, and a voter-governed mode of selecting the exact identity of the make up members dependent on votes earned in the respective districts. Anyone can vote for compromise, or uncompromisingly, without any requirement of multiple choices.

The outcomes I think would achieve all that is claimed for cardinal choice globally if not locally, and is simpler to implement as far as vote tabulation is concerned.

Even voting maniacally for one’s ruthlessly pushed self interest does not automatically cause polarization to extremes, because getting a proportional body elected is just step one; to amass a single party that can rule a chamber unilaterally itself requires extensive log-rolling compromise among many disparate interests to achieve 50 percent plus one, and such a coalition, with positive voting enabling all to weigh in, is unlikely to lack causes for empathy and sympathy for other actors that will morally check the power to some extent. Realistically, you can see why I am not so concerned with fissiparous tendencies, these are kind of good in that they tend to block such a single party from ever forming.

The dynamic within the body forces strong advocates of specialized positions to reason together and seek to build consensus on specific issues, and as different issues will naturally bring together different 50 percent plus one majority coalitions, the practice overall shall be for all members to learn civility and mutual respect of disparate positions–not necessarily to find some kind of static Aristotelean “middle,” but to negotiate a course that gives enough people a positive stake in the outcome to amass solid support.

Compromise, or rather positive cooperation, is vital because human society operates fundamentally on combination of human ability toward shared goals. This is how our species came to dominate the planet, and if we have any hope to survive the Anthropocene age we have created, we must generalize this to ever more elaborate forms. Politics is how human beings do this, democratic politics is how we enable everyone to participate equally and effectively.

The alternatives to democracy exist, and are rather ugly! And perhaps liable to assure our self destruction too.

I object to preconceptions about what cooperation must look like, to notions that men in the middle are automatically and necessarily its creative leaders. Certainly the center should have great weight, but culling out the extremes clouds and blurs our creative vision. Let the people judge who the creative and hopeful leaders actually are and support them!