[EM] [CES #15255] Re: PAR: nearly-equivalent rules

[Jameson Quinn]

I'm still working on getting PAR expressed in the best format. Here's the
latest:


   1. *Voters Prefer, Accept, or Reject each candidate.* On ballots which
   don't explicitly use "Reject", or for candidates with less than 25%
   "Prefer", blanks count as "Reject"; otherwise, blanks count as "Accept".
   2. *Tally 1 point for each "Prefer"* for each candidate.
   3. Out of the candidates (if any) with no more than 50% "Reject", find
   the one with the most points. *For every ballot which doesn't "Prefer"
   this frontrunner, add 1 point for each "Accept".*
   4. If the frontrunner changed, add 1 for each "Accept" that's not yet
   tallied (the ones which "Prefer" the original frontrunner). *Most points
   wins.*


I now believe that the system as expressed above meets the voted majority
Condorcet criterion. Which means that FBPPAR (almost) meets both FBC and
voted majority Condorcet! Impossible, you say? No; approval meets both of
these criteria (because it reduces "voted Condorcet" to a triviality), and
FBPPAR reduces to approval when voters strategize expecting a Condorcet
cycle.

What do I mean by "(almost)" above? Well, FBPPAR allows voters to rate a
candidate as "prefer, but do not make them frontrunner because of my vote".
This is useful for cyclical and near-cyclical situations (that is, for A>B
voters who know that most B votes are B>C and that C beats A). But if this
option is used in cases where it is not actually strategic, it breaks the
voted majority Condorcet property.

So FBPPAR is a system that meets FBC; deals with center squeeze via a
fairly strong Condorcet-like property; deals with chicken dilemma without a
slippery slope; can be counted in at most 3 rounds, each of which is O(N)
summable; meets majority and mutual majority; meets a weakened version of
later-no-help; outputs tallies that are summable with other approval
tallies; and is basically all-around awesome. Personally, I feel that
FBPPAR essentially dominates other 3-rank systems in terms of strategic
properties; and that PAR is, in the real world, a very close approximation
of FBPPAR that's justified by its greater simplicity.

2016-11-13 18:04 GMT-05:00 Jameson Quinn <jameson.quinn at gmail.com>:

> Yet another revision of the rules. This one fixes it so that, if no
> candidates pass both thresholds, "accept" votes count.
>
>
> Prefer Accept Reject (PAR) voting works as follows:
>
>    1. *Voters Prefer, Accept, or Reject each candidate.* On ballots which
>    don't explicitly use "Reject", blanks count as "Reject"; otherwise, blanks
>    count as "Accept".
>    2. *Of the candidates that are both "viable"* (at least 25% Prefer) *and
>    "acceptable"* (no more than 50% reject), *the one with most "Prefer"s
>    is called 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.*
>
>
> If I could do it without it sounding too complicated, I'd make it so that
> explicit "accept" votes can count for non-viable candidates. But I don't
> think it's worth even the minor extra complication it would take to explain
> that.
>
> Note that changing the above system so that it passes FBC requires only
> giving a "prefer for the purposes of step 3, but count step 2 as if I
> rejected" option.
>
> I think this system is pretty great in outcomes; and that, while it's
> certainly not the simplest method, it's not too complex.
>
> 2016-11-12 23:33 GMT-05:00 Jameson Quinn <jameson.quinn at gmail.com>:
>
>>
>>
>> 2016-11-12 17:45 GMT-05:00 Neal McBurnett <nealmcb at gmail.com>:
>>
>>> I haven't been paying that much attention.  But this definition doesn't
>>> define what this means "a rival is explicitly rejected".  Is "rejected" the
>>> opposite of "viable"?  Or does it mean that no other voter cast any
>>> "reject" vote for any other candidate?  Or ???
>>>
>>
>> If candidates are ABCD, a ballot that prefers A and leaves the rest blank
>> counts as rejecting BCD, but one that prefers A and rejects B and leaves
>> the rest blank counts as accepting CD.
>>
>>
>>
>>> So if I have an "accept" on a ballot that doesn't "prefer" the leader,
>>> that means 0 points?
>>> Since votes depend on how other votes are interpreted and who the leader
>>> is, is the tally guaranteed to be attracted to a single stable equilibrium
>>> tally?
>>>
>>> Thanks,
>>>
>>> -Neal
>>>
>>> On Sat, Nov 12, 2016 at 05:27:53PM -0500, Jameson Quinn wrote:
>>> > 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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>>
>>
>
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