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 satisfy the latter.
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."
Voting systems which are not independent of irrelevant alternatives suffer from strategic nomination considerations.
Some text of this article is derived with permission from http://condorcet.org/emr/criteria.shtml
