[Election-Methods] Why monotonicity? (was: Smith + mono-add-top?)
SEppley at alumni.caltech.edu
Tue Jan 1 13:15:38 PST 2008
Diego Santos wrote:
> This method meets mono-add-top and
Why care about monotonicity criteria, apart from the fact that many
people have written about them? Aren't they just aesthetically pleasing
"consistency" criteria, like the Reinforcement criterion satisfied by
the Borda method and failed by all Condorcetian methods?
Reinforcement: Candidate X must be elected if
the voters can be partitioned into two or more
groups that each elect candidate X.
(Don Saari, a proponent of Borda, annoyingly uses the generic name
Consistency for the Reinforcement criterion.)
Reinforcement is unimportant because the rules can easily be set to
prevent a minority from deciding whether to partition the voters. This
would prevent minorities from manipulating the outcome, in scenarios
where the voting method fails reinforcement.
Are monotonic methods less manipulable than non-monotonic methods? I've
never heard any evidence of that.
Clone independence is a consistency criterion too. But it's much more
important than most consistency criteria, since a small number of people
can manipulate by strategically nominating clones if the method fails
clone independence. (It would be undesirable to set the rules so that
nomination requires a huge number of supporters.) In public elections,
manipulation by strategic nomination is a more serious problem than
manipulation by large numbers of strategizing voters, in my opinion.
There's little evidence of strategic voting in public elections; to the
contrary, empirical evidence shows non-strategic voting behavior. Mike
Alvarez of Caltech served as expert witness on this when the California
Supreme Court considered the constitutionality of the ballot proposition
that had "opened" primary elections to voters registered outside the
party. (The court eventually ruled the proposition unconstitutional,
calling the political parties "private organizations" that cannot be
forced to count votes of voters outside the party. The solution to
force open the primaries, I think, is to pass another ballot proposition
that denies public funding of closed elections.)
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