[EM] Manipulation Free?

[Forest W Simmons]

It appears that the answer to the question is no, but not too bad.

Taking into account suggestions by Warren, Mike, and Dave, I offer a 
simpler version.

The basic ballot is ordinal. Everything else is optional.

Voters with opinions about who has the best chance of winning can put a 
mark next to the name of a candidate.  If they think that there are 
several candidates that are all nearly maximally likely to win, then 
they can mark all of those candidates.

Furthermore, the voters that make the optional marks have the 
additional option of indicating a level of confidence (alpha).  For 
them the default value of alpha is 50%.

If you have your mind made up about whom you want to approve and whom 
you don't, then you can simply rank all your approved candidates equal 
first, and truncate the others, and that is how your ballot will be 
counted.

So voting is as simple as ranking or approval for voters that opt out 
of guessing for whatever reasons.

Now here is my suggestion about how to use this information to choose a 
winner.

Each ballot is going to be converted into an approval ballot with the 
help of a probability distribution specific to that ballot.

The ordinal ballots without any of the optional marks will make use of 
the "community distribution," which is a weighted average of all of the 
distributions submitted by the other voters.  In this case the weights 
are the cofindence levels of those voters.

Each of the other ballots will make use of a distribution which is a 
weighted average of the community distribution (described above) and 
the distribution implied by the optional marks on the ballot.  The 
weights are 100% minus alpha, and alpha, respectively.

Once you have the distribution specific to the ballot, you simply 
approve every candidate that is ranked above more probability than it 
is ranked below.

Once all of the ballots are converted to approval ballots the approval 
winner is elected.

FWS