Evaluations: Clones, Teaming and Independence Criteria 1

Independence of Irrelevant Alternatives (IIA)

This criterion requires that the relative ranking of two candidates in the election outcome must only depend on the individual voter rankings of these two candidates. The performance of other candidates or alternatives should be irrelevant. If the addition or withdrawal of any alternative candidate reverses the relative rank order of the two candidates in the outcome rankings, then this independence condition is not satisfied. Similarly, if the rank of the alternative is promoted or demoted in relation to the two candidates, then again to comply with this independence requirement the relative outcome rank order of these two candidates must not change.

Before considering whether GV meets this requirement, this independence criterion is best illustrated using an example. In a particular CHPV election, one hundred voters (V = 100) cast their ranked ballots as given in the table opposite. Using CHPV weightings of 4, 2 and 1 for first, second and third preferences respectively, A beats B and C as the candidate tallies (T) are as follows.

• T_A = (45x4)+(30x1)+(25x2) = 260
• T_B = (45x2)+(30x4)+(25x1) = 235
• T_C = (45x1)+(30x2)+(25x4) = 205

If candidate B had decided to withdraw rather than fight and lose, A should still beat C; at least according to the independence criterion. Rerunning the election with the same relative voter preferences of A over C or vice versa as before - but without B present - produces the 100 ballots as given in the table opposite. The two candidate tallies (using the same first and second preference weightings as earlier) are now as follows.

• T_A = (45x4)+(30x2)+(25x2) = 290
• T_C = (45x2)+(30x4)+(25x4) = 310

Merely by a losing and irrelevant candidate (B) dropping out of the election, the result changes from A beating C to the exact opposite despite each voter maintaining their earlier preference of A over C or the reverse. Clearly, B is not actually an irrelevant candidate but a crucial one for the outcome. As voter preferences relative to A and C have not changed yet the resultant A versus C outcome ranking has, then this example demonstrates that it does not satisfy the IIA condition.

Although this illustrative example shows that CHPV fails the Independence of Irrelevant Alternatives criterion, is there any GV common ratio other than r = 1/2 that satisfies it? In common with all positional voting systems, the answer is no!

• For all r, GV does not satisfy the IIA condition.

When candidates are added or deleted purely to try to overturn the result of an election, this action is called strategic nomination. As GV is not IIA compliant, how are elections affected by such nominations? Under what conditions is it helpful or harmful for a political grouping to add another identical candidate (called a clone) to the contest? Or to remove one or more clones? Since CHPV and GV fail to satisfy IIA, the remainder of this chapter analyses these strategic nominations and related issues and then assesses their performance in response to such behaviour.

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