AssetVotingAdvocacy: AssetVotingAdvocacy: 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

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.

AssetVotingAdvocacy: AssetVotingAdvocacy: 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”)

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.