Strategic Nomination - Independence of Irrelevant Alternatives

Independence of Irrelevant Alternatives

If the winner of an election were not running in the first place, then obviously someone else would have won instead. Similarly, if a candidate gets "added" to an election, it becomes possible for the new candidate to win. If these are the only cases in which a change in the candidate set leads to a different election outcome, then the voting system is independent of irrelevant alternatives and therefore immune to strategic nomination.

Independence of irrelevant alternatives, however, is a very hard property for a voting system to satisfy. This is illustrated by the following example of Condorcet's voting paradox:

• 40 voters preferring candidate A to B to C
• 35 voters preferring candidate B to C to A
• 25 voters preferring candidate C to A to B

With the above preferences and whatever candidate an election method chooses as a winner, another candidate can always secure a majority of votes against that winner by removing the third candidate. Since the absence of any candidate would leave the impression that the preference of the group of voters as a whole is a clear majority when by definition it is not when we consider the third candidate, one can argue that none of these candidates are actually "irrelevant."

The candidates in the example above form a cycle known as the Smith set - their combined presence provides conflicting information (both to the election system as well as to observers) about who the greatest candidate is. Strategic nomination, then, involves hiding this information from the voting system by excluding one of the candidates. Because of this strange relationship between the candidates and the voters, strategic nomination through this manner is doubtful as it becomes very much a question of whether the presence or absence in an election of a potential "cycle-maker" (provided one exists and can be found) can be decided by those who seek to gain from it.