[EM] Condorcet system, or Condorcet efficiency? (was:... wrt Burlington et al.)

[Kristofer Munsterhjelm]

Jameson Quinn wrote:
> 
> 
> 2011/11/29 robert bristow-johnson <rbj at audioimagination.com 
> <mailto:rbj at audioimagination.com>>
> 
> 
>     IRV, with its kabuki dance of transferred votes, is more complicated
>     than Condorcet.  when i was asked by one of the leaders in this town
>     of the anti-IRV movement to explain Condorcet simply (since that was
>     most of their case against IRV - most of their signs said "Keep
>     Voting Simple"), i answered "If more voters agree that Candidate A
>     is a better choice for office than Candidate B, then Candidate B is
>     not elected."  pretty simple and hard to argue with.
> 
> 
> This is a good description. However, it still conflicts with most 
> people's mental paradigm for how an election works, and so it seems more 
> complex than it is. Most people think an election is something like this:
> 
> 1. People vote.
> 2. Those votes are translated into a score for each candidate.
> 3. The best score wins.
> 
> Plurality, Borda, Majority Judgment, Approval, and Range all fit that 
> paradigm. (That's why people are so prone to reinventing Borda.) Even 
> IRV and SODA can be shoehorned in, though it's a stretch. But Condorcet 
> depends on a matrix, not a list of scores; and that just doesn't fit 
> inside people's heads.

If IRV can be stretched to fit that, then surely the Smith-Approval 
method we gave to Clinton Mead would also fit. "Rank the candidates in 
order of how many voters explicitly ranked them on their ballots. Take 
the two candidates closest to losing, and consider them free of the 
other candidates' interference: eliminate the one who is preferred to 
the other less often than the other is preferred to him. Keep 
eliminating until you have a single winner".

If you want to coat it appropriately, you could probably phrase it in 
terms of a duel between the losers, a saving chance at being redeemed 
from elimination, something like that.

Or Minmax: "Each candidate's score is the number of votes he'd get in 
the second round of a runoff against the rival who'd have the strongest 
showing against him. The candidate with the greatest score is strongest 
even at his weakest, so he should win". That one is a little more 
matrix-y, but it still only implicitly mentions it.

> I agree absolutely. That's why I think Range is not nearly as good as 
> Bayesian Regret would lead us to think. So, how much does each system 
> burden voters with the need to strategize, and how much does it punish 
> them for not strategizing?

I wonder if that could be simulated. I seem to recall reading a paper 
that showed that methods that are monotone can be very easily 
manipulated when there exists some sort of strategy that can make one of 
exactly two candidates win. That is, it can find such a strategy in 
polytime if there is one.

Given such a quick strategy-finding algorithm, one could then let only 
one side strategize, and see if that would make the method shift the 
winner. Then one could compare the simulated utility for the candidate 
that wins under one-sided strategy to the one that wins under no 
strategy. Good rules would tend to permit only "relatively good" 
candidates to win through strategy, compared to what you'd get under 
honesty.

It wouldn't be perfect, of course. The strategy might be very complex to 
pull of in practice, and it wouldn't cover the cases where there are 
multiple candidates that can be made to win through strategy.