[EM] Problem solved (for pure rank ballots): ICC & AFB incompatible (essentially)

Markus Schulze Markus.Schulze at alumni.TU-Berlin.DE
Thu Jan 25 08:36:00 PST 2007

Dear Warren,

you wrote (24 Jan 2007):

> Theorem:
> These criteria, for a single-winner voting system based on
> pure-rank-order-ballots, are incompatible:
> (...)
> 6. adding a new candidate to the election whom all voters unanimously
> rank unique-bottom, does not change the winner.
> (...)
> Remark 4.
> Range voting obeys all 6 axioms if all range votes are
> "normalized" so voters (obeying the recommendations for voting on the
> http://rangevoting.org front page) always give the best candidate the
> top score and the worst the bottom score in a 2-candidate election
> [i.e. in practice with voters who are not idiots].
> (...)
> So we have proven a sense in which range is superior to EVERY
> pure-rank-ballot voting method, and using two of the most important
> voting criteria AFB and ICC.

When the votes are normalized, then range voting violates criterion 6.

Markus Schulze

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