[EM] Truncation criticized by IRVists

[Michael Rouse]

Here is an idea to prevent strategic truncation and ties (while still
allowing people to truncate or tie if they truly don't know/don't care/are
too lazy to choose).

Let's assume the following:

1. Voters have no preference between candidates they truncate or tie -- if a
person votes for Candidate A and B but leaves C and D off the list, then it
does not matter to the voter whether C is chosen ahead of D or vice versa.

2. If we can increase the value of one person's vote without decreasing the
value of another's, we get a net gain in social utility. For example, if
voter A does not have a preference between candidate C or D, but voter B
prefers C to D, the C should be selected ahead of D.

3. We get a net gain in social utility if we replace truncations and ties
with the order preferred by the majority of voters who expressed a
preference. As an example, suppose we had six candidates: A, B, C, X, Y, and
Z. One voter ranks them ABC and truncates (XYZ). Another ranks them AXBYCZ.
We would increase overall happiness if we then changed the "no preference"
vote to the order XYZ -- in other words, the first voter would now have
ABCXYZ and the second would still have AXBYCZ.

This can be done by looking at each pair of candidates. If more people
prefer Candidate A to Candidate B in a pairwise comparison, then A would be
placed ahead of B on the ballots of everyone who showed no preference.
Continue comparing pairs of candidates until the entire preference list is
complete for all voters, then use the complete list in whichever voting
method you prefer.

There are several nice qualities for this method. It gives people a positive
incentive for ranking everyone they have a preference for, but doesn't
punish them if they truly do not have a preference. It increases the social
utility, the "happiness" of the electorate as a whole. It increases the
number of votes for the winner or winners, giving them more of a mandate. It
makes it easier to calculate who the winner is in various voting methods. My
guess is that it would also make circular ties less likely, because there is
a good chance that one or two of the candidates would be ranked even on a
truncated ballot, making the placement of the remaining candidates easier.

One possible problem would be if a voter left three or more candidates
unranked and these candidates formed a circular tie with voters who had a
preference. In that case, you might run an initial pass and order all the
ballots possible, then use the new ballot rankings and see if it will
resolve circular ties. If it doesn't, use your favorite circular tie-breaker
and then finish the ballot rankings. Then you can use the full ballot
rankings and run it through your favorite election method.

Michael Rouse
mrouse at internetcds.com