Irrelevant Alternatives

In other words, because some voters changed their minds about C, the rankings of A and B were reversed. Intuitively, the ranking of A and B should depend on how voters view A and B and not on what they think of some other alternative. (We call C an irrelevant alternative in ranking A and B.)

So where are we so far? Although we might find quite a long list of "fair" criteria for a voting method, the three mentioned so far are:

  1. There is no dictator.

    2.  
  2. If every voter prefers A to B then so does the group.

    3.  
  3. The relative positions of A and B in the group ranking depend on their relative positions in the individual rankings, but do not depend on the individual rankings of any irrelevant alternative C.
Before adding any more criteria, we can ask if any of the three methods we have seen so far satisfy just this short list of conditions.