Theorem About Strategy and Popularity?

[William Waugh]

Is there a theorem that implies that in all possible voting systems, the voting strategy with the highest expected value of moving the needle in a direction preferred by the voter takes into account some estimate of the levels of approval enjoyed by the various candidates from the other voters?

Even if so, it is possible that different voting systems require different levels of attention to such considerations, and that something other than Range, yet still balanced, might be less sensitive to the effects of such attention than Range is?

I have had either someone who favors IRV or someone who would accept IRV or Score whichever seems more popular with advocates, believing that either would work against 2PD, express that a + with IRV is that until your favorite is eliminated, your vote counts fully for your favorite. This person said he'd prefer not to have to think about how other voters are likely to vote. I believe that for a voter who prefers a compromise candidate to the worst candidates, in Range, that voter must adjust her level of support for the compromise candidate according to her estimate of the amount of support for the respective candidates from the other voters. Is there a theorem that implies that the hope of my interlocutor for a system that would make estimates concerning other voters unimportant is a forlorn hope?

I have in mind a system that seems to my intuition (I know my intuition is generally likely to be wrong) independent of estimates on other voters. Each voter decides to vote High or Low. The voter also provides a partial order over the candidates. This means an ordered series of ranks where each rank can be populated by the voter with one or more candidates. One end of the series is favored and the other end disfavored. The voter distributes the candidates among the ranks; no candidate can be placed by the voter in more than one rank, nor fewer. The tally proceeds in rounds, where each round eliminates one candidate. The last candidate standing wins. Each round trims from both ends of each partial order provided by a voter, the ranks naming only candidates who have been eliminated already. Then the round calculates an Approval ballot from the trimmed partial order. If the voter chose High style, this ballot approves everyone in the top remaining rank and disapproves everyone else. If the voter chose Low style, the Approval ballot calculated disapproves the candidates in the bottom remaining rank and approves all the other candidates. The round then tallies the resulting Approval ballots like in Approval Voting, then eliminates the candidate receiving the lowest count of approvals.

[Ted Stern]

Hi William,

There are several Condorcet-style methods that might be used as a basis for the method you envision.  They all involve ranking plus an approval cutoff, either fixed or specifiable.  One way to implement that would be to have a Range-voting like ratings ballot with scores of 9 to 0, with an approval cutoff at, say, 5.  That is, all candidates rated at 5 and below would be disapproved.  Then infer rankings from the ratings.

Warren had some things to say about some of these methods many years ago:

http://election-methods.electorama.narkive.com/eynX0jPD/not-totally-successful-attempt-to-summarize-mdda-dmc-ica

ICA (http://wiki.electorama.com/wiki/Improved_Condorcet_Approval) is probably closest to what you're envisioning, though there has been a fair amount of discussion over the last month on the EM mailing list (cc'd above) regarding more recent variants.  See also http://wiki.electorama.com/wiki/Majority_Defeat_Disqualification_Approval .

Jameson Quinn's PAR (http://wiki.electorama.com/wiki/Prefer_Accept_Reject_voting) has also been discussed recently on both lists and shares some characteristics.

None of these methods is conducted in rounds as you describe.  However, they have been working to find methods that satisfy CD (chicken dilemma), FBC (favorite betrayal criterion), mono-add-top and other criteria that might be considered important to those who currently favor IRV.

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[Kevin Baas]

My modified STV method is optimal in this sense.

With it, there's essentially no advantage from knowing everyone else's vote vs complete ignorance.

Adding something like range voting makes this less feasible, as the "pivot points" so to speak are at exact scores, dependent on all the other votes.

[Kevin Baas]

also i might add there are two systems that satisfy this criteria rather trivially:

* dictatorship

* lottery