If (in order to share costs) all the participants were to contribute (to a transportation pool) the average cost of getting to the winning city, then it would be to their economic advantage to choose the city minimizing the average voter distance (assuming that flight costs were proportional to distance).
But that's a pretty big "if."
I mention in another post today that Alcoholics Anonymous decided years ago to hold their national Conference in one city (New York, where the national office is located) and to equalize travel expenses. Generally AA Intergroups or regional organizations, I forget the exact details, pay delegate expenses, which are equalized. Essentially, this made the choice of Conference city largely irrelevant. Yes, some city might be chosen which optimized total expense, but the variation would not be great, since delegates are coming from all regions, and having the Conference where the office was located lowered organizational expenses (for travel of staff and the like).
However, where a group of participants are travelling to a city by car, cost would be one factor, travel time, which is also a kind of cost, would be another. Theoretically, that could also be equalized in some way, but it gets more complicated.... If travel is by air, once you are flying it is not all that important how far you are flying, much of the difficulty is in getting in and out of the airports.
Anyway, creative devices like travel equalization, thus avoiding contention, can be much better than sophisticated election schemes which assume that only one outcome, one winner, is possible. If you have to choose one city, and there is no equalization device, there are going to be winners and losers and the support of the losers for whatever system is doing this to them will be weakened. Multiply this by hundreds of such choices and most people end up feeling pretty alienated.
To me, an ideal organizational system will maintain the enthusiastic support of participants that is common in new organizations. The trick is to maintain the kinds of relationships that exist in new, small organizations, as the organizations grow and mature. I think there is a way, I've been writing about it.
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