[EM] Simpson-Kramer Method

[Markus Schulze]

Dear Mike,

the assumption that each voter casts a complete ranking
of all candidates is on page 5 (i.e. in the introduction)
of their paper (Jonathan Levin, Barry Nalebuff, "An
Introduction to Vote-Counting Schemes", Journal of
Economic Perspectives, vol. 9, no. 1, pp. 3--26,
Winter 1995):

> For our purposes, we assume that voters rank all the
> candidates on their ballots, and do not score candidates
> as ties. Many theorists have addressed the issue of how
> to deal with voters who either fail to rank some candidates,
> or rank two or more candidates as tied. Because of the
> immediate complications these issues generate, we try to
> avoid raising them in the general discussion.

The description of the Simpson-Kramer method is on page 15
(i.e. in section 10) of their paper:

> The Simpson-Kramer min-max rule adheres to the principles
> offered by Condorcet in that it emphasizes large majorities
> over small majorities. A candidate's "max" score is the
> largest number of votes against that candidate across all
> head-to-head matchups. The rule selects the candidate with
> the minimum max score. A Condorcet winner will always be a
> min-max winner. When there is a cycle, we can think of the
> min-max winner as being the "least-objectionable" candidate.

Therefore, it is clear that Levin and Nalebuff only want
to say that they don't want to discuss partial individual
rankings and not that an election should be null and void
when some voters cast only partial individual rankings.

Markus Schulze