[EM] PAR: nearly-equivalent rules

[Jameson Quinn]

I now realize that FBPPAR can be expressed in this format, and it's less
confusing that it is when added to the regular PAR format. Here's FBPPAR:

   1. Voters can Prefer, Accept, or Reject each candidate. Default is
   "Reject" for voters who do not explicitly reject any candidates, and
   "Accept" otherwise. For any preferred candidate, voters may also check
   "stand aside". (This is rarely useful; it is only worthwhile if they think
   that the candidate might become the leader in step 3 and stand in the way
   of a stronger compromise leader.)
   2. Candidates get 1 point for every ballot that prefers them.
   3. Candidates with over 25% Prefer, and less than 50% Reject, are called
   viable. If there are any such candidates who would still be viable if all
   "prefer/stand aside" votes were counted as "reject", the one pith the most
   preferences is designated the leader.
   4. Viable candidates get 1 point for every ballot that accepts them and
   does not prefer the leader.
   5. Winner is the highest score.


If I'm not mistaken, this system passes FBC, majority, mutual majority, and
LIIA, among others. It handles the Tennessee center squeeze with a strong
Nash equilibrium on naive ballots, and does well on naive-ballot chicken
dilemma with no slippery slope.

2016-11-12 15:26 GMT-05:00 Jameson Quinn <jameson.quinn at gmail.com>:

> OK, I'm still working on expressing the rules as simply as possible. The
> following is again a small change from what I'd said previously, but it is
> simpler and nearly equivalent:
>
>    1. Voters can Prefer, Accept, or Reject each candidate. Default is
>    "Reject" for voters who do not explicitly reject any candidates, and
>    "Accept" otherwise.
>    2. Candidates get 1 point for every ballot that prefers them.
>    3. Candidates with over 25% Prefer, and less than 50% Reject, are
>    "viable". Viable candidates get 1 point for every ballot that accepts them
>    and does not prefer the most-preferred viable candidate.
>    4. Winner is the highest score.
>
>
> 2016-11-12 14:04 GMT-05:00 Jameson Quinn <jameson.quinn at gmail.com>:
>
>> Another nearly-equivalent way of stating it that gives valid approval
>> scores for all candidates as a byproduct:
>>
>>
>>    1. *Voters can Prefer, Accept, or Reject each candidate.* Default is
>>    "Reject" for voters who do not explicitly reject any candidates, and
>>    "Accept" otherwise.
>>    2. *Candidates over 25% Prefer, and less than 50% reject, are
>>    "viable"*.
>>    3. Each candidate gets 1 point for each "prefer".
>>    4. Each candidate with over 25% prefer gets 1 point for each "accept"
>>    on a ballot that prefers no viable candidates.
>>    5. Each candidate with over 25% prefer gets 1 point for each "accept"
>>    on a ballot that prefers some viable candidate, but does not prefer the
>>    candidate who's leading after step 4.
>>    6. The winner is the candidate with the highest points.
>>
>>
>> 2016-11-12 13:47 GMT-05:00 Jameson Quinn <jameson.quinn at gmail.com>:
>>
>>> Thinking about PAR and the electoral college, I realized that there is a
>>> different way to state the PAR rules:
>>>
>>>
>>>    1. *Voters can Prefer, Accept, or Reject each candidate.* Default is
>>>    "Reject" for voters who do not explicitly reject any candidates, and
>>>    "Accept" otherwise.
>>>    2. A candidate is "viable" if they are rejected by under 50%.
>>>    3. Each ballot gives 1 point to each candidate it prefers. Ballots
>>>    which prefer no viable candidates also give 1 point to each candidate they
>>>    accept, so long as that candidate is preferred by at least 25%.
>>>    4. Now find the viable candidate with the most points, if any, and
>>>    redo step 3 from scratch as if only that candidate were viable.
>>>    5. The winner is the candidate with the most points.
>>>
>>>
>>> This could potentially differ from PAR in that it waits slightly longer
>>> to "reveal" the preferences of candidates with under 25% preferences. In
>>> practice, I doubt this would typically make any difference.
>>>
>>> The procedure above is more complicated than PAR's, but the advantage is
>>> that it produces counts which include the disqualified candidates, and thus
>>> is suitable for combining with totals from non-PAR systems such as
>>> approval, plurality, or "pre-elimination totals" from IRV.
>>>
>>
>>
>
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