Disclaimer: Doubtless some situations require deterministic election methods. This message has nothing to do with any such situations. Simple Lottery Method: If there is an alternative that pairwise defeats the approval winner A, then toss a coin to decide between A and the most approved alternative that pairwise defeats A. Otherwise just elect A. Note that this method is monotone, because if only one alternative improves its position relative to one or more of the other alternatives, whether pairwise or in approval count, then the probability of that alternative cannot decrease from 1 to less than one, nor from 1/2 to zero. Example1 (assume sincere preferences): 40 A>>C>B 35 B>C>>A 25 C>A>>B In this example the Approval winner A and the Condorcet winner C share the odds equally, and it wouldn't change the result if the A supporters reversed the C>B preference, unless they decided to approve B, which they would regret doing, because then A would share the probability with B, instead of C. The exact same analysis applies to the following example as well. Example2 (assume sincere preferences): 49 B 24 A>>C>B 27 C>A>>B I wonder if this lottery method isn't adequate for most situations that require a non-deterministic method. I am interested in comments from everbody except those people who (through lack of imagination) cannot believe in the existence of stochastic election methods applications. Forest
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