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

[Jameson Quinn]

One other bad mistake I noticed on http://scorevoting.net/MedianVrange.html
:
"Suppose this *"unhappy with all choices" scenario* happens. When it does,
every candidate's median score will be exactly zero. (In contrast: Their *
average* scores will generally be distinct nonzero values, and everything
will be fine.) Hence Balinski & Laraki's tiebreaking procedure will be
invoked. It will elect the candidate with the fewest 0s, which is exactly
antiPlurality <http://scorevoting.net/Glossary.html#antipl> voting."

This is not antiplurality voting, it's just approval voting, with any
non-zero value representing approval, and the additional assumption that no
candidate has a majority of approval. It's a bad situation, with voters who
overall dislike all candidates, but it's not the worst voting system to
handle the situation.

JQ

2011/10/12 Jameson Quinn <jameson.quinn at gmail.com>

>
>
> 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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