[EM] Copeland//Plurality --- can it beat IRV?

[Kristofer Munsterhjelm]

On 28.01.2022 13:53, Toby Pereira wrote:
> I think the problem with these long threads is that there are rarely
> concluding thoughts at the end, so unless you're following very closely,
> you might miss the best stuff. Understandably people post stuff as it
> comes to them, so you get people's "stream of consciousness", but I
> think it would be good if, once a discussion is dying down, the main
> contributors then posted a summary of their overall thoughts and
> findings, and which things they would take forward.

That's a good idea, though I guess in some cases it could get a bit
difficult to determine when a conversation is over :-)

But for my threads, the exact spatial model one was discussing how we
could get a better approximation of the probability that a random
election in say a (10 voters, 4 candidates, 3 issues) spatial model will
be a particular given election. This would be useful for constructing
optimal strategically resistant methods in spatial models, and optimal
methods trading off between unmanipulability and VSE.

But unfortunately doing so seems to require determining a Voronoi map
for each instance of the spatial model (with candidates fixed); in
essence integrating over area of the intersection of some Voronoi
regions, over every possible position of the candidates in issue space.
Which looked pretty daunting to me, so I thought that the best we could
do is sampling the volume of the region with candidates fixed, and then
integrating that.

Then Daniel and Forest discussed ways to estimate this (I think? Or to
exactly evaluate something close to what I'm looking for), but my diff
eq skills are not nearly up to the task of following them.

There was also another thread where I was trying to extend my fpA-fpC
method to more than three candidates by making use of a recursive notion
inspired by IRV. I found a more elegant phrasing of the three-candidate
version (with a different tiebreaker when there's a pairwise tie), but
nothing conclusive out to four and beyond; though I do think the
recursive approach itself could be useful later. (Off-list I used the
recursive approach to find out that letting A's score be the minimum of
A's score in any three-candidate sub-election is monotone and preserves
DMT -- though it likely doesn't preserve DMTBR.)

And this thread (that I'm replying to) is about Copeland//Plurality and
IRV-flavored Condorcet methods. Forest suggested Minmax-elimination,
i.e. Raynaud. The "gross loser" he's referring to is, I think, by
Benham, which restores Plurality compliance to the method.

-km