[EM] Methods, and the criteria they satisfy

[Markus Schulze]

Dear Diana,

suppose "d[X,Y]" is the number of voters who strictly prefer
candidate X to candidate Y.

Condorcet:

   Suppose that there is a candidate A with d[A,B] > d[B,A]
   for every other candidate B. Then "Condorcet" says that
   this candidate A must be elected.

Smith:

   The "Smith set" is the smallest non-empty set of candidates
   with d[A,B] > d[B,A] for every candidate A of this set and
   for every candidate B outside this set. "Smith" says that
   the winner must be a candidate of the Smith set.

Participation:

   "Participation" says that adding a set of identical ballots
   on which candidate A is strictly preferred to candidate B
   must not change the winner from candidate A to candidate B.

mono-add-top:
  
   "mono-add-top" says that adding a set of identical ballots
   on which candidate A is strictly preferred to every other
   candidate must not change the winner from candidate A to
   another candidate.

mono-delete-bottom:

   "mono-delete-bottom" says that adding a set of identical
   ballots on which every other candidate is strictly preferred
   to candidate B must not change the winner from another
   candidate to candidate B.

Participation implies mono-add-top and mono-delete-bottom.

Condorcet and participation are incompatible.

Condorcet, mono-add-top, and mono-delete-bottom are compatible.
For example: The MinMax method satisfies Condorcet, mono-add-top,
and mono-delete-bottom.

It is not known whether Smith and mono-add-top are compatible.
It is not known whether Smith and mono-delete-bottom are compatible.

Participation is met e.g. by First-Past-The-Post (FPP), Borda,
Approval, and Woodall's "Descending Acquiescing Coalitions" method:

http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf

Here are examples that my beatpath method and Tideman's ranked
pairs method violate mono-add-top and mono-delete-bottom:

http://groups.yahoo.com/group/election-methods-list/message/12014
http://groups.yahoo.com/group/election-methods-list/message/12051

Markus Schulze