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<TITLE>RE: [EM] 0-info approval voting, repeated polling, and adjusting priors</TITLE>
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<DIV dir=ltr><FONT size=2>Jobst wrote ...<BR><BR>A point which troubles me is
this: The justification of placing the approval cutoff at the expected or median
utility according to the current priors is based upon the two assumptions that
(1) given a top tie between two candidates, the events "x is among the two tied
candidates" and "y is among the two tied candidates" are *independent* and that
(2) the priors give the respective probabilities of these events. But neither do
I believe that this independence can be assumed, nor do I believe that the
probability of winning the poll is the same as the probability of being one of
the two tied candidates given a top tie...<BR><BR>Does anybody know a solution
to this?<BR><BR>I reply:</FONT></DIV><FONT size=2></FONT></DIV>
<P><FONT size=2>I don't know a solution, but perhaps if we gave definite meaning
to the probabilities we could make some progress. It might be easier to
talk about winning probabilities if those probabilities have a more definite
roll in picking the winner.</FONT></P>
<P><FONT size=2>Suppose for example, that at each stage a marble is drawn
(with replacement) at random from a bag containing one red
and 999 green marbles, and that the first time the red marble is
drawn, the winner is to be chosen by a lottery based on the current
set of probabilities. Suppose further that at each stage the only thing
reported back to the voters is who won the previous stage. If two
candidates tie at some stage, then the tie is broken by coin toss before
reporting the winner, so the voters don't know about the tie.</FONT></P>
<P><FONT size=2>Under these circumstances and from the point of view of the
voters how would the probabilities evolve from one stage to the next?</FONT></P>
<DIV dir=ltr><FONT size=2>Forest<BR></FONT></DIV>
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