[EM] compromise proposal number one: a most (but perhaps too) simple version

[Jobst Heitzig]

Dear James!

Here's a first, very simple and perhaps too simple version of a method
which distinguishes between more and less important binary preferences:


Each voter answers pairwise comparisons with the possible answers "A>>B"
(strong preference), "A>B" (weak preference), "A=B"
(equivalence/indifference), "A<B", "A<<B", and "A|B" (abstention).
	The defeats are determined by taking both weak and strong preferences
into account, their strengths however are defined via strong preferences
only.
	Then some pairwise method like Tideman, river, or beatpath is applied.


In your example:

26: B >> D  > K
22: B >> K  > D
26: D  > K >> B
 1: D  > B  > K
21: K  > D >> B
 4: K  > B  > D

would give defeats B>D (52), D>K (1), K>B (51), so that K wins.


Here the ballot remains simple, it is not necessary to resolve cycles of
second order, and the strengths of preferences are only compared within
each voter's prefs and not inter subjects.

The methods inherits monotonicity and hopefully many other nice
properties from the base method.

So, do you think it is absolutely necessary to consider more than two
"degrees" of preference?

Yours,
Jobst