[EM] New Criterion

Forest Simmons fsimmons at pcc.edu
Mon May 19 16:16:56 PDT 2014

```For methods based on range or score ballots we could use either Range
Sorted Margins (RSM) or Majority Enhanced Range (MEA) in place of MAM to
find the winner of the sincere ballots.  Both of these methods are ideal
for majoritarian use of sincere cardinal ratings ballots.

A method satisfies SS(RSM) if and only if a semi-sincere modification of
sincere preferences leads to a strategic equilibrium ballot set from which
the method elects the sincere RSM winner.

And a method satisfies SS(MER) if and only if a semi-sincere modification
of sincere preferences leads to a strategic equilibrium ballot set from
which the method elects the sincere MER winner.

By the way both RSM abd MER obey the reverse symmetry criterion: if all of
the scores are replaced by their additive inverses (and re-scaled to fit in
the specified range) the winner will change (as long as there are a least
two non-tied candidates in the running).

On Mon, May 19, 2014 at 12:15 PM, Forest Simmons <fsimmons at pcc.edu> 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>
>> To: cbenham at adam.com.au,        "election-methods at electorama.com"
>>         <election-methods at electorama.com>
>>
>> Subject: Re: [EM] New Criterion
>> Message-ID:
>>         <
>> CAOKDY5DYQZtEnaoxoV8NG3OxyFBsw+59x2vpZU8maFZZEuJiqA 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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