[EM] [CES #15267] Re: PAR: nearly-equivalent rules

[Ted Stern]

The first round of Step 3 could be made summable with the addition of an
NxN array where row i accumulates, from a ballot that does not Prefer the
i-th candidate, Accept points cast for any candidates besides the i-th
candidate.

I'm not sure if that same array could be used for step 4, however.  In
fact, step 4 is not entirely clear to me.

Ted

On Mon, Nov 14, 2016 at 10:14 AM, Jameson Quinn <jameson.quinn at gmail.com>
wrote:

> 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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