[Election-Methods] Why monotonicity? (was: Smith + mono-add-top?)

Steve Eppley 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.)

--Steve Eppley

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