Monotonicity comments

[Richard Moore]

Forest Simmons wrote:

> See Martin Harper's treatment of monotonicity in dyadic ballots in his
> EM posting dated 4 Apr 2001 at the URL:
> 
> http://groups.yahoo.com/group/election-methods-list/message/7165
> 
> 
> Forest


I'd say things are slightly complicated by the fact that the same ballot
type, dyadic, could be used in Approval, CR, and Borda. All three are
monotonic (by CR, I am referring to the method that elects the candidate
with the highest total, or highest mean, rating; CR ballots can be used
in ways that aren't monotonic). Yet, you would have to define "favoring
X" differently in each case.

  - In Approval, a change favors X if it moves X from a position to the
    right of the cutoff point (which is, probably, the longest ">>...>"
    string) to a position to the left of the cutoff point.
  - In CR, whatever formula is used to get ratings out of the ballots
    would be used to evaluate X's margin vs. the other candidates before
    and after the change.
  - In Borda, a change favors X only if X's position moves to the left
    of some candidate that X was previously to the right of.

  -- Richard