MIKE OSSIPOFF wrote: > But is there a demonstration that the voter's expectation is > maximized by voting for all the candidates who are better than > the voter's expectation in the election?
No, in fact I already showed a counter-example. > As for the delta-p method, the delta-p are less fundamental, and > farther from what's estimatable, as compared to the Pij, or especially the > Wi. Estimating the Wi is at least not out of the question. Directly > estimating the delta-p is out of the question. Richard would have to > show a way to calculate estimates of the delta-p, one that makes good > on that freedom from approximation that he spoke of. That method would > have to not use approximations like the assumption that ties will > be 2-way, and would have to not use the Pij to calculate the delta-p. delta-p are actually more fundamental, though maybe harder to determine. Any increase in probability of a win for a candidate with utility U represents an increase in the expected utility equal to the product of delta-p and U. It falls out of differentiating the expected utility with respect to votes for a particular candidate. In terms of accuracy, I would rank the four methods I listed as method 1 > method 2 > (method 3 ~= method 4). I don't know which of the last two is better. In terms of ease of use, I would rank them as method 4 > method 3 > method 2 > method 1. But the gap between methods 3 and 2 is much greater than the other gaps. > Richard, what's a precise way to calculate an estimate of the delta-p? A challenging question, that. I'll look into it if I can. > By the way, you left out Crannor's and Hoffman's ways of estimating > the Pij, from the vote totals in a previous election. It seemed to > me that Crannor's descripion of her method didn't give enough > information about it. If anyone understands Crannor's method, would > they explain it? It sounds good, because it avoids the great > amount of calculation work and complexity of Hoffman's method. I don't know either of those methods. Could you fill me in? -- Richard
