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)
“...there was the annual Fourth of July picketing at Independence Hall in Philadelphia. ...I thought it was ridiculous to have to go there in a skirt. But I did it anyway because it was something that might possibly have an effect. I remember walking around in my little white blouse and skirt and tourists standing there eating their ice cream cones and watching us like the zoo had opened.”
—Martha Shelley, U.S. author and social activist. As quoted in Making History, part 3, by Eric Marcus (1992)
“Long enough I had heard of irrelevant things; now at length I was glad to make acquaintance with the light that dwells in rotten wood. Where is all your knowledge gone to? It evaporates completely, for it has no depth.”
—Henry David Thoreau (1817–1862)
“The last alternatives they face
Of face, without the life to save,
Being from all salvation weaned
A stag charged both at heel and head:
Who would come back is turned a fiend
Instructed by the fiery dead.”
—Allen Tate (1899–1979)