[EM] u/a for criteria. u/a FBC. Voter's Choice. SSCS. Strong FBC.

[Kristofer Munsterhjelm]

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