[EM] manipulation free method?
Forest W Simmons
fsimmons at pcc.edu
Thu Jun 28 14:42:34 PDT 2007
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
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