Stable voting

rob

In the Quadratic voting thread, @brozai said:

regarding Condorcet methods, some professors I've been in contact with did a series of three works on the methods "Split Cycle" and "Stable Voting" you may like to read.

https://arxiv.org/abs/2004.02350
https://arxiv.org/abs/2008.08451
https://arxiv.org/abs/2108.00542

Below I responded (and moved them to this new thread)

rob

@brozai I like most of what they say in the Stable voting one, except that I think their new method is probably not necessary and probably is far less feasible in the real world in terms of it actually being adopted. (compared to certain existing methods)

I thought this was interesting in their intro (emphasis mine):

As of July 2021, the Ranked Choice Voting Election Database maintained by FairVote2 contains 149 IRV elections from the United States for which the existence of a Condorcet winner can be determined from public data; and in every election, there was a Condorcet winner. Thus, in all of these elections, a Condorcet method would settle the election simply by the identification of
the Condorcet winner, rather than the many rounds of iterative elimination of candidates and transferring of votes involved in some complicated IRV calculations. Moreover, in all but one of the elections, IRV chose the Condorcet winner anyway. Indeed, proponents of IRV claim that one of its advantages is that it almost always selects the Condorcet winner. The one case in the database in which IRV did not elect the Condorcet winner — the 2009 Mayoral Election in Burlington, Vermont, discussed below — was a source of controversy. All of this raises the question: why not always simply elect the Condorcet winner?

They go on to describe their method which does indeed "simply elect the Condorcet winner," if there is one.

But it is a fairly complex method they propose, and it would need to be described in legislation. To get a new voting system approved and implemented, lots of people need to understand the wording of the legislation, or, as is the case with IRV, simply be confident that similar wording in other places has been tried and tested and seems to work.

So I wonder why not simply elect the Condorcet winner if one exists, and fall back on IRV if not. (i.e. Bentham) Notice that in every single one of those 149 IRV elections, it would not have had to fall back on IRV, since there was a Condorcet winner in all of them. And if it did fall back on IRV, well..... what is the big problem with that? It would have to be an extremely tight election anyway, and IRV has been used enough that people can be confident in it.

Since people already are comfortable with IRV and there is existing legislation and a history of usage that can be studied, that's a good start. And since saying "first pick the Condorcet winner if they exist" is quite easy to wrap your head around and see the benefits of, there is no big barrier there either. (admittedly they probably need to word that in the legislation a bit differently)

So yeah, that is what I take away from that article. Condorcet is good. And we don't need to propose something really complex with a bunch of uncertainties to get it implemented.

@rob Yes it is quite a complex method. The problem of determining a Stable Voting winner is likely outside P (and NP, for that matter). Nonetheless, it has some great theoretical properties.

I agree it is probably too intricate for the average voter to accept when compared to any of the much simpler condorcet methods like minimax, btr, coombs', benham's, etc.

However I think it's still useful to study such methods, as you never know how voters' moods will change, and maybe a simpler method like one I listed can act as a stepping stone towards a more complex one.

As far as deterministic methods (on ranked ballots) go, I have not seen any with more attractive theoretical properties than Stable Voting. Another fun read if you invite randomness into the electoral process is this proposal by Rivest: https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/rivest.pdf

Although perhaps these topics deserve their own thread, I seem to have derailed the discussion away from quadratic voting

rob

However I think it's still useful to study such methods, as you never know how voters' moods will change, and maybe a simpler method like one I listed can act as a stepping stone towards a more complex one.

Yeah, I'm ok with that. There's certainly nothing wrong with studying them, and it seems to be a good method if complexity isn't an issue.

And I totally understand why they published it the way they did. If all they did was provide a reason to switch to a better existing method, well.... that would be a pretty lame academic paper.

I just felt that their lead up was very good, they called out two real problems with IRV, then suggest that there are only two options:

we must consider which of the following approaches is preferable:
(1) deciding almost every election in a simple way—just elect the Condorcet winner—and rarely applying a more complicated backup plan, perhaps more complicated than IRV, or
(2) deciding many elections with a fairly complicated iterative elimination of candidates and transferring of votes, which may cause controversy when failing to elect a candidate who beats every other?

Without mentioning a third:
3) deciding almost every election in a simple way—just elect the Condorcet winner—and rarely applying the tried and tested IRV method

I should add, there are two kinds of complexity. IRV is complex in that it goes through this messy process which seems to delay election results (presumably because of its lack of precinct summability? I mean, computers are fast so that alone shouldn't be an issue. )

But IRV is easy enough to explain, and it has already been put into legislation, so all you have to do is copy and paste from, say, San Francisco's law.

The other kind of complexity is what we have with Stable Voting. It is recursive and seems pretty hard to explain, especially in a way that can be put into legal code.