On 1.10.2012, at 5.05, robert bristow-johnson wrote: >> But in typical political elections top cycles of 4 should be very rare. > > and my understanding is that Schulze, RP, and Minmax all elect the same > candidate for case of a simple 3-choice cycle and, of course, they all elect > the same candidate when there is no cycle.
Yes, with three candidates the choice depends only on the used comparison method, i.e. margins, winning votes etc. If there is a fourth candidate outside the 3-choice top cycle, Minmax can elect also the fourth candidate if the worst losses of all the cycled candidates are worse than that of the fourth candidate. This is also a very rare case. The justification behind that choice is that the level of opposition against the chosen winner (in favour of any single one of the competitiors) will be lowest this way. In Minmax(margins) the fourth candidate would also need the least amount of additional votes to become a Condorcet winner. Juho
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