[EM] Condorcet How?

[Abd ul-Rahman Lomax]

At 05:28 PM 4/12/2010, Juho wrote:
>On Apr 12, 2010, at 10:59 PM, Abd ul-Rahman Lomax wrote:
>>One point should be made clear: any candidate who recommends that
>>voters not vote sincerely is probably shooting himself or herself in
>>the foot. It isn't a winning strategy, generally, it really looks
>>bad (even if the strategy makes some sense.)
>
>Yes, I believe this is true in most societies (and for most parties).
>
>>
>>So if B is, say, leading C, but these candidates are really close in
>>preference for the set of B,C supporters, if B attacks C, B will
>>quite likely reduce his or her own support. There will be C
>>supporters who don't like that!
>
>Yes, this is important. If the overall attitude is against strategic
>plotting then election methods need less defence against such
>behaviour. (Note however that this doesn't stop strategic voting - it
>just reduces the public side of it (both at party and individual
>level).)

What it stops is, indeed, attempts to orchestrate true strategic 
voting. Dissing your opponent doesn't encourage strategic voting, 
though arguing that your opponent doesn't have a chance might. But 
that only would prevent lower preferences from being expressed if the 
voting system were poor. Like Plurality, as the obvious example, and 
in this case, it is obviously foolish for the supporters of B and C 
to allow this contest to take place in the final election.

Privately orchestrating "strategic voting," meaning other than how 
the voters will naturally vote based on the interface between their 
real preferences and preference strengths, and their own assessment 
of probabilities (which requires no coordination), is difficult to 
pull off, given that such a campaign targeting enough voters would be 
almost certain to become public. Imagine trying to keep a conspiracy 
secret when you have to influence, with it, a very large fraction of voters.

>>I believe I just showed that WV, if it elects B in the scenario
>>given, and assuming that the votes are sincere, is low-performing. I
>>don't know if the scenario was reasonably possible, and, indeed, it
>>wasn't realistic.
>>
>>I don't think we want to reform voting to use systems that produce
>>poor results if people vote sincerely!
>
>Yes, that is important. (One may also need make some compromises to
>eliminate some strategic threats.)

The threat of "spontaneous bullet voting," though, isn't a "strategic 
threat." A "spontaneous" bullet voter is sacrificing a say in certain 
pairwise elections, and does this because of the value of the first 
preference over all the other candidates. It's a way of saying, "I 
don't care so much about the choice between those others," and, for 
quite a few of them, they may not care because they literally don't 
have an opinion.

>>It is enough that a system does not reward preference reversal, and
>>approval/range systems don't do that. They do reward suppressing
>>minor preferences, while expressing major ones.
>
>It is not enough to solve one problem only. One needs a balanced
>approach where all identified vulnerabilities are analyzed and
>appropriate fixes are implemented where needed and where possible
>(often no action is needed; often there are no good fixes).

To assess whether a vulnerability requires action, one would need to 
assess both the likelihood of the vulnerability and the damage done, 
and compare this to possible damage done by the possible fix.

What has been preposterously proposed are "solutions" like:
If we allow equal ranking, then some voters will decline to equal 
rank when "really" they approve both candidates, hence "gaining a 
strategic advantage," by selfishly voting only for their favorite. 
I.e., by voting in a way which used to be called "sincere." The 
behavior, under the terms of the "problem," yields only a minor 
advantage -- and may, indeed, risk loss! Therefore, the argument 
goes, we should not allow equal ranking, to avoid its "abuse" by 
people who don't use it.

Eh? Equal rankings systems don't require equal ranking, unless they 
are rank-restricted. Notice that RCV, i.e., 3-rank IRV, *does* 
require equal-ranking bottom, if there are more than four candidates. 
IRV in general allows equal ranking bottom, except in 
mandatory-voting jurisdictions in Australia.

