[EM] Re: Richard's criteria

[Richard Moore]

Last night I wrote that I would add a provision to my definitions to
ensure they apply to more than rank methods. Unfortunately I became so 
focused on interpreting the allowable strategies in the original 
definitions that I forgot to include that phrasing. I realized my 
error only after shutting down for the night. D'oh!

The condition I initially suggested, "The method allows full ranking 
of all candidates", is too strong. Something more complicated is 
required. Here are the modified definitions:

SFC:
For any set of ballots that either are ranked ballots or allow 
rankings to be uniquely calculated, let X be the Condorcet winner of 
this set of ballots. Let Y be any other candidate. Transform all of 
the ballots into ballots that can be accepted in the method under 
consideration, subject to the following two constraints: (1) If X is 
voted higher than Y on a ballot, then for any two candidates A and B, 
A is voted higher than B on the new ballot if and only if A is voted 
higher than B on the original ballot, and (2) If X is not voted higher 
than Y on a ballot, then for any two candidates A and B, A is voted 
higher than B on the new ballot only if A is voted higher than B on 
the original ballot. However the ballots are transformed subject to 
these constraints, Y cannot win an election with the resulting set of 
ballots in the method under consideration.

GSFC:
For any set of ballots that either are ranked ballots or allow 
rankings to be uniquely calculated, let X be a candidate in the Smith 
set of this set of ballots. Let Y be a candidate outside of that Smith 
set. Transform all of the ballots into ballots that can be accepted in 
the method under consideration, subject to the following two 
constraints: (1) If X is voted higher than Y on a ballot, then for any 
two candidates A and B, A is voted higher than B on the new ballot if 
and only if A is voted higher than B on the original ballot, and (2) 
If X is not voted higher than Y on a ballot, then for any two 
candidates A and B, A is voted higher than B on the new ballot only if 
A is voted higher than B on the original ballot. However the ballots 
are transformed subject to these constraints, Y cannot win an election 
with the resulting set of ballots in the method under consideration.

SDSC:
For any set of ballots that either are ranked ballots or allow 
rankings to be uniquely calculated, transform all of the ballots into 
set ballots that can be accepted in the method under consideration, 
subject to the following two constraints: (1) If X is not voted higher 
than Y on a ballot, then for any two candidates A and B, A is voted 
higher than B on the new ballot if and only if A is voted higher than 
B on the original ballot, and (2) If X is voted higher than Y on a 
ballot, then for any two candidates A and B, if A is voted higher than 
B on the original ballot then either A is voted higher than B on the 
new ballot, or no candidate is voted lower than A or B on the new 
ballot and A is voted equal to B on the new ballot. However the 
ballots are transformed subject to these constraints, Y cannot win an 
election with the resulting set of ballots in the method under 
consideration.

WDSC:
For any set of ballots that either are ranked ballots or allow 
rankings to be uniquely calculated, transform all of the ballots into 
set ballots that can be accepted in the method under consideration, 
subject to the following two constraints: (1) If X is not voted higher 
than Y on a ballot, then for any two candidates A and B, A is voted 
higher than B on the new ballot if and only if A is voted higher than 
B on the original ballot, and (2) If X is voted higher than Y on a 
ballot, then for any two candidates A and B, if A is voted higher than 
B on the original ballot then A is voted higher than or equal to B on 
the new ballot. However the ballots are transformed subject to these 
constraints, Y cannot win an election with the resulting set of 
ballots in the method under consideration.

  -- Richard