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

Steve Eppley SEppley at alumni.caltech.edu
Wed Jan 2 07:13:45 PST 2008

Hi Jobst et al,
> Dear Steve!
> Many times I was angry when an otherwise nice looking method turned out not to satisfy basic monotonicity criteria. This is partly because my experience tells me that lacking monotonicity is often an indicator that something else may be problematic with the method, too. Often, non-monotonic methods turn out to have strategic vulnerabilities, too.

But monotonic methods have strategic vulnerabilities too. 
(Gibbard-Satterthwaite theorem, etc.)  Is there evidence that 
monotonicity reduces manipulability?

Can you recall an example where non-monotonicity was related to 
something else problematic with a method?

> Also, it seems difficult to sell a method when you must admit that advancing an option X may actually reduce X's winning probability...

That doesn't seem to be a problem for the Instant Runoff campaign.  ;-)  
Do you recall an example where it was difficult to sell a method due to 
its non-monotonicity?

*All* voting methods violate some desirable properties, making it 
difficult in general to sell election method reform.  Why is 
monotonicity desirable, apart from its aesthetic value and the fact 
that, perhaps due to the "publish or perish" maxim, so many academicians 
have written about it (nearly always without attempting to justify it)?

I'm pleased that the method I like best (MAM) and some other good 
methods are monotonic, but not because I think monotonicity is 
intrinsically important.  It's because of my fear that if a good voting 
method being proposed to the public isn't monotonic, a well-funded 
anti-reform campaign could claim monotonicity is important, leading to a 
technical argument that a poorly funded reform campaign would have 
trouble dealing with.

> Yours, Jobst
>> -----Ursprüngliche Nachricht-----
>> Von: "Steve Eppley" <SEppley at alumni.caltech.edu>
>> Gesendet: 01.01.08 22:15:55
>> An: election-methods at electorama.com
>> Betreff: [Election-Methods] Why monotonicity? (was: Smith + mono-add-top?)
>> Diego Santos wrote:
>> -snip-
>>> This method meets mono-add-top and
>> -snip-
>> --------------------
>> 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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