Does VA Schulze violate SEC?
Markus Schulze
schulze at sol.physik.tu-berlin.de
Tue Oct 6 13:01:01 PDT 1998
Dear Blake,
you wrote (06 Oct 1998):
> On Fri, 02 Oct 1998 20:23:41 Markus Schulze wrote:
> Dear Markus,
> >Dear Blake,
> >
> >you wrote (02 Oct 1998):
> >> I think you're mistaken about Schulze and Tideman because both of
> >> these methods are identical to Condorcet(EM) in the 3 candidate
> >> case. So, if you agree that Condorcet(EM) encourages random-fill
> >> and violates SEC, then the same must be true of Schulze and Tideman
> >> for three candidates. Because your argument would seem to apply
> >> to three candidates examples as well as any others, I have to
> >> conclude that it includes an error. Furthermore, I don't see
> >> why adding additional candidates beyond three would fix these
> >> problems where they exist.
> >
> >I don't agree. For example: When I say, that the Copeland method
> >can be manipulated by cloning candidates, then this means, that
> >you will never have a disadvantage if you present clones and that
> >you will sometimes have an advantage if you present clones.
> >
> What if I proposed a method where clones could sometimes hurt, but
> almost always helped. Wouldn't that encourage more clones too.
> So, to prevent the cloning strategy, it would be necessary either that
> clones had no effect, or that they were as likely to hurt as help.
>
> >But you say, that already if there is only one situation, where
> >an election method can be manipulated using a certain strategy,
> >this election method has this strategical problem.
>
> I intend to prove that the strategy works, not in only one case, but on
> average. Only the average can be proven for Condorcet(EM), but
> you have in the past been willing to conclude it has the problem.
>
> Let me review what I think we agree on:
> 1. In Condorcet(EM), if two candidates are ranked as equal, the
> chance is better that one of them will win, than if they had been
> differentiated. So, voters are encouraged to differentiate candidates
> at the end of the ballot and not at the beginning.
> 2. These strategies can sometimes back-fire, however, on average they
> succeed, and so #1 holds.
> 3. To prove that this is true for Schulze, it is only necessary to
> show this effect on average, not that it will never back-fire.
> 4. Schulze is equivalent to Condorcet (EM) in the 3 candidate example.
> And so will have this effect if there are only 3 candidate.
>
> In fact, because you have said that statement #1 also holds for
> Smith//Condorcet(EM), and because this is equivalent to Schulze
> when there are 3 or fewer candidates in the Smith set, #1 will
> have this effect in cases where the Smith set has 3 or fewer
> members.
>
> You make a strong intuitive case that if we do not consider problems
> of limited Smith set examples, Schulze will not have this effect, but
> neither will it have the opposite effect.
>
> >This is not true. By ranking the less favourite candidates,
> >the worst beat-path from a more favourite candidate to a
> >less favourite candidate could be increased. But it could
> >also happen, that -by ranking the less favourite candidates-
> >the worst beat-path from a less favourite candidate to a
> >more favourite candidate is increased (especially if the
> >worst beat-path from this less favourite candidate to that
> >more favourite candidate contains other less favourite
> >candidates and is limited by the pairwise defeat between
> >two less favourite candidates).
>
> So, since under Schulze, for size 3 Smith set, differentiation
> decreases combined chances, and as the Smith set increases in
> size this has less effect, moving towards equality, and since
> the Smith set could be under size 3, don't we have to conclude
> that on average the strategy will work for Schulze. In the same
> sense that it works for Condorcet(EM).
>
> The only way Schulze could recover from the difference with the
> size 3 Smith set is if higher Smith set size actually experienced
> the opposite effect that could cancel out the effect for the size
> 3 Smith set case.
>
> Note that I am not saying that just because the strategy holds in the
> three candidate example, the strategy holds over all. However, because
> the strategy works well in the three-candidate example, and you yourself
> seem to argue that it is not deterred as you increase the number of
> candidates, I conclude that it works on average.
>
> >You wrote (17 Sep 1998):
> >> Sincere Expectation Standard
> >> Given that a voter has no knowledge about how others will
> >> vote, a sincere vote must be at least as likely as any
> >> insincere vote to give results that are in some way better
> >> in the eyes of the voter.
> >
> >I don't think that this standard is important, because if
> >the voters have no knowledge about how others will vote,
> >then every election method is strategy-proof.
> That's just my point; that isn't true for VA. Of course, it is
> easy to imagine a marginal version of Schulze that wouldn't have
> this problem. That's the system I advocate.
The problem with Condorcet[EM] is the fact, that the random-fill
strategy _always_ works. The random-fill strategy cannot
back-fire. That means: A voter is _never_ punished for using
this strategy, but _sometimes_ rewarded for using this strategy.
I would never have criticized Condorcet[EM], if the random-fill
strategy had worked only on average.
[Random-fill strategy means: Even if you don't have different
opinions about your least favourite candidates, give different
ranking to your least favourite candidates.
The random-fill strategy always works, because the worst defeats
of your least favourite candidates _sometimes_ increase but
_never_ decrease, if you rank these candidates differently.]
Markus Schulze
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