New voting method? What is 'minmax-TD'?

masiarek

My brain melts when reading this article: Are Condorcet and Minimax Voting Systems the Best? by Richard B. Darlington:
https://arxiv.org/pdf/1807.01366.pdf

What is 'minmax-TD' and how does it compare to STAR Voting?
Are the conclusions correct in this article?

thank you
adam
https://arxiv.org/pdf/1807.01366 - current version: [v10] Mon, 9 May 2022 13:44:20 UTC (506 KB)

rob

@masiarek It's a good article.

Minimax TD is defined in the article as such:

TD differs from other versions of minimax in three main ways. First, it uses Smith/minimax, as recommended to me by Nicolaus Tideman. The Smith set is the smallest set of candidates in which every candidate in the set beats every candidate outside the set in a majority-rules two-way race. TD picks its winner from within the Smith set. That set is easy to identify, because every member of the Smith set wins more two-way races than anyone outside the set. Thus, you can start with an empty set, rank the candidates by the number of races they won, and add candidates to the set in that order until everyone in the set beats everyone outside.
TD’s second difference from other versions of minimax is that it defines candidate X’s value of LL as X’s largest margin of loss. Other versions of minimax define LL as the largest number of voters who voted against X in any race which X lost, or as the largest number who voted against X in any race at all. Section 7 explains why I prefer the definition using margins. TD’s third difference is a new tie-breaking system for minimax which is simple and intuitively reasonable, breaks nearly all ties, and is shown by and is shown by simulations to pick better winners than random tie-breakers.

I like minimax for its simplicity, and for the fact that it should be precinct summable since the winner can be determined solely from a pairwise matrix. I'm not 100% sure this variation is precinct summable, I haven't given it enough thought.

Regardless I think the article gets a lot of things right. I definitely agree with regard to its complaints about score and approval. Specifically with regard to approval, voting seems simple at first blush, but it really isn't -- at least not for those voters who think with nuance and consider strategy -- because of all the work the voter needs to do to best pick an approval threshold (which of course benefits from knowing who the front runners are). It also notes the problem with score, which in addition to the above issue, also has the problem that it doesn't necessarily reduce down to electing the majority winner of a two-way race.

The main thing I think it gets wrong is that it doesn't really account for the diminishing returns on increasing complexity. I doubt that the added complexity of minimax TD over minimax is worth it, when considering issues such as "likelihood of being adopted." In that sense, I think the article is subject to inventor's bias. The "D" in "TD" is for Darlington, the author of the article, and I think he over-values the improvements he adds to standard minimax.

One thing I think every new method should do is write sample legislation to enact it. The shorter and simpler the wording, the better. (complexity can be measured a lot of ways of course: amount of code to implement it, amount of computation, amount of words to explain it, how complex would visualizations of a single election be, etc)

Jack Waugh

@rob said in New voting method? What is 'minmax-TD'?:

approval threshold

Again, I doubt whether the threshold technique is correct. Insufficient granularity.

rob

@jack-waugh said in New voting method? What is 'minmax-TD'?:

Again, I doubt whether the threshold technique is correct. Insufficient granularity.

What specific technique are you speaking of? This is what the article says about approval threshold. Is there something in particular they got wrong?

But approval ballots may make voting easier than ranked-choice ballots for the least-informed voters but more difficult for better-informed ones. If a voter ranks the candidates ABCD, the approval ballot forces them to also choose where to draw the line between “approved” and “unapproved” candidates. To do this rationally, the voter should consider whether the difference in merit between A and B exceeds that between B and C or between C and D. And for maximum impact a voter will also want to draw their line between the two candidates most likely to receive the most approvals from other voters, and therefore must guess who those two are. Thus a voter using an approval ballot must make three types of judgment not needed in a ranked-choice ballot. First, they must assess the relative sizes of differences in merit between various pairs of candidates. Second, they must guess which candidates are most likely to win. Third, they must decide how to combine these two judgments into a final ballot choice

Honestly, the technique described is actually simpler than what can happen in reality. Basically, the article was too kind.

