[EM] PAR is awesome part 1/2: FBC?

[C.Benham]

On 11/11/2016 10:14 PM, Jameson Quinn wrote:

> I think that simple PAR is close enough to FBC compliance to be an 
> acceptable proposal.

I'm afraid I can't see any value in "close enough" to FBC compliance.  
The point of FBC is to give an absolute guarantee to (possibly uninformed
and not strategically savvy)  greater-evil fearing voters.

> It elects the "correct" winner in a chicken dilemma scenario, 
> naive/honest/strategyless ballots, without a "slippery slope" (though 
> of course, this is no longer a strong Nash equilibrium). 

How do you have a "chicken dilemma scenario" with 
"naive/honest/strategyless ballots" ?

35: C >> A=B
33: A>B >> C
32: B >> A=C  (sincere is B>A >> C)

In this CD scenario your method elects B  in violation of the CD criterion.

Since you are apparently now content to do without FBC compliance  and 
you imply that electing the CW is a good thing,
why don't you advocate a method that meets the Condorcet criterion?

What is wrong with Smith//Approval?  Or Forest's nearly equivalent Max 
Covered Approval?

Chris Benham



On 11/11/2016 10:14 PM, Jameson Quinn wrote:
> Here's the definition of PAR 
> <http://wiki.electorama.com/wiki/Prefer_Accept_Reject_voting> again:
>
>  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 with a majority of Reject, or with under 25% Prefer,
>     are disqualified*, unless that would disqualify all candidates.
>  3. Each voter gives 1 point to each non-eliminated candidate they
>     prefer; and any voter who gave no such points (because their
>     preferred candidates were all eliminated) gives 1 point to each
>     non-eliminated candidate they accept. *The winner is the candidate
>     with the most points.*
>
>
> Note that since originally proposing this method, the only substantive 
> change to the process above has been a slight adjustment in the 
> default rule: the part where default is "Reject" for voters who do not 
> explicitly reject any candidates.
>
> As previously discussed, this method does not meet FBC. For instance, 
> consider the following "non-disqualifying center-squeeze" scenario:
>
> 35: AX>B
> 10: B>A
> 10: B>AC
> 5: B>C
> 40: C>B
>
> None are eliminated, so C wins with 40 points (against 35, 25, 35 for 
> A, B, and X). However, if 6 of the first group of voters strategically 
> betrayed their true favorite A, the situation would be as follows:
>
> 29: AX>B
> 6: X>B
> 10: B>A
> 10: B>AC
> 5: B>C
> 40: C>B
>
> Now, A is eliminated with 51% rejection; so B (the CW) wins.
>
> Is this violation of FBC a serious defect in the system? I would argue 
> it isn't. In the above scenario pair, candidates A, B, and C are the 
> clear frontrunners, with X being merely a distraction. In that 
> context, the 10 B>AC voters are clearly not using their full voting 
> power. If they voted their true preferences, whether those are B>A>C 
> or B>C>A, then either A or C would have to be eliminated, and B would win.
>
> More generally, one can "rescue" FBC-like behavior for this system by 
> restricting the domain to voting scenarios which meet the following 
> three restrictions:
>
> Each candidate either comes from one of no more than 3 "ideological 
> categories", or is "nonviable".
> No "nonviable" candidate is preferred by more than 25%.
> Each voter rejects at least one of the 3 "ideological categories" 
> (that is, rejects all candidates in that category).
>
> If the above restrictions hold, then PAR voting would meet FBC. It is 
> arguably likely that real-world voting scenarios will meet the above 
> restrictions, except for a negligible fraction of "ideologically 
> atypical" voters. For instance, in the first scenario above, the three 
> categories would be {AX}, {B}, and {C}, and the B>AC voters, who 
> violate the third restriction, would probably actually vote either B>A 
> or B>C, which wouldn't violate that restriction.
>
> Also, note that in any scenario where PAR fails FBC for some small 
> group, there is a rational strategy for some superset of that group 
> which does not involve betrayal. For instance, in first scenario 
> above, if 11 of the AX>B voters switch to >AXB, then A is eliminated 
> without any betrayal.
>
> If you're really concerned about FBC failure, then you can always use 
> FBPPAR <http://wiki.electorama.com/wiki/FBPPAR> instead:
>
>  1. Voters can Prefer, Accept, or Reject each candidate. Default is
>     "Accept"; except that for voters who do not explicitly reject any
>     candidates, default is "Reject". Voters can also mark a global
>     option that says: "I believe that voters like me should be the
>     first to compromise."
>  2. Candidates with a majority of Reject, or with under 25% Prefer,
>     are eliminated, unless that would eliminate all candidates. If a
>     candidate would have been eliminatable considering all the
>     "prefer" votes they got on "compromise" ballots as "rejects", then
>     they are considered "eager to compromise"
>  3. The winner is the non-eliminated candidate with the highest score.
>     Voters give 1 point to each candidate whom they prefer; and, if
>     all the candidates they gave points to are "eager to compromise",
>     they also give 1 point to each candidate whom they accept.
>
>
> However, I think that FBPPAR is just a theoretical curiosity. The 
> "compromise" option adds significant extra complexity, and would 
> almost never be used. I think that simple PAR is close enough to FBC 
> compliance to be an acceptable proposal.
>
> Other than FBC, PAR has some pretty excellent properties. It elects 
> the CW in most realistic chicken dilemma scenarios, giving a strong 
> Nash equilibrium with naive/honest/strategyless ballots, as shown in 
> the Tennessee example. It elects the "correct" winner in a chicken 
> dilemma scenario, naive/honest/strategyless ballots, without a 
> "slippery slope" (though of course, this is no longer a strong Nash 
> equilibrium).
>
> PAR voting passes the majority criterion, the mutual majority 
> criterion, Local independence of irrelevant alternatives (under the 
> assumption of fixed "honest" ratings for each voter for each 
> candidate), Independence of clone alternatives, Monotonicity, 
> polytime, and resolvability.
>
> There are a few criteria for which it does not pass as such, but where 
> it passes related but weaker criteria. These include:
>
>
>   * It fails Independence of irrelevant alternatives, but passes Local
>     independence of irrelevant alternatives.
>   * It fails the Condorcet criterion, but for any set of voters such
>     that an honest majority Condorcet winner exists, there always
>     exists a strong equilibrium set of strictly semi-honest ballots
>     that elects that CW. (Note that though this is in some sense a
>     "weaker" criterion, it is actually not met by most strictly-ranked
>     Condorcet systems!)
>   * It fails the participation criterion but passes the semi-honest
>     participation criterion.
>   * It fails O(N) summability, but can get that summability with
>     two-pass tallying (first determine who's eliminated, then retally).
>   * It may pass the majority Condorcet loser criterion (?). If not, it
>     certainly passes some weakened version.
>   * It fails the later-no-help criterion, but passes if there is at
>     least one candidate above the elimination thresholds (which is
>     always true, for instance, if there are some three candidates who
>     get 3 different ratings on every ballot).
>
>
> It fails the consistency criterion, reversibility, the majority loser 
> criterion, the Strategy-free criterion, and later-no-harm.
>
> All-in-all, I think it's a great method: reasonably simple and 
> intuitive, passes FBC on a restricted but essentially-realistic 
> domain, handles center-squeeze and CD with naive ballots, and cloneproof.
>
>
>
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