[EM] Favorite Betrayal in DMC

Simmons, Forest simmonfo at up.edu
Sat Sep 17 15:00:09 PDT 2005

One of the nice things about DMC is that it is easy to pinpoint the precise circumstances in which there is a Favorite Betrayal incentive, i.e. where Favorite Betrayal is more likely to payoff than not.   It seems to be much harder to pin this down in Schulze.
Here are the conditions that must all obtain simultaneously for there to be a Favorite Betrayal incentive:
1. There must be a faction V of voters coordinating (by ESP or otherwise) their strategy trying to decide whether to vote Compromise C above Favorite F.
2. Without this betrayal by faction V, candidate F beats C pairwise.
3. With this betrayal by faction V, candidate C  beats F pairwise.
4. Even with full approval of C by faction V,  candidate F has more approval.
5. There must be some candidate X that doubly defeats F.
6. Candidate C must not be doubly defeated by any candidate other than F, not even X.
7. The members of V must be convinced that conditions (3) and (6) are almost surely true despite all of the evidence (conditions 2, 4, and 5) to the contrary.
Think about this.  Conditions 2 and 4 say that F doubly defeats C even when the F supporters that consider C as a compromise give full approval to C.  Condition 5 says that F is doubly defeated by some other candidate X.  If double defeat were transitive, then we would conclude that X doubly defeated C, too, and there would be no point in ranking C ahead of F.
Of course, double defeat is not transitive, but in absence of very strong evidence to the contrary, it is the safest bet.  How would you bet if your were told that X doubly defeats F doubly defeats C?  Would you put your money on C is not doubly defeated by anybody but F, or on C is doubly defeated by someone other than F (like X)?
But this is not all.  Suppose you were willing to put your money on C not being doubly defeated by anybody but F.  How likely would it be that your betrayal would help C defeat F, given that your faction V approving C was not enough to raise C's approval above F's approval?
In sum, because there is a tension of conditions 2, 4, and 5 versus conditions 3 and 6, it is hard for condition 7 to hold.  But if even one of these conditions is believed to fail, then there is no betrayal incentive.
I believe that it is practically impossible for all seven of the above conditions to obtain simultaneously.
Who can make a similar analysis for Shulze(wv) ?
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