[EM] A modified Random Ballot that supports compromising

[Simmons, Forest]

Jobst, 
 
how about this slight variation on your suggestion?
 
1. Ranked ballots with truncation.
 
2. Draw a ballot at random.
 
3. Draw additional ballots at random until there is one that has at least one ranked candidate in common with the first ballot, or until all ballots are exhausted.
 
4. If the ballots are not exhausted, then the winner is the candidate that is ranked in common on the first and last drawn ballots which is ranked highest on the first ballot.
 
5. Otherwise .... [various possibilities for this unlikely case].
 
 
This variation makes it more likely that your ballot will play the second role, that of supplying a list of approved possibilities, than the first role, picking the top candidate from the approved list.  So this variation discourages bullet votes slightly more strongly than the two ballot version.

Does it still satisfy all of the nice properties?

Forest

 



Jobst wrote ...
......
Another modification of Random Ballot that encourages election of good
compromise candidates, using ranked ballots (instead of approval ballots
as in AP-RB):

1. Ranked ballots with truncation.
2. Draw two ballots at random.
3. If no candidate is ranked on both, elect the one ranked top on the
first ballot.
4. Otherwise, elect from those candidates ranked on both ballots the one
ranked topmost on the first ballot.

In the example with true preferences and utilities

a times  A:1 > C:alpha > B:0
b times  B:1 > C:beta  > A:0

and ballots

a-d times  A
d   times  A>C
e   times  B>C
b-d times  B

the winning probabilities are A:a-de, B:b-de, C:2de, so that the
expected utilities are

a+(2alpha-1)de for the A-supporters and
b+(2beta -1)de for the B-supporters.

That is, no matter how many of the A-supporters rank C 2nd, it is
advisable to do so for all B-supporters if and only if beta>1/2, and
similarly for all A-supporters is alpha>1/2. In particular, no
prisoners' dilemma arises! Since it encourages *full* cooperation
instead of only partial cooperation, this method leads to even better
social welfare than AP-RB.

Like AP-RB, this method is monotonic and cloneproof, and any proportion
of p% of the voters can distribute p% of the probability as they like
(by bullet-voting accordingly). On the other hand, the approval winner
need not get a winning probability proportional to her approval
proportion as it was the case with AP-RB.

Again, this method can be safeguarded against dangerous candidates by
elimination all who are stricken-out by more than 75%.

Yours, Jobst




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