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:
“It is my duty to prevent, through the independence of Cuba, the U.S.A. from spreading over the West Indies and falling with added weight upon other lands of Our America. All I have done up to now and shall do hereafter is to that end.... I know the Monster, because I have lived in its lair—and my weapon is only the slingshot of David.”
—José Martí (1853–1895)
“... we’re not out to benefit society, to remold existence, to make industry safe for anyone except ourselves, to give any small peoples except ourselves their rights. We’re not out for submerged tenths, we’re not going to suffer over how the other half lives. We’re out for Mary’s job and Luella’s art, and Barbara’s independence and the rest of our individual careers and desires.”
—Anne O’Hagan (1869–?)
“I don’t know what immutable differences exist between men and women apart from differences in their genitals; perhaps there are some other unchangeable differences; probably there are a number of irrelevant differences. But it is clear that until social expectations for men and women are equal, until we provide equal respect for both men and women, our answers to this question will simply reflect our prejudices.”
—Naomi Weisstein (b. 1939)
“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)