[EM] voting strategy with rank-order-with-equality ballots

[Chris Benham]

Kevin,

"I have found that Schulze(wv) had little favorite betrayal incentive. In simulations I mentioned in June 05, out of 50,000 trials, Schulze(wv) showed incentive 7 times, compared to 251 for Schulze(margins), 363 for Condorcet//Approval, and 625 for my erroneous interpretation of ERBucklin(whole)."

What was this "erroneous interpretation"?  How can a method that meets Favourite Betrayal, such as ER-Bucklin(whole) ever show "favourite
betrayal incentive"?

Chris Benham


 

Kevin Venzke wrote (9 June 2009):

Hello,

I think in Schulze(wv) and similar, decent methods, you shouldn't rank the worse of two frontrunners or below. I don't think that's a big problem though.

I have found that Schulze(wv) had little favorite betrayal incentive. In simulations I mentioned in June 05, out of 50,000 trials, Schulze(wv) showed incentive 7 times, compared to 251 for Schulze(margins), 363 for Condorcet//Approval, and 625 for my erroneous interpretation of ERBucklin(whole).

The simulation worked by examining the effects of introducing a strict ranking between two candidate ranked tied at the top. So a method showed favorite betrayal incentive when introducing a strict ranking A>B moved the win to one of these candidates from a third candidate.

You can look at incentive to compress at the top, but it's not as informative. There is compression incentive where introducing the A>B strict ranking moves the win e.g. from B to a third candidate. This happened hundreds of times for the methods I looked at (1200 for ICA).

I guess you could look at the odds that a strict ranking will help or hurt compared to an equal ranking, overall. I'm not sure that would be very informative either though. For one thing, it would only tell you about the zero-info case. And it wouldn't consider utility, which should be important: Whether or not you should compress at the top probably depends on how much you like those candidates compared to the other candidates.

Kevin Venzke


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