>All
>Condorcet methods are vulnerable to preference reversal but in real
>life elections it is quite difficult to implement any strategies that
>would make use of that vulnerability. The discussed example (or one
>explanation of the vote set) addressed one potential problem of WV
>(where only truncation was used, not reversal). I'd say that is a
>vulnerability. Note however that WV based methods have been used in
>academic circles for a while without problems. So far that
>vulnerability has thus not been a vulnerability in real life elections.

I think it's a red herring. I'm more concerned about the behavior of 
the system in the presence of natural truncation.

Concern about Favorite Betrayal is not a concern that it will result 
in some coordinated strategy, but that such a strategy would be 
necessary to improve the outcome! If the outcome would only be 
improved by a minority of voters, from their point of view, by 
Favorite Betrayal, but the outcome without it is actually utility 
maximizing, I'm not concerned. Under the terms of the problem, the 
preference strength necesssary to motivate "insincere voting" would 
not be there.

In Burlington, we saw a likely utility maximizer lose under IRV due 
to Center Squeeze, which means that Favorite Betrayal would have 
improved the outcome overall. That loss of overall satisfaction is 
the real problem, not the spectre of strategic voting, which can be, 
indeed, difficult to pull off. Burlington should have woken up and 
realized that IRV held out the promise of being able to vote 
sincerely, but that promise was a lie. IRV is not as vulnerable to 
vote-splitting as Plurality, but when you have three major parties, 
vote-splitting, in the form of Center Squeeze, comes back with a 
vengeance, where the loss of utility is much greater than in a 
vote-splitting problem from a small party.

>Even if the vulnerabilities are quite clear on paper, as in the given
>WV example, in real life the environment is much noisier, and
>controlled strategic voting is not very easy to implement. You also
>mentioned the important point that often strategists may lose more
>support because of their plots than they win as a result of a
>successful implementation of a strategy (not to mention failed
>strategic attempts). In WV I am maybe more worried about the
>performance of WV with sincere votes (also a property that you
>mentioned above) than about strategies.

Yup.

I'm noting that the study of voting system performance through 
preference order alone, without a study of underlying utilities, can 
be quite misleading. That's what we saw in this case as likely.

>Note also that Approval and Range do have very similar vulnerabilities
>(probably more difficult to handle) when people suppress some of their
>preferences and exaggerate some others, and they do not provide ideal
>results if voters don't indicate their sincere preferences but some
>strategically exaggerated ones. The discussed WV example where we have
>two competing left wing candidates is a typical and difficult problem
>scenario in Approval and Range.

The process of translating internal utilities to votes *inherently 
involves* "suppressing some ... preferences," and "exaggerat[ing] some others."

I pointed out that there is no problem with this scenario if the 
method is Bucklin. If, indeed, B and C are "competing left wing 
candidates," which must mean that their supporters are more or less 
happy with either outcome, that is, they have a favorite among B and 
C but will be thrilled to see either one win (especially compared to 
seeing the election result where they truncate, even a little, and 
thus lose to A), then we can really expect to see the B and C 
supporters add the other left-wing candidate at a lower preference.

In three-rank Bucklin, some will add the candidate in second rank, 
and some in third rank. Because of this difference, the voting will 
very likely go to three rounds of counting before a majority is found.

If it is found. If it is not found, there could be a runoff. Between 
which two candidates? I gave a hint at how to determine that, beyond 
the simplist possibility, the top two candidates in Bucklin. It could 
hinge on whether those voters add the votes for the other of B or C 
in second rank or third rank.

(Warren, in simulating Bucklin quite some time ago, did not realize 
that Bucklin allowed leaving the second rank empty, and that, as 
well, it allowed equal ranking -- at least in third rank in Duluth, 
and if we are going to try to go for Bucklin now, with what we know 
about Approval Voting, there is absolutely no reason to prohibit 
equal ranking in the other ranks. It's an option which can be, for 
some voters, a more accurate vote. Bucklin-ER is far closer to Range 
voting in theory and, my guess, in performance, than the simulations revealed.)