[EM] [CES #3852] condorcet & range voting -- which one yields more condorcet winners?

[Jameson Quinn]

2011/10/12 Clay Shentrup <clay at electology.org>

> On Wednesday, October 12, 2011 11:16:52 AM UTC-7, Jameson Quinn wrote:
>>
>> Warren and I had a long technical discussion about strategy incentive in
>> MJ versus range. He did some clever calculations, and I picked holes in
>> them, and we repeated it for several rounds. At the end we hadn't quite
>> completely converged on a consensus, but we both agreed that Range had a
>> greater strategy incentive than MJ. That result seems more robust than a
>> bald assertion from you.
>>
>
> I *think* you're confused. I presume that what you were talking about was
> how often strategy makes a difference, or how much of a difference it makes
> on average. I *don't* believe this changes the ideal strategy one iota.
> You give any candidate you like better than the expected value a max score,
> and others a min score.
>
> This should be *reeeally* obvious. If you think X=7, Y=3, and the scores
> are X={9, 7, 0}, Y={8, 8, 3}, then you vote X=10, Y=0. Now the scores are
> X={10, 9, 0}, Y={8, 8, 0}. X wins. I.e. you just polarize, so that you may
> get lucky enough to have your otherwise median score move the median up or
> down.
>

This is true. But as the argued below, you can be essentially arbitrarily
certain of getting the same result, if you vote outside a certain band. For
instance, X=9, Y=1 would get you 99% certainty, and X=8, Y=2 would get you
90% certainty, and your honest X=7 Y=3 would get you 70% certainty. (These
are arbitrary numbers; in real life, they'd be based on historical scores of
the top two candidates)

>
>
>>  The point is, even with zero information on a particular candidate, you
>> have a pretty good historical benchmark for the median scores of the first
>> and second place candidates. Outside of that range, you have a safe leeway
>> to be honest.
>>
>
> This is a flawed argument. You're saying it's very improbable that the
> scores will exceed those historical norms, so you should take the tiny risk
> of casting a weak vote, for the sake of honesty/expressiveness. But with
> ordinary Score Voting, there's an incredibly tiny probability that your vote
> will make a difference, so you might as well be honest. This is
> statistically equivalent.
>

Not comparable at all. In any voting system at all, your chances of being
decisive are epsilon. In this case, your chances of even having any impact
at all on the margin of victory are epsilon. The chance of that impact then
being decisive are epsilon squared. Separate issues.


>
>
>> And it seems that MJ reacts much worse to such plausible behaviors.
>>>
>>
>> ??? What are you even talking about? If everyone exaggerates, MJ and range
>> are identical; they're both approval. And if a fixed X% of voters
>> exaggerate, it has a bigger effect on Range than MJ; that's an implication
>> Warren's result that I mentioned above. So you're 180 degrees wrong here.
>>
>
> If most (but not all) exaggerate, then you can get very weird results like
> Warren describes here.
> http://scorevoting.net/MedianVrange.html
>

Are you talking about the bimodal distribution stuff at the bottom? That's
an issue when one candidate is exaggerated but others aren't. But if some
voters exaggerate across the board, it is at worst as bad as approval. It
degrades to approval less smoothly than range - that is, the effect of
exaggeration is smaller if few people exaggerate, and larger if many people
exaggerate. I believe that that's superior, because it makes
all-honest-voting into a more stable state (actually an equilibrium under
certain plausible assumptions, but even if not an equilibrium, still more
stable than Range).


>
> I speculate that you may be misunderstanding Warren's result. But it would
> be nice to see Warren's result instead of speculating. Could someone post it
> here or add it to the page?
>

http://scorevoting.net/MedianAvg1side.html

>
> Oh, and aside from calculations of how often strategies work and such, did
> Warren ever get actual BR figures for MJ?
>

I don't know.

JQ
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