[Election-Methods] final attempt for a strategy-free range voting variant, and another proportionally democratic method

[fsimmons at pcc.edu]

Here's a proof of part (f):

In phase II if my ballot is not one of the ones drawn, then it has no influence.  

So suppose that it is one of the drawn ballots.  If all of the drawn ballots,
including mine, approve the phase I winner, then she is elected., and my utility
for the result is exactly what I ascribe to her.

In the other case, the winner is my favorite (if my ballot is the first drawn)
or the benchmark lottery winner (if my ballot is not the first drawn). And since
the number of ballots drawn is at least five, the result follows.

 > f) If every voter i prefers the compromise option W to a lottery in> which
i's favourite is elected with 20% probability and the Random> Ballot lottery is
applied with 80% probability, and all voters > know that> this is the case, then
it is likely that all voters will say > "yes" in> phase II and W will be the
sure winner.>