[EM] New Criterion

C.Benham cbenham at adam.com.au
Tue May 20 11:23:38 PDT 2014


I've been meaning to remind you: for  IRV and  Benham   (and Woodall and 
similar) I'm strongly opposed to allowing voters to do any equal-ranking
apart from truncating because it makes Push-over strategizing much less 
risky and more likely to succeed.

Two versions of ER-IRV have been discussed, one where an A=B ballot 
gives a "whole vote" to each and one where it gives half a vote to each, 
ER-IRV(whole) and  ER-IRV(fractional).   The problem I referred to is 
much worse for the former and so I consider the latter to less bad.

But if we insist on allowing above-bottom equal-ranking and don't mind a 
lot of extra complexity, I have this suggestion:

*Before each elimination, order the candidates according to their 
ER-IRV(fractional), (so that among continuing candidates a ballot that 
ranks n candidates give 1/n of a vote to each).

Then assign each of the ballots that equal-top rank more than one 
candidate to whichever of them is highest in that order.

Then eliminate the candidate with the fewest ballots assigned to hir.*

34 A=B
31 B
35 C

So in this example of Forest's, to create the initial order the 34 A=B 
ballots give half a vote each to A and B, to give the scores
B (31+17=48) > C35 > A17.

B is above A in this order, so all of the A=B ballots are assigned to B. 
This gives the scores B65 > C35 > A0.  A has the lowest score so
A is eliminated and B wins.

Chris  Benham

On 5/20/2014 4:45 AM, Forest Simmons wrote:
> Chris and Mike,
> your combined comments gave me an idea for a more practical version of 
> semi-sincerity:
> A method satisfies Semi-Sincerity Relative to MAM or SS(MAM) if and 
> only if a semi-sincere modification of the sincere preferences leads 
> to a strategic equilibrium ballot set from which the method elects the 
> the sincere MAM winner.
> This criterion recognizes the superiority of MAM under ideal 
> conditions while allowing the method in question to comply with CD, 
> for example.
> Suppose our method is Benham, and sincere votes are
> 34 A>B
> 31 B
> 35 C
> A semi-sincere ballot modification results in a Nash equilibrium for 
> Benham that elects B, the MAM winner of the sincere ballot set (not to 
> mention the modified set).
> 34 A=B
> 31 B
> 35 C
> Forest
>     Date: Sun, 18 May 2014 14:46:30 -0400
>     From: Michael Ossipoff <email9648742 at gmail.com
>     <mailto:email9648742 at gmail.com>>
>     To: cbenham at adam.com.au <mailto:cbenham at adam.com.au>,      
>      "election-methods at electorama.com
>     <mailto:election-methods at electorama.com>"
>             <election-methods at electorama.com
>     <mailto:election-methods at electorama.com>>
>     Subject: Re: [EM] New Criterion
>     Message-ID:
>     <CAOKDY5DYQZtEnaoxoV8NG3OxyFBsw+59x2vpZU8maFZZEuJiqA at mail.gmail.com <mailto:CAOKDY5DYQZtEnaoxoV8NG3OxyFBsw%2B59x2vpZU8maFZZEuJiqA at mail.gmail.com>>
>     Content-Type: text/plain; charset="utf-8"
>     Chris--
>     One comment that I can make right away is that FBC is almost surely
>     incompatible with CD + MMC.  ...just as FBC is incompatible with
>     Condorcet.
>     So, in Green scenario or ideal majoritarian conditions, FBC would
>     be too
>     costly. So, if the 2nd of Forest's criteria, too, is incompatible
>     with the
>     criteria desirable for the Green scenario, that's favorable to a
>     likening
>     of that criterion to FBC. Sure, the differences are great too..
>     Of course you have a point about the desirability of sacrificing one's
>     favorite in order to save the winner under sincere voting.
>     It could be argued that the thing being measured for is the
>     _possibiity_ of
>     easily (without reversal) preserving the sincere winner, whether
>     or not
>     it's always desirable, and that that's a matter of interest, just
>     because
>     it _could_ be desirable.
>     Mike
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