Strategic Nomination - Independence of Clones

Independence of Clones

In order to simplify the issue, academic attention sometimes focuses on a specific kind of strategic nomination: the kind that involves clones. Clones in this context are candidates such that every voter ranks them the same relative to every other candidate, i.e. two clones of each other are never both strictly separated by a third member in the preference ranking of any voter, unless that member is also a fellow clone. Trivially, the set of all candidates makes up a clone set as does every subset consisting of one candidate. It thus makes no sense to just call a candidate a clone unless it is in the context of a clone set which contains at least two elements and is a proper subset of the set of all candidates.

It is desirable for the outcome of an election to be essentially unaffected by the addition or removal of clones. Adding or removing a clone candidate should only change the winner if the old winner, the new winner, and the candidate added or removed are all clones of each other. A voting system that satisfies this criterion is considered "independent of clones". Independence of clones was first formulated by Nicolaus Tideman.

The existence of a true clone set in a public election is improbable, as it only takes one voter to break up a clone set. As a result of this fact, some argue that the independence of clones criterion has limited relevance to real-world elections. This criterion is still used in academic analysis, however, as many voting systems behave similarly when handling both clones and closely affiliated candidates with common supporters.