[EM] The rationale under the "winning votes" defeat strength measure

[Kevin Venzke]

Hi Grzegorz,

> Thanks for all your comments, axioms and explanations! From what I see, the
> justification of WV is indeed rather pragmatic and strategy-oriented, which is
> quite a problem for me. I would really prefer to avoid answering the question:
> "Why did your rule elect a bad candidate in this election?" by saying "Well,
> because you might have been dishonest in some specific way, and then this
> candidate wouldn't be so bad". I also agree with Juho that "in large public
> real life Condorcet elections it is very difficult to implement and coordinate
> successful malicious strategies".

I would point out that in my discussion I never said anything about malicious
strategies. My /check webpage doesn't either. The strategies I talk about are
favorite betrayal, which are not malicious strategies, but strategies where
voters are trying to compensate for a method not working well enough.

I think this is a mistake in how WV is often defended. It's true that if you
take care to minimize compromise incentive (which is, I think, what WV wants to
do; and actually, I dare say, it's what Condorcet wants to do) then this can be
useful in stopping other voters from carrying out a scheme. But this isn't the
*goal* of minimizing compromise incentive.

> For example, the second example of Chris rather convinces me to support margins
> and oppose WV, than the other way around. Let's see:
> 46: A
> 44: B>C
> 10: C
> WV elect C here, while margins elect B. In fact, if the above preferences are
> honest, then B is clearly the best candidate, since he is the closest to be the
> Condorcet winner. Electing A or (especially) C would be extremely unstable - if
> just one voter changes his preference from A to B, the result would switch to B
> under any Condorcet rule. Moreover, B has much broader support than C (assuming
> that A's supporters are truly indifferent between both). I really can't find a
> logical justification of electing C here if the voters are honest.

Alright, but I think it would be very strange if these were honest votes in a
public election. I look at that, as a real election, and suspect a similarity
between candidates B and C, and that the A voters dislike both and don't want to
risk helping either against the other.

(You could say I'm assuming the incentives are as under WV, but I think we've
seen that even IRV voters truncate like this.)

> On the other hand, if we assume that voters were strategic and the honest
> opinion of the middle voters is B or B>A, then it means that a massive number
> of voters colluded to vote strategically, in a situation where (1) the result
> of the race between A and B was unpredictable before the election and B had
> real chances to win anyway, (2) a lot of voters had a fragile preference of
> either B=A or B=C, and such a "dirty" operation of B could easily change their
> minds to (respectively) A>B and C>B. I just don't see this happening in
> practice. I can agree that such a theoretical possibility is bad, because
> violating strategyproofness generally is bad, but there's nothing particularly
> worrisome for me here.

For me this is a strange example. If you plug it into /check, there is no
compromise incentive issue with electing B. Rather, you're defending a failure
of the Plurality criterion. Typically such scenarios aren't used to speculate
about malicious strategy potential. Tentatively I'd agree that it's not
"worrisome" in that way.

Kevin
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