[EM] Still looking for a simple system: PAR?

[Jameson Quinn]

I've been talking about MAS (aka U/P, etc) and MSV for some time now. The
idea is to have an FBC-compliant system that's easy to describe and that
handles both chicken dilemma (primarily by avoiding the slippery slope, not
by punishing defectors unless their faction is under 25%) and center
squeeze (ideally, without requiring truncation). Both MAS and MSV were
designed so that even if a large number (say, 51%) of voters are lazy,
using the default for all but their favorite and least-favorite, the
chicken dilemma and center squeeze are still workable.

This is a hard problem, and I'm still not fully satisfied with either MAS
or MSV. MAS has too-complicated a default rule; and MSV has 4 ratings when
only 3 of them are strategically ideal for any given voting faction. Both
of these problems come from the same source: the things that help with CD
tend to be a problem with center squeeze and vice versa.

So, let me try yet again. Here's a new idea, using an optional SODA-like
logic to deal with center squeeze:

   - Candidates can optionally designate some subset of the other
   candidates as "preferable" (as compared to those not in the subset). This
   information is included on or with the ballot.
   - Voters can Prefer, Accept, or Reject each candidate. Default is Accept.
   - Candidates with a majority of Reject, or with under 25% Prefer, are
   eliminated, unless that would eliminate all candidates.
   - For each non-eliminated candidate X, tally the number of "prefers",
   plus the number of ballots that accept X and prefer only eliminated
   candidates who found X "preferable". Highest tally wins.

Hmm. No. This proposal is obviously harder to explain than either MAS or
MSV. Yes, it deals with center squeeze better than the former, and has a
simpler ballot than the latter. But it doesn't really have any advantages
at all over MSDSV.

Here's MSDSV again:

   - Voters can Prefer, Accept, or Reject each candidate. Default is Accept.
   - Candidates with a majority of Reject, or with under 25% Prefer, are
   eliminated, unless that would eliminate all candidates.
   - The winner is the non-eliminated candidate rated equal-or-above any
   other non-eliminated candidate on the most ballots.

This is a solid system, and the above description avoids the problems with
my original formulation involving changing ballots. Perhaps it could be
called PAR voting, after the rating categories.

Its greatest problem is the lack of simple summability. Still, if you allow
for two-pass counting (first, find which candidates are eliminated; then,
once that's known, count ballots again to find the tally for each
non-eliminated candidate), that's resolvable.

I think I'm favoring this system over MAS or MSV. I guess I should make it
a page on the wiki...
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