[EM] 0-info approval voting, repeated polling, and adjusting priors

[Simmons, Forest]

What I wrote below doesn't make sense because I got two different ideas mixed together.
 
I wrote (emphasis added to highlight the mistake):


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.

Under these circumstances and from the point of view of the voters how would the probabilities evolve from one stage to the next?

For a more coherent idea, replace the underlined phrase with "by approval according to the current approval cutoffs."
 
Of course, these cutoffs would be based on the voter estimates of the current probabilities.
 
The other idea involved keeping the voters informed of an evolving default lottery that would be employed if their repeated pollings did not meet some condition by the stage the red marble was drawn.
 
Forest
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