[EM] Re: Richard's criteria

[Richard Moore]

I wrote:
> Mike,
> 
> Thanks for feedback. I will address as many points as I can tonight, 
> but I will have to get back later with revised versions of the first 
> four criteria.

Actually I was able to get to those revisions tonight also. It's 
possible that I've still made errors in the interpretation of the 
electionmethods.org wording, but I hope not. I'm sure I'll hear from 
Mike if I did.

In the new definitions, I use the following terms:

"Collapsing", meaning two (or more) candidates that are not voted 
equal on an original ballot being voted equal on the modified ballot. 
It includes truncation as the special case where no candidate is voted 
lower than the two (or more) candidates involved in the collapsing 
transformation on the modified ballot. Where truncation is allowed, 
but general collapsing is not, I specify "truncation".

"Spreading", meaning the opposite of collapsing: two (or more) 
candidates that are voted equal on an original ballot not being voted 
equal on the modified ballot. I include the caveat that no order 
reversal is allowed to result from spreading; i.e., if A > B on the 
original ballot, then B > A is not allowed on the modified ballot.

SFC: If X is the Condorcet winner of an election, and X is voted over 
Y on a majority of the ballots, then however the ballots outside that 
majority are modified through collapsing, Y cannot win.

GSFC: If X is in the Smith set of an election and Y is not in the 
Smith set, and X is voted over Y on a majority of the ballots, then 
however the ballots outside that majority are modified through 
collapsing, Y cannot win.

SDSC: If X is voted higher than Y on a majority of the ballots, then 
either Y does not win, or ballots in that majority can be modified 
through any combination of truncation and spreading (without order 
reversal) in such a way that Y does not win.

WDSC: If X is voted higher than Y on a majority of the ballots, then 
either Y does not win, or ballots in that majority can be modified 
through any combination of collapsing and spreading (without order 
reversal) in such a way that Y does not win.

  -- Richard