[EM] DH3 and honest Condorcet winners

Kristofer Munsterhjelm km_elmet at t-online.de
Sun Jul 18 09:21:29 PDT 2021

On 18.07.2021 18:05, Daniel Carrera wrote:
> On Sun, Jul 18, 2021 at 3:59 AM Kristofer Munsterhjelm
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
>     But in practice, if you're aiming for a particular Condorcet method...
>     any Condorcet is better than no Condorcet! (Well, pathological methods
>     notwithstanding.)
> I'm learning a lot from this discussion. Here's my question: do you
> count Copeland as a pathological method? I quite liked Copeland when I
> first learned about it but I quickly realized that it frequently
> produces times, and then later I learned about the clones issue. I think
> Copeland (especially if there's a runoff to resolve ties) is probably
> superior to any non-Condorcet method I've heard of including STAR and
> approval, but I'd like to to hear from someone that understands voting
> methods better than I do.

Because it produces ties so often, I consider it more a set than a
method. Thus it needs a tiebreaker, or a method that elects from the
Copeland set according to some unified logic.

The Copeland set has some nice game theory properties, as it's an easy
to compute subset of the uncovered set. But any method that elects from
it will inherit its clone problems. My numerical experiments with
Copland also shows that it's not particularly robust to worst-case strategy.

So, yes, if the choice is between something that elects from the
Copeland set and something that doesn't satisfy Condorcet at all, I'll
pick the former.

But if I were proposing a method, I would instead choose either
something like Ranked Pairs (to make it absolutely clear there's no
clone problem) or Smith-IRV (to be directly robust to strategy instead
of having to rely on possible game theory arguments).

(By not being particularly robust to worst-case strategy I mean that if
A wins, there often exists a strategy for voters who prefer some B to A
can use to make B win instead. It might well be that the strategy is
unstable in the sense that voters who prefer A can defensively employ
strategy so that any attempted strategy by B-voters make C win instead.
My analysis can't detect that kind of defense - it assumes the first
election is honest. But when arguing that a method is robust to
strategy, it's easier to just say "under impartial culture, B voters can
only make B win 10% of the time" than to argue that there exist moves
and countermoves that neutralize the strategy in an equilibrium.)


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