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

[Forest Simmons]

Great summary!

Update on Hamiltonian MonteCarlo (HMC) that Da will and I were considering
... it is more adapted to sampling constant energy states.

Putting aside the HMC/ergodicity idea for now, we can still use the
"electo-potential" idea for finding different kinds of equilibria...
depending on which L_p norm is understood in the steepest descent equation

dr/dt=-grad V(r),

Where the "electo-potental" V(r) is defined as

V(r)=Sum(over voter positions R) of the product  ||R-r||f(R), where f(R) is
the fraction of the voters concentrated at R.

It looks like the L_1 norm is most suitable for an issue space in the form
of a Cartesian product of issue axes.

Also argmin{||gradV at k|| : k in K}, where K is the set of candidates,
seems to be a previously unknown Smith efficient election method.

It should be highly manipulation resistant because the norm of grad V at k
is possibly the best measure of the combined voter pull on candidate k away
from its position in "electo-space".

El sáb., 29 de ene. de 2022 5:35 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> 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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20220129/9569206e/attachment.html>