Regretted Turnout. Insincere = ranking.

[Markus Schulze]

Dear participants,

a few months ago, I asked whether there is an election method,
that meets Local Independence from Irrelevant Alternatives and
that meets the No Punishment Criterion, i.e., that guarantees,
that a sincere voter is never punished for going to the polls.
(If it is not possible to create an election method,
that never rewards tactical voters, then -to my opinion- the
next question is whether it is possible to find an election
method that never punishes sincere voters.)

Unfortunately, I have just found an article that proves, that
the Condorcet Criterion and the No Punishment Criterion are
incompatible. The article is "Condorcet's Principle Implies
the No Show Paradox" by Herve Moulin (Journal of Economic
Theory, vol. 45, p. 53-64, 1988). The author uses the name
"No Show Paradox" but he means the No Punishment Paradox.

No Show Paradox:

   Suppose, candidate X does _not_ win the election.
   Then it can happen that a set of additional voters, who vote
   identically and who strictly prefer every other candidate to
   candidate X, change the winner from another candidate to
   candidate X.

No Punishment Paradox:

   Suppose, candidate X does _not_ win the election.
   Then it can happen that a set of additional voters, who vote
   identically and who strictly prefer candidate Y to
   candidate X, change the winner from candidate Y to
   candidate X.
   
Markus Schulze