[EM] strategy-free Condorcet method after all!

[fsimmons at pcc.edu]

Here's a way to incorporate this idea for large groups:

Ballots are ordinal with approval cutoffs.

After the ballots are counted, list the candidates in order of approval.

Use just enough randomly chosen ballots to determine the Lull winner with 90%
confidence: let L(0) be the candidate with least approval.  Then for i = 0, 1,
2, ... move L(i) up the list until some candidate L(i+1) beats L(i) majority
pairwise (in the random sample). If the majority is so close that the required
confidence is not attained, then increase the sample size, etc.

Then with the entire ballots set, apply Jobst's Reverse Lull method:  Start with
candidate A at the top of the approval list.  If  a majority of the ballots rank
A above the Lull winner (i.e. the presumed winner if A is not elected) then
elect A. Otherwise, go down the list one candidate to candidate B.  Let L be the
top Lull winner with approval less than B.  If a majority of ballots rank B
above L, then elect B, else continue down the list in the same way.

In each case the comparison is of a candidate C with the L(i) with the most
approval less than C's approval.

If the decisions are all made in the same direction as in the sample, then the
Reverse Lull winner is the same as the Lull winner, but occasionally (about ten
percent of the time) there will be a surprise.

If a voter knew that her ballot was going to be used in the forward Lull sample,
she would be tempted to vote strategically.  But in a large election, most
voters would not be in the sample, so there would be little point in them voting
strategically.  If sincerity had any positive utility at all, it would be enough
to result in sincere rankings (in a large enough election).