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.
Read more about this topic: Strategic Nomination
Famous quotes containing the words independence of, independence, irrelevant and/or alternatives:
“I am savage enough to prefer the woods, the wilds, and the independence of Monticello, to all the brilliant pleasures of this gay capital [Paris].”
—Thomas Jefferson (1743–1826)
“In a famous Middletown study of Muncie, Indiana, in 1924, mothers were asked to rank the qualities they most desire in their children. At the top of the list were conformity and strict obedience. More than fifty years later, when the Middletown survey was replicated, mothers placed autonomy and independence first. The healthiest parenting probably promotes a balance of these qualities in children.”
—Richard Louv (20th century)
“If the Nazis have really been guilty of the unspeakable crimes circumstantially imputed to them, then—let us make no mistake—pacifism is faced with a situation with which it cannot cope. The conventional pacifist conception of a reasonable or generous peace is irrelevant to this reality.”
—John Middleton Murry (1889–1957)
“Clearly, society has a tremendous stake in insisting on a woman’s natural fitness for the career of mother: the alternatives are all too expensive.”
—Ann Oakley (b. 1944)