[EM] Condorcet Meeting: Narrowing the Field

[Kristofer Munsterhjelm]

I think I'm more or less done with this subject, as I don't feel like 
I'm getting anywhere much. But I will reply to this:

On 9/1/23 17:47, Colin Champion wrote:
> It seems to me that the position is this. Condorcet voting works well 
> under certain assumptions, which include voters sincerely ranking all 
> candidates in order of preference. Strategic voting turns out to be less 
> of a problem than one might fear, but drastic truncation is fatal.
>     The merits of Condorcet voting lie partly in its not penalising 
> minor parties, so you'd expect it to lead to an explosion in the number 
> of candidates.
>     So you're organising a presidential election, hoping to take 
> advantage of the merits of Condorcet voting, and you expect 500 
> candidates to put themselves forward. What do you do?
>     One no-brain solution is to run a Condorcet election with 500 
> candidates. Another is to rely on administrative procedures, eg. only 
> the 5 candidates with most supporting signatures get onto the ballot. 
> This isn't a bad idea; something like it is widely practised. I think 
> the Virginia meeting is intentionally allowing it as an option. Can we 
> do better?

I guess that with numbers around 500, nothing will really work well, and 
that we would bump against the, for lack of a better term, "aristocratic 
nature" of elections. That is, if we don't do anything to counteract it, 
such a field will naturally thin itself out by who's got the best 
marketing; by what candidates are able to amplify their voice and get 
their message out the most, and that undoing this bias will require a 
more thorough redesign than changing the way votes are tallied.

If that's right, then it would seem the only option is to augment the 
electoral procedure itself. Do something like asset voting or have a 
representative sample dig deep into the candidates policies and pick the 
finalist set. For 500 candidates, the voters would otherwise face a 
burden just getting to know what they're about, no matter the voting 
system, and the 100:1 "compression ratio" down to a finalist set of 5 is 
so high that it's very difficult to get the right set if they skip on 
that burden. Any consistent bias will greatly shrink that 500-candidate 
set with time.

If we suppose that all of the 500 have a chance to get into the finalist 
set, there has to be a considerable period before the general happens, 
so that finalist set can inform the electorate of their positions.

The more we consider the possibility that anybody could be a good 
winner, the more elections, as a mechanism, is at a disadvantage from 
the start. My intuitive feeling is that at a 100:1 ratio, if you only 
choose centrists, then the non-centrists are disincentivized as you say. 
If you don't only choose centrists, then there's not enough room for the 
full variety of the 500 to be represented in a set of size 5 anyway. So 
something has to give.

Even if I'm wrong, the contention about clone dependence suggests to me 
that we don't really know how to make a voting system that does what's 
asked of such a primary. In a sense, it's not just that we don't know 
how to solve the puzzle, but we're uncertain what kind of puzzle it is 
(what the desiderata and dynamics are). But you said in another post that

> I posted some figures a while ago indicating that as the level of
> truncation increased, some strange reversals set in just after the
> half-way mark: the Borda count briefly gained in accuracy while
> Condorcet methods started a headlong fall.

This in turn suggests that you could at least determine if a particular 
suggestion would be good by simulating the two-stage process:

- Lots of candidates present themselves
- Voters vote in the primary according to the method to be tested 
(possibly with some noise)
- Then the voters' hypothetical correct no-truncated ranking (of 500 
candidates!) is used as a basis for the general method, but after 
everybody but the finalist set is eliminated.
- Now determine the VSE, strategic resistance, or other figure of 
interest wrt the winner of the general.

Maybe by tinkering with this, it would be possible to get some idea of 
what works and what doesn't. But note that it doesn't incorporate the 
idea that getting acquainted with candidate positions is very expensive 
when there are 500 of them, unless the primary deliberately takes that 
into account.

-km