[EM] manipulation free method?

[Forest W Simmons]

I was happy to see Alex Small's progress on the FBC.

It inspired me to take another crack at some way of getting around the 
basic impossibility of manipulation free deterministic methods based on 
standard ranked ballots.

Obviously, to surmount this basic obstacle we need other information 
from the voters besides their ranked ballots.

What if that information were simply an optional check mark next to the 
name of the candidate that they thought had the best chance of winning?

Since this extra information is only about perceived "chance of 
winning," it is not a betrayal to put that mark next to the name of a 
non favorite.  In fact, putting it next to a favorite would be setting 
your favorite up as a sitting duck, which you probably wouldn't want, 
unless your favorite happened to be a Condorcet winner.

How could this extra information be put to good use?

How about this?

1. After the ballots have been collected, determine an estimate of the 
(prior combined perceived) probability of winning for the candidates by 
counting the number of extra marks next to their names, and dividing by 
the total number of extra marks.

2. Then on each ballot approve every candidate that is ranked above 
more than half of the total probability, and disapprove every candidate 
that is ranked below more than half of the total probability.

3. Approve any remaining candidate only if it is ranked above the 
candidate with the extra mark (on that ballot).  If there is no extra 
mark on that ballot, then approve remaining candidates only if they are 
ranked above more probability than than they are ranked below.

4. Then count the approvals to determine the winner.

I believe that this method would be monotone, but not quite clone free, 
since twining a marginal loser might turn one of the twins into a 
winner, especially if the least liked twin is given more probability of 
winning than the better liked twin.

If this is troubling to you, then you could modify step 3 above in 
favor of a tentative approval cutoff.  In other words, if (on some 
ballot) a candidate is neither ranked above fifty percent of the 
probability nor below fifty percent of the probability, then approve 
that candidate only if it was tentatively approved.

Does it do the job?

Thanks,

Forest