[Election-Methods] Why monotonicity? (was: Smith + mono-add-top?)
davek at clarityconnect.com
Tue Jan 1 23:24:48 PST 2008
Before diving into the jungle:
Each voter ranks candidates at as many ranks as chosen, assigning
one or more candidates at each rank.
The above information from all the ballots in a race can be recorded
in an array and analyzed by Condorcet rules to determine winner.
The information can be recorded in multiple arrays such as for
precincts, and the arrays summed for exactly the same results, provided
all the ballot information from all the ballots is included.
Provided cycles are not involved, and all the ballot information is
recorded in two or more arrays, and those arrays indicate the same winner,
then the single full array better indicate that same winner.
Ballots are not part of the analysis, once their information has
been recorded in an array.
This should agree with what the complex words below should be trying to say.
Does not promise what might happen with a sorta-Condorcet election
that extracts other ballot information.
As to "closed" primary elections:
They make sense to me for Plurality general elections.
Defense might be to do away with Primaries for Condorcet general
elections, which get little benefit from such.
On Tue, 1 Jan 2008 17:09:03 -0600 Paul Kislanko wrote:
> 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
> 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
> 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:
>>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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