@toby-pereira sure, that's a reasonable doubt. I'll respond in three ways:
(1) In section 5 of our paper we perform experiments to check whether our rules decrease the total social welfare of the voters (measured by Borda scores - I believe that any other measure would yield similar results). This is not the case, so we do not sacrifice the voters' satisfaction by taking parties into account.
(2) The rule I described in the post is Condorcet-consistent, so over 90% of time when the voters' ballots clearly indicate the winner, alliances do not matter. They start to matter only if there are cycles, which means that no candidate has a clear support from the voters.
(3) Besides, this rule cannot elect weak candidates only because they are from the winning alliance. E.g. if there is a candidate who'd be Condorcet winner if they are the only nominate of their party, they'll be the winner.

Hi everyone,

Let me share with you my recent paper on single-winner elections. We propose here a few simple methods with good spoiler-proof properties. Let me describe one of them which I personally like the most (SW-Maximin in the paper). Basically, this is a Maximin with a simple twist:

• before the election, a group of candidates sharing similar views (e.g., from the same party) can register as "allies", who do not want to hurt one another in favor of other candidates,

• voters vote using ranked ballots. We perform head-to-head pairwise comparisons and compute the Maximin score of each candidate (worst performance in the matchups).

• the twist is that we do not compare allies to each other. Only if there are multiple allies who defeated all their opponents, we remove the remaining candidates, compare the finalists to each other and update their scores.

• the candidate with the highest score wins.

I believe this twist should be very natural and easy-to-understand to people (it's clear that two similar candidates should first fight against their common enemies, and only then against each other). Besides, Maximin is a very easy rule to explain by itself*.

On the other hand, the "bad example" commonly pointed out for Maximin (three similar candidates beating each other strongly, one different candidate beated by everyone weakly) is no longer a problem here.

From the axiomatic point of view, this rule is (1) Condorcet-consistent, (2) monotone, (3) if clones are allies, then it is also cloneproof, (4) even if allies are not clones, they have an absolute guarantee that they will not be spoilers to each other. The last fact allows them to 100% safely opt out of primaries, which is a common false claim e.g., in case of IRV (consider the motivating example from the linked paper).

What do you think about the method? I'd love to hear any feedback from you, especially if you can find some disadvantages or things that need further study.

.................................................................
Ad. *) Expecially if we don't care too much about strategy-oriented variants of Maximin like MMPO. Although the described method can be joined with different ways to measure the score, I believe the following one is the simplest to explain: look at the percentage results of each candidate in the matchups (ignoring their turnout) and take the worst. So if if Ann wins against Bob 54% to 46%, loses with Carol 49% to 51%, and loses with Denis 47% to 53%, then the score of Ann is 47%. The higher score, the better, e.g., score above 50% means that all the matchups were won.

@toby-pereira that's correct. And I believe that if this teaming is honest (the candidates are actually similar and don't want to spoil each other) then it is not the problem. Note that under standard (not spoiler-proof) voting rules, one of the candidates in the cycle could just quit the election, allowing the other candidate to win. We get rid of such strategic considerations here.

On the other hand, dishonest teaming shouldn't happen, since it is only profitable for the candidate who wins, not for the ones who lose nevertheless. Besides, in close battles, the very fact of dishonest teaming can outrage the voters (especially the supporters of the still losing candidate) and affect their preferences enough to change the whole situation.

@jack-waugh they'd probably have to decide which issues are the most important to them. But in real life they still have to make such decisions (e.g. by deciding if they want to be in the same party or not).
In general, as I replied above, even if the candidates fail to form a good alliance, most of the time this won't matter since the rule will just elect the Condorcet winner.

@toby-pereira sure, that's a reasonable doubt. I'll respond in three ways:
(1) In section 5 of our paper we perform experiments to check whether our rules decrease the total social welfare of the voters (measured by Borda scores - I believe that any other measure would yield similar results). This is not the case, so we do not sacrifice the voters' satisfaction by taking parties into account.
(2) The rule I described in the post is Condorcet-consistent, so over 90% of time when the voters' ballots clearly indicate the winner, alliances do not matter. They start to matter only if there are cycles, which means that no candidate has a clear support from the voters.
(3) Besides, this rule cannot elect weak candidates only because they are from the winning alliance. E.g. if there is a candidate who'd be Condorcet winner if they are the only nominate of their party, they'll be the winner.

@lime Yes - I agree that your method is a significant improvement of STAR.

However, a separate discussion to me is which voting rule should be recommended for ranked ballots. I feel that this is important because ranked ballots are cognitively easier for the voters and easier to promote in places that currently use IRV. With my rule, you could say to a city council: "Look, you don't need to change the ballots. It means that (1) switching from IRV to our method will not be too expensive, (2) there is no risk that voters will be confused, they will just vote as they are used to."

Hi everyone,

Let me share with you my recent paper on single-winner elections. We propose here a few simple methods with good spoiler-proof properties. Let me describe one of them which I personally like the most (SW-Maximin in the paper). Basically, this is a Maximin with a simple twist:

• before the election, a group of candidates sharing similar views (e.g., from the same party) can register as "allies", who do not want to hurt one another in favor of other candidates,

• voters vote using ranked ballots. We perform head-to-head pairwise comparisons and compute the Maximin score of each candidate (worst performance in the matchups).

• the twist is that we do not compare allies to each other. Only if there are multiple allies who defeated all their opponents, we remove the remaining candidates, compare the finalists to each other and update their scores.

• the candidate with the highest score wins.

I believe this twist should be very natural and easy-to-understand to people (it's clear that two similar candidates should first fight against their common enemies, and only then against each other). Besides, Maximin is a very easy rule to explain by itself*.

On the other hand, the "bad example" commonly pointed out for Maximin (three similar candidates beating each other strongly, one different candidate beated by everyone weakly) is no longer a problem here.

From the axiomatic point of view, this rule is (1) Condorcet-consistent, (2) monotone, (3) if clones are allies, then it is also cloneproof, (4) even if allies are not clones, they have an absolute guarantee that they will not be spoilers to each other. The last fact allows them to 100% safely opt out of primaries, which is a common false claim e.g., in case of IRV (consider the motivating example from the linked paper).

What do you think about the method? I'd love to hear any feedback from you, especially if you can find some disadvantages or things that need further study.

.................................................................
Ad. *) Expecially if we don't care too much about strategy-oriented variants of Maximin like MMPO. Although the described method can be joined with different ways to measure the score, I believe the following one is the simplest to explain: look at the percentage results of each candidate in the matchups (ignoring their turnout) and take the worst. So if if Ann wins against Bob 54% to 46%, loses with Carol 49% to 51%, and loses with Denis 47% to 53%, then the score of Ann is 47%. The higher score, the better, e.g., score above 50% means that all the matchups were won.