robert bristow-johnson wrote:
On Nov 15, 2010, at 8:40 PM, Bob Richard wrote:
On 11/15/2010 4:58 PM, [email protected] wrote:
When majority rules, a 51 percent majority can have their way in
election after election. But what other
possible standard is there for democracy and fairness besides
"majority rule?"
For seats in legislative bodies, proportional representation.
for which STV or a more Condorcet-like ordering (what would the name of
that be? Kristofer Munsterhjelm had a Schulze ordering for Oakland) does
well. here in Vermont we just had an election where for my state senate
district, we voted for 6 out of about 15 and the top 6 vote getters win
seats, but that method sorta sucks.
Condorcet doesn't give proportional representation. If you have an
example like:
51: D1 > D2 > D3 > D4
49: R1 > R2 > R3 > R4
and pick the first four, all the Ds will win.
Proportionality is something different. Quota-based proportionality is
best shown by the Droop proportionality criterion, that if more than x
Droop quotas rank y candidates first, at least the minimum of x and y of
those candidates should be included in the outcome. A Droop quota is
here (number of voters)/(number of seats + 1).
I suspect that one can't have both quota proportionality and
monotonicity, so I've been considering divisor-based proportional
methods, but it's not clear how to generalize something like Webster to
ranked ballots. I did try (with my M-Set Webster method), and it is, to
my knowledge, monotone, but it's not very good in the single-winner
instance.
Perhaps one could make multiwinner Condorcet logic, something like "if
the voter ranks both A and B over both C and D, then consider that a win
of the {A,B} council over {C,D}", and then treat the matrix as a
Condorcet matrix. The problem with this is that while you can't split up
single candidates, you can split up councils - e.g. by voting A>C>B>D -
and it's quite unclear how to score such splits in a "contest of councils".
for me, if it's a single winner: "If a majority of voters select
Candidate A over Candidate B then, if at all possible, Candidate B
should not be elected" is the only sensible rule, because of the
converse is so clearly contrary to the concept of the will of the
majority. Any method that cannot be guaranteed to accomplish that risks
the question: e.g. "Why should Bob Kiss be the mayor of Burlington when
587 more voters expressed on their ballots that they thought Andy
Montroll was a better choice?".
i think you can argue that Condorcet compliant is always preferable out
of point by contradiction. if there is a CW and you elect someone else,
that is always a failure.
I think counterarguments would make use of that the majorities are not
necessarily the same. Those who see no point in Condorcet would say: "if
the leftists prefer A to B and the right-wingers prefer A to C, that's
still short of majority rule".
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