It can be a more complex decision if it isn't crystal clear who the two front runners are... then you bring in probabilities and use them to weigh against how strongly you feel about the merits of each candidate. Of course, I'd expect that typical people, who have been using approval for a while, will intuitively make this sort of calculus, and not many are going to explicitly try to work out the math.

Regardless I'm not sure what technique you are referring to.

Jack Waugh

@rob I am talking in general about using a threshold for deciding an Approval vote.

Instead, I think the optimal technique involves these steps:

Decide your tactical/strategic vote as though the voting system were continuous Score. This entails exaggerating your support for your lesser-evil candidate to almost, but not quite, equal to your support for your favorite(s). The gap depends on how popular you think your favorite is with the other voters.
Use a relative-frequency strategy to simulate continuous Score using coarse Score (which is what Approval is).

Your "faction" consists of the people who have the same values as you have toward the candidates. You might not know the other members and the faction might not be organized. However, there is a way that each individual member can behave that will result in aggregate behavior that sets the average score from the faction equal to the value determined by decision sub-procedure #1 above. This involves obtaining a random number and using it to decide whether you are rounding up or rounding down. You can do this at home, before proceeding to the voting place.

multi_system_fan

@rob you say "The main thing I think it gets wrong is that it doesn't really account for the diminishing returns on increasing complexity. I doubt that the added complexity of minimax TD over minimax is worth it, when considering issues such as "likelihood of being adopted."
I have to disagree completely. I'm convinced :

"rare complexity" does not interest or worry voters.
"rare complexity" does not interest politicians if experts explain to them its rare, fair and not worthy of a political fight for different voting rules.
So my conclusion: minimax-TD has to become my newest favorite

rob

@multi_system_fan Ok, well I think the method is fine, but I am not convinced that no one cares about such details. They may be rare, but the details have to be put into legislation, and anywhere that the method is explained needs to explain the whole thing. So I think it is a barrier to getting it implemented if you can't describe it in a few sentences.

That's not to say that I couldn't be convinced that this method is so much better than the simpler one, that it's worth it. Maybe it is. Maybe the complexity isn't really that much.

But I certainly don't agree with just outright dismissing the potential for complexity creating a barrier to adoption.

multi_system_fan

@rob you could be right for certain contexts like a state in the US. But I live in The Netherlands and often in these forums many assumptions are made without being aware of them.
for instance:

complexity stemming from incompatible vote counting machines...in NL no vote counting machines are used so this is not relevant
political and legal worries: In NL it is not possible for citizens to propose a law, let alone the wording of it. This happens by nonpolitical civil servants in talks with goverment. Many very complex texts become law with minor discussions. Some details may not even have to become law but can be decided by ministers or other functions.
the current voting rules in NL have some complex details that almost no-one knows and have never been in mainstream discussions.

rob

@multi_system_fan Ok well I don't know about The Netherlands, I'm speaking mostly of the US. There is obviously a lot of distrust here toward anything voting related, with conspiracy theories and the like. Complexity could play into that.

multi_system_fan

@rob I understand this problem, altough I doubt simplicity of voting methods or rationality in general will prevent this.
I'm interested in electionguard software combined with a paper-printed ballot of each vote and the possibility of online checking wheather one's (still anonymous!!) vote is actually tallied. But in this case I do see a similar problem. It's designed to enhance trust but many people would probably distrust everything. For instance because of some connection to Bill Gates.

rob

@multi_system_fan said in New voting method? What is 'minmax-TD'?:

I understand this problem, altough I doubt simplicity of voting methods or rationality in general will prevent this.

It won't prevent it, but it would help in terms of adoption when there is already resistance coming from people who think they'd lose power if such a system is enacted.

But yeah, from what I know of the political system of The Netherlands, all of this should be a lot easier there. I envy you.