On 05/11/2012 11:31 PM, Michael Ossipoff wrote:
Also, no one has suggested that any method other than Approval can meet
Strong FBC.
Antiplurality meets strong FBC.
Every rated method that:
- gives each candidate a score based on a function f(x) where x is the
aggregation of ratings for that candidate (and nothing else),
- the candidate with highest score wins, and
- rating a candidate higher never makes him lose and rating him lower
never makes him win,
meets strong FBC. This includes Range and MJ.
Every weighted positional system that gives the first n candidates in a
ranking equal points, for n >= 2, meets strong FBC.
The classical nondeterministic methods (Random Winner, Random Pair) meet
strong FBC.
I'll look into the u/a definition later.
By the way, speaking of Approval and criteria, it's been some time since
I looked at Arrow's criteria, but it seems to me that the only
one of those that Approval fails is a _rules_ criterion, as opposed to a
_results_ criterion. It's a "criterion" that requires that the method be
a rank method.
I have no use for rules "criteria".
Those who'd like more granular control over their ballots - to draw in
true grayscale or color rather than having to dither down to black and
white - may feel differently.
But Approval might fail some of Arrow's results criteria, too. If
preference refers to a voter's actual preference rather than what's
stated on the ballot (i.e. a preference criterion rather than a
votes-only criterion), then Approval fails Majority. It is not clear
whether to refer to Majority based on actual preference or on the vote
alone, however. See
https://en.wikipedia.org/wiki/Majority_criterion#Application_of_the_majority_criterion:_Controversy
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