Independence of irrelevant alternatives

In voting systems, independence of irrelevant alternatives is the property some voting systems have that, if one option (X) wins the election, and a new alternative (Y) is added, only X or Y will win the election.

A less strict property is sometimes called local independence of irrelevant alternatives. It says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the Smith set.

All Condorcet methods fail the former criterion, but some (e.g. Cloneproof Schwartz Sequential Dropping) satisfy the latter.

Borda count, Coombs' method or Instant-runoff voting do not meet either criterion.

An anecdote which illustrates a violation of this property has been attributed to Sidney Morgenbesser:

After finishing dinner, Sidney Morgenbesser decides to order dessert. The waitress tells him he has two choices: apple pie and blueberry pie. Sidney orders the apple pie. After a few minutes the waitress returns and says that they also have cherry pie at which point Morgenbesser says "In that case I'll have the blueberry pie."

However, this anecdote improperly compares the preferences of a large population to a single person, while a large population can reasonably have more confused preferences than a single person.

Voting systems which are not independent of irrelevant alternatives suffer from strategic nomination considerations.

The independence of irrelevant alternatives criterion, however, is a flawed criterion. There are cases where failing the criterion is expected rational behavior of a voting population. For example, if a population slightly preferred candidate"B" to candidate "A", but candidate "A"'s supporters were far more loyal, then an introduction of a third candidate could split B's support far more than A's, leading to a win by A. In cases where one candidate's supporters feel they are compromising far more than the other candidate's supporters do, failing IIAC is not a flaw. In other words, IIAC makes an implicit assumption that all voters feel equally represented by their choices, which is a poor assumption to make in practical terms. Interestingly, this also makes Arrow's Impossibility Theorem fairly irrelevant.

Condorcet methods do not fail the IIAC when they have a single Condorcet Winner both before and after the introduction of the new candidate. In other words, the IIAC can never replace one Condorcet Winner with another.

Some text of this article is derived with permission from http://condorcet.org/emr/criteria.shtml

See also

• Spoiler effect
• List of democracy and elections-related topics