Approval Voting is better without runoffs

Most of my research deals with various voting systems and how they can be manipulated by insincere voters.  For many reasons, I think approval voting is the best voting system for single-winner elections.  That's why I have supported The Center for Election Science.  Unfortunately, they've been inconsistent in their proposals for voting reform in different American cities.

Here's a simple example that shows why I don't recommend using runoffs with approval voting:  Say 100 voters are voting in an approval election with a runoff, and they have the following sincere preferences over three candidates A, B and C:

• 45%:  A > B > C
• 20%:  B > C > A
• 35%:  C > B > A

Given these preferences, B would win an A/B runoff, C would win an A/C runoff and B would win a B/C runoff.  A would not win any runoff.  So, if all voters are at least roughly aware of the other preferences and are strategic, we may reasonably assume the following:

• The A>B>C voters want an A/B or B/C runoff.
• The B>C>A voters want an A/B or B/C runoff.
• The C>B>A voters want an A/C runoff.

Therefore, the dominant approval strategies in the general election are

• A>B>C voters:  B only
• B>C>A voters:  B only
• C>B>A voters:  A and C

Then, depending on the runoff rules, either B wins immediately or wins the runoff.  (Voting in the runoff itself is straightforward; insincerity is never rewarded.)  So the sincere Condorcet winner wins the election at equilibrium.  What's wrong with this result?  Well, the required strategy is complicated, which would amplify the power of the most sophisticated voters.  But, more importantly, the best strategies for 80% of the voters turned out to be strongly insincere:  They had to approve one candidate without also approving all candidates they preferred, destroying what is one of approval voting's most desirable properties.

Of course, this reasoning applies equally to range (or score) voting, which is why I don't support STAR voting, though it's certainly better than IRV (often now known as "RCV").