Fwd: PAR is awesome part 1/2: FBC?
Whoops. I sent the below just to Chris, not to EM. Here it is:
2016-11-11 12:50 GMT-05:00 C.Benham cbenham@adam.com.au:
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.
Yes. The guarantee you can give is "as long as the world is somewhere in
this restricted domain — that is, essentially, as long as there are no
Condorcet cycles and each voter naturally rejects at least one of the 3
frontrunners — this method meets FBC". This is much broader than any
guarantee you could give for a typical non-FBC method. For instance, with
IRV, the best you could say would be "as long as your favorite is
eliminated early or wins overall, you don't have to betray them", which
unlike PAR's guarantee is not something which could ever be generally true
about all real elections for all factions.
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.
You're suggesting that the sincere preferences are
35: C >> A=B
33: A>B >> C
32: B>A >> C
If you are 1 of the B>A>>C voters considering whether to strategically vote
B>>A=C, you have no strong motivation to do so, because your vote alone is
not enough to shift the winner to B. This is what I mean by "no slippery
slope".
I believe that in the election you gave, there is no way to tell what the
sincere preferences are. Perhaps the B voters are strategically truncating
A; perhaps the C voters are strategically truncating B. So the "correct
winner" could be either A or B, but is almost certainly not C. The "CD
criterion" requires the system to elect C, merely to punish the B voters; I
think that's perverse, because, among other things, it means that a system
does badly with center squeeze, allowing the C faction to strategize and
win.
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?
Largely, it's because I think that Condorcet systems are strategically
counterintuitive, and hard to present results in. I think that will lead to
more strategy than a system like PAR. That's because PAR can make
guarantees that Condorcet systems can't.
In a system like MJ or Score, you can give a number to each candidate,
based on their own ratings alone, and the higher number wins. That is an
easy way to get monotonicity, FBC, and IIA.
In Condorcet, no candidate has any number except in relation to all other
candidates. That's good for passing the Condorcet criterion (obviously) but
it breaks FBC and IIA.
In PAR, candidates are compared to absolute thresholds, and then to the
other candidates that failed to meet those absolute thresholds. It doesn't
have the cleanness of MJ or Score, but it also doesn't have the infinite
recursive depth that Condorcet has. At the end of the day, each candidate
gets a number, and cycles simply never happen.
I understand that the neither-fish-nor-fowl nature of PAR makes it worse
for criteria compliance (though it's still better than something like IRV);
but its performance in realistic scenarios is excellent.
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.
Election-Methods mailing list - see http://electorama.com/em for list info
Election-Methods mailing list - see http://electorama.com/em for list info