Andrew Myers wrote:
A lot of Condorcet election methods use randomness to elect a winner, but in a way that I think voters will find unsatisfactory. They simply produce a winner as part of a complex algorithm that uses randomness at various points. MAM is an example of such an algorithm.
Actually, MAM does not use randomness at various points.
It only uses randomness at the beginning when it determines the Random Voter Hierarchy (RVH). Once the RVH has been computed, it is remains the same and only used to break ties when required.
If one uses the same RVH for each subsequent calculation using MAM, one will always get the same winner back - and MAM is always guaranteed to return a single winner.
A voter might reasonably wonder whether the random number generator has been "fixed" to generate the desired result.
It seems to me that it would be more easy to justify the election method if it consisted of two phases:
1. Deterministically generate a separate probability in [0,1] for a win by each alternative (i.e., no randomness is used).
2. Randomly choose among the alternatives according to their respective probabilities. This can be done outside the electronic system to make it completely clear that the procedure is fair.
You can imagine "lifting" existing algorithms to satisfy this description. For example, with MAM you could consider all possible permutations of the ballots. Of course, the problem is that this is very expensive.
Thoughts?
Unless I am mistaken, the use of randomness is required to pass several desirable criteria of an election method. Passage of these criteria helps minimize the potential for strategic manipulation of the election.
This is one of the reasons why MAM is currently my favorite Condorcet variant.
Of course, Steve could provide further details...I am merely repeating my understanding of his method based on past conversations with him.
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