[EM] PAR: nearly-equivalent rules

[Jameson Quinn]

I think this is the best phrasing I've come up with so far for PAR. I think
it's not exactly equivalent to the definitions I've given before, but it is
close enough to meet all the same properties and give the same result in
any basic scenario type.

Prefer Accept Reject (PAR) voting works as follows:

   1. *Voters can Prefer, Accept, or Reject each candidate.* Blanks count
   as "Reject" if no rival is explicitly rejected; otherwise, blank is
   "Accept".
   2. *Candidates with at least 25% Prefer, and no more than 50% reject,
   are "viable"*. The most-preferred viable candidate (if any) is the
   leader.
   3. Each "prefer" is worth 1 point. For viable candidates, each "accept"
   on a ballot which doesn't prefer the leader is also worth 1 point. *Most
   points wins.*


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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