Condorcet, IIA, monotonicity in RCV IRV
masiarek last edited by
ordered majority rule - Condorcet, IIA, monotonicity-not desirable properties ?!
A Majority Rule Philosophy for Instant Runoff Voting
IRV is the only voting method to satisfy ordered majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose. Ordered majority rule determines the relative social order between any two candidates by counting only ballots from those voters who do not prefer another major candidate, while ignoring all minor candidates.
Ordered majority rule is incompatible with the Condorcet criterion and independence of irrelevant alternatives because Condorcet and IIA demand that the relative social ranking between two candidates should depend on the relative social ranking of these candidates on all ballots. In addition, it is incompatible with monotonicity because monotonicity demands that if supporters of minor candidates have influence over lower ranked candidates, then supporters of major candidates should have equal or greater influence, while IRV does not grant influence over the social ranking of two candidates by voters who prefer a different major candidate. For situations where allowing supporters of a major candidate to have influence over the relative social ranking between other major candidates is deemed inappropriate, compliance with Condorcet, independence of irrelevant alternatives, and monotonicity are not desirable properties of a voting system.
One of the authors is from "FairVote".
The Arrow theorem only applies to ranking systems, but the article states that it applies to all systems.
The article does not mention Frohnmayer balance.
I can't say that I understand what all the verbiage is getting at. Some of it, to a degree, but not all.
It says that ranking ballots don't tell us whether the voters support or oppose a candidate. I suggest rating ballots so we'd know.
@masiarek just from the start, the article claims to do things that it does not do (I bolded parts of curiosity):
“ We show how IRV is the only voting method to satisfy ordered majority rule, for a self-consistently determined distinction between major and minor candidates, and that ordered majority rule is incompatible with the properties of Condorcet compliance, independence of irrelevant alternatives, and monotonicity.”
They most certainly do not show how this is true. They just repeat the claim without proof. I think the document makes a lot of claims without also giving effective demonstrations of them.
Here’s another suspect passage in my opinion, and I can elaborate:
“ The IRV majority rule philosophy
IRV adheres to the philosophy of ordered majority rule. It determines the relative social order between any two candidates by counting only ballots from those voters who do not prefer another "major" candidate, and ignoring all "minor" candidates. Major and minor candidates are self-consistently determined by the social order created by the voting method. For any candidate Y, all candidates below Y in the social order are minor candidates with respect to Y and all other candidates are major candidates with respect to Y. Every candidate, X, placed higher than Y in the social order, beats Y by counting only ballots from voters that do not prefer another major candidate with respect to Y over the higher ranked of X and Y, while ignoring all minor candidates with respect to Y. Candidates X and Y effectively compete in a head-to-head election composed of voters who prefer X or Y to every other major candidate with respect to Y.”
Ok, so (1) there is no proof of the claim that IRV is the only voting system to satisfy their property. And (2) their property has not even been fully defined outside of the context of IRV.
Finally, (3) how can it be that the social ordering is determined by the “major-minor” ordering, whereas the “major-minor” ordering is determined by the social ordering? That’s patently circular logic. Clarity is missing, as is ease of reading.
If you can find appropriate responses to these issues I have, I’d definitely like to see them too.
IRV is the only voting method to satisfy ordered majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose.
I'm not sure that this is even a good thing. If there are two candidates who might win - A and B - why should only people who like A and B get any say in who is elected? Someone might dislike them both, but still much prefer one to the other. I see this as a bad criterion.
Also, I haven't read the paper so don't know how they technically define that criterion, but it doesn't pass it as it's worded in English. Say we have:
35: A>B>Everyone else
33: B>A>Everyone else
32: Everyone else>B>A
Under IRV, B will win this election. That doesn't pass "majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose."