[EM] Method definitions

[Markus Schulze]

Dear participants,

a few months ago I wrote that Condorcet proposed a Copeland
method. Now I found a translation by McLean of that paper by
Condocet. McLean translates this paper as follows (Iain McLean,
Fiona Hewitt, "Condorcet," Edward Elgar Publishing, 1994, page
176-177):
> To compare just 20 candidates two by two, we must examine
> the votes on 190 propositions, and for 40 candidates, on 780
> propositons. Besides, this will often give us an unsatisfactory
> result; it may be that no candidate is considered by the
> plurality to be better than all the others, and then we would
> have to prefer the candidate who is just considered better
> than a larger number; and when several were considered better
> than the same number of candidates, we would have to choose
> the candidate who was either considered better by the greatest
> plurality, or worst by the smallest plurality. However, this
> preference is sometimes difficult to determine: the general
> rule would be complicated and awkward to put into practice.
> This form of election is therefore only really suitable when
> we do not need to make an immediate choice, or when new electors
> can be quickly summoned if the elections is undecided; moreover,
> even this last solution does not assure success, but makes it
> more probable.

McLean interprets this paper by Condorcet as follows (page 45-46):
> If there is a cycle, we must choose among the candidates who are
> 'considered better than the same number of candidates' (those in
> the top cycle, in modern jargon). We should choose 'the candidate
> who was either considered better by the greatest plurality, or
> worst by the smallest plurality'. Well, which? These two-choice
> rules may give different results.

It seems to me that McLean interprets Condorcet's proposal as
Smith//plurality or Smith//anti-plurality.

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de