[EM] Top Three Runoff

[Forest Simmons]

If the the Smth set has exactly three members S1, S2, and S3, and one of
them is a sincere CW, then optimal complete information strategy will elect
that Sincere CW by use of any runoff ballot of the form

S1 vs (S2 vs S3)

On the other hand, if the top cycle is sincere, then this runoff ballot may
give S1 a strategic advantage.

So which candidate should get the S1 position on the ballot?

I suggest that S1 be the Classical Condorcet winner ... i.e. the candidate
that wins when the weakest defeat is reversed.

The heuristic for this choice of  S1, the Classical Condorcet choice, is
that when two majorities disagree, the smaller of the two majorities is the
one more likely to be in error.

So why not just elect S1 period, and forget about the possibility of a
sincere CW that is not S1?

Because in that case the heuristic of two competing majorities has no
bearing.  If there is a sincere CW, then all sincere majorities favor it.
In every pairwise contest involving it regardless of what the ballots say.

In other words, when there is a sincere CW, there can be no cycle based on
sincere ballots.

In other words, when there is a cycle in the presence of sincere ballots,
the problem is not mistaken judgment, the problem is insincere voting.

And what motivates insincere voting?

One example is compromise incentive ... as in IRV ... but compromise does
not generally create cycles.... it is more likely to overcome or suppress a
cycle, if anything.

Burial is an easy way for a manipulator to subvert a sincere CW into mere
top cycle membership. The Classical Condorcet heuristic does not address
this issue at all ... it's basically in denial ... treating cycles created
by intentional order reversals as though they were created by honest
misjudgments.

fws
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