Though there must be a good mathematical strategy for few voters & 0-info, it might be quite a job. Fist of all, since, as Richard pointed out, your other votes affect the worth of voting for i, or even the worth of voting i over j, then, except with 3 candidates, we must evaluate the worth to you of every combination of candidates that you could vote for. The obvious thing to do is use a computer program to evaluate the worth to you of every combination of altenatives that you could vote for, with every possible equiprobable combination of ways the other people could vote. I guess "permutation" is a more accurate word than "combination" here. The trouble with that is that it quickly becomes prohibitively time-consuming. One very rough estimate would be to just use above-mean when the voters & candidates are numerous enough to render that exhaustive computer study too time-consuming. But I'd expect that something less time-consuming is possible. A few days ago Richard posted suggestions for symbols to represent the various kinds of ties possible with 3 candidates. It could of course be extended to more candidates. He pointed out that each type of tie is equally likely no matter which candidates are which in that tie. That kind of equality is enough when there are lots of voters, and only one kind of tie is likely. But when all sorts of ties can happen, we have to consider the actual probability of the various kinds of ties. That could be calculated, but, just as with the exhaustive computer approach, we have to be able to say how people can be assumed to vote in a 0-info election. Can we assume that each voter is equally likely to vote for 1 candidate, 2 candidates, 3 candidates...or N candidates (other than voting for favorite and not voting for last choice)? Richard suggested such an assumption if voters are assumed to be using above-mean strategy. But if other people are voting that way, then above-mean strategy is surely not what you want to use. In that case, they know that and we shouldn't expect them to use it. Does that mean that we shouldn't expect them to be equally likely to vote for 1, 2, 3...N candidates aside from favorite (which they vote for) and last choice (which they don't vote for)? What then, assume that for each voter every possible ballot is equiprobable? For instance, with 3 candidates, these are the possible ballots: A, B, C, AB, AC, BA, BC, CA, CB So I don't even know what kinds of ballots should be considered equally likely for a voter in a 0-info election. That's the 1st thing to decide, before strategy can be calculated. Mike Ossipoff _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com
