[EM] New Criterion (typo at end of previous message)
Forest Simmons
fsimmons at pcc.edu
Wed May 21 17:40:04 PDT 2014
That last A faction should have been 45 A>B instead of 41 A>B.
On Wed, May 21, 2014 at 5:24 PM, Forest Simmons <fsimmons at pcc.edu> wrote:
>
>
>
>
> Date: Wed, 21 May 2014 19:19:21 +0930
>>
>> From: "C.Benham" <cbenham at adam.com.au>
>> To: election-methods at lists.electorama.com
>> Subject: Re: [EM] New Criterion
>> Message-ID: <537C76A1.60105 at adam.com.au>
>>
>> Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"
>>
>> > "for Benham, what if we count fractional (for equal rank top) as you
>> > suggest when doing the IRV eliminations, but check at each step for a
>> > pairwise beats all candidate in the usual way?"
>>
>> Forest, That wouldn't be too bad. But it seems to me that it would
>> make Pushover strategizing less risky (than not allowing above-bottom
>> equal-rankings) and since the method
>> fails FBC I didn't see sufficient justification for the extra complexity.
>>
>>
>> > "In your example below, since B beats A pairwise 31 to zero and B
>> > beats C 65 to 35, no IRV elimination step is required, so how equal
>> > rank top is counted in this example does not seem to matter."
>>
>> Yes, Benham has less of a Pushover vulnerability problem than IRV. I
>> don't understand your other question. Benham only checks for a single
>> CW. "Symmetrically completing" pairwise
>> contests can't make any difference to that.
>>
>
> True, symmetric completion wouldn't make any difference but I was
> wondering if perhaps you intended counting 20 A=C as 10 A and 10 C.
>
>>
>> A better example of my suggested way of getting extra "pushover
>> resistance":
>>
>> 04: A=C (sincere is A or A>B)
>> 41 A
>> 28 B>A
>> 27 C>B
>>
>> B>A 55-45, A>C 69-27, C>B 31-28. Top Preferences (erf): A43 >
>> C29 > B28
>>
>> B is the sincere CW (and so also the sincere Benham winner) and the
>> sincere IRV winner. Benham and IRV elect A.
>>
>> My suggested variant looks at the order of candidates according to their
>> TP(erf) scores and on seeing that A is higher in that order than C
>> assigns the whole value of A=C ballots to A
>> (and none of it to C) to give A45 > B28 > C27 (purely for the purpose
>> of the IRV component and not the pairwise component in Benham) and then
>> eliminates C and elects B.
>>
>
> I'm glad that you have found a good way of allowing equal top ranking into
> IRV and Benham, because without the possibility of equal top ranking it
> would (more often) be impossible to find a semi-sincere Nash equilibrium
> that preserved the sincere CW.
>
> In that regard, if the sincere preferences are (according to one of your
> suggestions)
>
> 45 A>B
> 28 B>A
> 27 C>B
>
> wouldn't the following ballot set be a Nash equilibrium (including
> deterrent for pushover) under both fractional and whole rules for equal top?
>
> 41 A>B
>
(should be 45 A>B)
> 28 B>A
> 27 C=B
>
>>
>> Chris Benham
>>
>>
>>
>> On 5/21/2014 9:12 AM, Forest Simmons wrote:
>> > Chris,
>> >
>> > for Benham, what if we count fractional (for equal rank top) as you
>> > suggest when doing the IRV eliminations, but check at each step for a
>> > pairwise beats all candidate in the usual way?
>> >
>> > In your example below, since B beats A pairwise 31 to zero and B beats
>> > C 65 to 35, no IRV elimination step is required, so how equal rank top
>> > is counted in this example does not seem to matter.
>> >
>> > Or is there some reason for doing a "symmetric completion" of equal
>> > rankings for the pairwise contests as well?
>> >
>> > Forest
>>
>
>
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