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

[Paul Kislanko]

Monotonicity is a requirement of any counting method that depends upon only
the summed tallies from precincts being counted at higher summary (district,
state...) It is quite different (possibly even opposite) the reinforcement
criterion as stated below. I think that you may be right that it "doesn't
matter" to a certain extent, because Condorcet-based counting methods only
fail if all ballots are not considered in the same counting; in other words,
BY DEFINITION to conduct a condorcet-based election you can't break the
electors into subsets and do separate counts for each subset without
violating either the rules for condorcet elections or monotonicity.

Trying to simplify the above: "separate elections each of which is condorcet
compliant cannot be combined to form a different condorcet-compliant
election." So if you're using a condorcet method, you can't use district
results to form state results, or state results to form national results.
But that is not a problem at all if you don't - if every ballot from all
precincts in the district is used to form the district result, and every
ballot cast in any precinct is used to form the national result, then
monotonicity is just an academic abstraction.

If the process is "here are the condorcet results for this precinct, to
calculate that for the district here are the ballots to be combined with
ballots from other precincts" and "here is the result for the district, to
calculate the state's results use all these ballots from all precincts in
all districts" and so on, whether the method satisfies monotonicity or not
is irrelevant. If the process is just "here are the precinct/district/state
winners but you don't get the ballots" then monoticity is an absolute
requirement.

I think that made sense. If not, it's because I'm following US College
Football bowl games instead of thinking.

-----Original Message-----
From: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Steve
Eppley
Sent: Tuesday, January 01, 2008 3:16 PM
To: election-methods at electorama.com
Subject: [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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