[EM] 3 ways of writing certain criteria

[Richard Moore]

Mike wrote:
> By the way, how would you write FBC as a votes-only criterion?
> 
> If you do that, then I'll have to admit that you beat me to it.

It's not 100% correct (it needs to be tweaked to work with methods 
that allow first-place tied rankings), but:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2002-January/007052.html

"A method M passes FBC iff there is no set of ballots S such that,
for some subset R of the set of all candidates, and some candidate
C not found in R, both of the following statements are true for
every ballot B:

	(1) M({B}) = C implies that M(S+{B}) is in R,
	and
	(2) there is a ballot B' for which M(S+{B'})is not in R.

In English:

A method (M) passes FBC if and only if there is no situation (S) such
that a voter can cast a ballot (B') that causes a result that is
different from every result (the candidates in R) that the voter
could get in situation S by voting a particular candidate (C) in first
place."

This was my shortened version of a definition proposed by Forest. 
Forest did include a hypothetical ballot that represented a voter's 
sincere preferences, so it might not qualify as "votes-only", but I 
think this simpler version does.

The point is that sincere voter preferences do not need to be known to 
find out if a method fails the criterion. Equivalence to the voter 
preference-based definition can be seen by hypothesizing a voter who 
has the sincere preferences (i.e., C being the voter's favorite, and 
the result of M(S+{B'}) being preferred by the voter to any of the 
candidates in R) that would make the failure of the criterion a 
betrayal of a favorite; but that voter is extraneous to the criterion 
itself.

In that original post I suggested how the tied rankings problem can be 
addressed. If there is some other point in which it doesn't agree with 
your FBC definition, Mike, let me know where you think the discrepancy 
is, and I'll see if I can improve it.

  -- Richard