Re: Constitutional amendment: Condorcet/Clone Proof SSD vote tallying
Hallo,
it is necessary to distinguish between the participation
criterion and the monotonicity criterion.
The participation criterion says that a set of additional
voters who strictly prefer candidate A to candidate B must
not change the winner from candidate A to candidate B. The
Condorcet criterion and the participation criterion are
incompatible (Herve Moulin, "Condorcet's Principle Implies
the No Show Paradox," Journal of Economic Theory, vol. 45,
pp. 53-64, 1988). Therefore, this criterion is _of no concern_
when we want to discuss which Condorcet method should be
adopted.
The monotonicity criterion says that (1) when some voters rank
a given candidate A higher without changing the orders in which
they prefer the other candidates then candidate A must not be
changed from a winner to a loser and (2) when some voters rank
a given candidate A lower without changing the orders in which
they prefer the other candidates then candidate A must not be
changed from a loser to a winner.
It is _not_ true that the monotonicity criterion implies
the participation criterion. It is also _not_ true that the
monotonicity criterion implies that when candidate A is
the original winner then adding voters who strictly prefer
candidate A to every other candidate must not change
candidate A into a loser.
Suppose that candidate A is the original winner. Suppose that
an ABC voter is added. Then on the one side this voter is
changed from a voter who ranks all three candidates equally
to a voter who strictly prefers candidate A to every other
candidate; therefore, one could expect that the monotonicity
criterion implies that candidate A stays the winner. However,
this voter is also changed from a voter who ranks candidate B
and candidate C equally to a voter who strictly prefers
candidate B to candidate C. Therefore, the requirement that
the orders in which the other candidates are prefered aren't
changed isn't met.
However, it is true that the monotonicity criterion implies
that when candidate A is the original winner then adding voters
who strictly prefer candidate A to every other candidate and
who rank all the other candidates equally must not change
candidate A into a loser.
Markus Schulze
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