[EM] Method Y

[Kristofer Munsterhjelm]

On 8/4/23 14:36, Forest Simmons wrote:
> For now this is is a manual Plurality runoff method:
> 
> At each runoff stage let Y be the candidate with the fewest votes.
> 
> Then by majority decision either eliminate Y or else elect Y by 
> eliminating all other candidates.
> 
> That's it.
> 
> Note that majority decision by rational informed voters will never 
> eliminate Y when it is the sincere CW of the remaining candidates.
> 
> Very simple, but monotonic, and burial resistant ... not to mention 
> strongly Condorcet efficient.

I think this would only be monotone in a "manual DSV" sense where the 
honest ballots are common knowledge.

The simplest IRV monotonicity case is where we have an ABCA cycle and 
some BAC ballots become ABC ballots, then C survives to the final round 
and beats A pairwise because B lost enough votes to be pushed down to 
third place.

If we have manual DSV, then in the first round, A's supporters would 
coordinate and decide that they're going to "donate" some first 
preferences to B so as to push C down to third place, then in the final, 
a majority (sincerely) indicates it prefers A to B, hence A wins.

But to me, that's kind of like the proof that a Condorcet winner is a 
Nash equilibrium under Approval: it requires too much coordination. 
Perhaps in a legislature, but in a public election, I wouldn't think 
this would be monotone.

It might be possible to make it more strongly monotone by doing all the 
manual DSV automatically, like a refinement of my "Contingent vote with 
donation" method. The calculations could become rather hairy, though, 
for more than three candidates.

But the idea that a majority will sincerely say "yes" when the CW 
appears is good! Perhaps something revelation principle based could be 
used to lessen the demands on the voters' calculation ability and the 
degree to which the honest ballot set needs to be common knowledge.

> In fact, it could accurately be called Sincere Benham (pending 
> permission from Chris) because if there is a sincere CW at any stage, 
> optimal strategy requires informed rational voters to elect it ... while 
> if only Y is eliminated at each stage, the ordinary Plurality runoff 
> candidate wins.
> 
> Note that since the sincere CW wins whenever there is one, there can be 
> no burial of a sincere CW ... which is the only kind of burial that 
> concerns us.
> 
> The main drawback is the potentially large number of manual votes required.
> 
> Is there a DSV version that gets around this problem?
> 
> Quickly finding the Smith set by some elegant manual method would 
> largely solve the problem for many deliberative assemblies including 
> parliaments, senates, summits, etc.
> 
> A Coombs version of this method is equally burial resistant, monotone, 
> Condorcet efficient, etc, while more decisive... less likely to tie for Y.

Antiplurality isn't burial resistant, so I wouldn't imagine this to be 
either - in a Condorcet cycle, at least.

Consider a "fixed Benham" version of the above, with some election 
method being used to set the elimination order, then we go from lowest 
ranked to highest, asking "elect or eliminate".

If there is an honest CW then any ordering will work: for every other 
candidate A that's checked before the honest CW, a majority will know 
that if they hold out for longer, they can say "yes" for the honest CW 
and then he wins.

If there's an honest cycle, then all bets are off. The benefit of using 
interleaved Plurality over something like (fixed or interleaved) Ranked 
Pairs or Antiplurality is that if there is an honest cycle, then you 
have some measure of burial resistance. It won't be perfect, as you 
can't have that and retain Condorcet, but you'll have some protection.

Just what amount of resistance you'll have depends on the original 
method, I think. Your initial suggestion is Benham; so there should be 
some kind of DMTBR analog - something like, if there's an honest cycle, 
then nobody who prefers a candidate outside the DMT set can benefit by 
behaving like they prefer some third candidate to the candidate who 
would otherwise win, when they do not actually prefer this third candidate.

I think. I'm not *entirely* sure.

-km