[EM] CR style ballots for Ranked Preferences

[Forest Simmons]

Recall that Ranked Preferences refers not only to the ranking of the
candidates but also to a ranking of the strength of preferences, so for
example the following candidates are ranked in alphabetical order but the
preferences are ranked in reverse alphabetical order (roughly speaking)
with the highest ranking preferences being those of other candidates over
D:

A > B >> C >>> D

A Cardinal Ratings style ballot with seven levels would be sufficient to
encode this information in a natural way:

Candidate  Rating
A          6
B          5
C          3
D          0

The gap sizes in the ratings correspond to the strengths of the
preferences.

In general, for N candidates a scale of zero to N(N-1)/2 is barely
sufficient to encode the relative preference strengths in this way.

For ten candidates that would require a scale of zero to 45.

A scale of zero to 100 would suffice for fourteen candidates, but not for
fifteen.

There are other more efficient ways to encode the same information, but
none that I know of that are more natural or simple for the
unsophisticated voter to use effectively. 

I am interested in ideas from other EM list readers for both
(1) other ballot styles for encoding Ranked Preference information, and
(2) election methods based on Ranked Preference information, especially
methods that satisfy the Condorcet Criterion, and preferably methods that
do not encourage insincere strategic ranking of the candidates.

Strategic ranking of the preference strengths in order to avoid rank
reversals among the candidates is the name of the game for the
sophisticated voter.  That's OK, in my opinion.

I have my ideas along these lines, and have already posted some of them in
one form or another, not necessarily under the heading of Ranked
Preferences.  But I want to hear your ideas before I prejudice you too far
one way or the other with mine.

In particular, given Ranked Preference information, how would you modify
Ranked Pairs in order to take advantage of the extra information?

The right election method based on Ranked Preferences might be acceptable
to those who believe that preferences are more meaningful and reliable
than numerical ratings per se. Maybe they wouldn't object to CR ballots if
the only information extracted from the ballots was the order of
candidates and order of preference strengths, i.e. the Ranked Preference
information.

Now, one last question, which I hope isn't too big of a can of worms:

Suppose that we have the following ballot with fully ranked preferences:

A >> B >>> C > D

Obviously the weakest preference is C > D and the next weakest is A >> B.

But how about the other four preferences (the ones that straddle the
triple ">>>" ) ?

Should they all be considered as equal in strength, as in Dyadic
Approval, or should some of them be considered stronger than B >>> C ?

This question comes up naturally because in Ranked Pairs, for example,
there are N(N-1)/2 pairs (N being the number of candidates) not just the
N-1 pairs of adjacent candidates on one ballot's ranking of the
candidates.

I will hold my opinions in reserve until I have heard yours.


Forest