[EM] CR style ballots for Ranked Preferences

[Roy One]

Forest Simmons wrote:
> 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.

Just for clarification, this implies that there must be a > for there
to be a >>, and a >> to be a >>>, etc. Hence the name "ranked
preferences": the relative strengths of the preferences are not
quantified, but it is known which jumps are bigger than others.

The Condorcet Criterion should be modified in some way to take
advantage of the extra information; however, it should not try to
quantify the >s (for example, weight >> twice as much as >). 

One (non-Condorcet) tabulation method I like is what I call Run-Off
Approval. It (or something similar) may have been describe
previously. I am pretty sure it is not summable. For each ballot,
count a vote for each candidate to the left of the Big Jump.
Eliminate all candidates who do not have a vote from a majority of
voters. If more than one candidate is still in contention, repeat the
process, using the biggest remaining jump on each ballot as the
dividing line. If all candidates are eliminated, choose the plurality
winner from the last round.

A Condorcet version of this might be to construct a pairwise matrix
marking only the victories across the Big Jump, and requiring a
quorum of votes to pick a winner. If no winner is found in the first
round, consider the top two biggest jumps on each ballot. And so on.
A liability here is that strategy might have voters choosing
preferences all of the same strength, so that every contest is
counted every round. One solution to that would be to count the
leftmost of any equal-sized jumps as the biggest (making A >> B >> C
> D the same as A >>> B >> C > D).

> Suppose that we have the following ballot with fully ranked 
> preferences:
> 
> A >> B >>> C > D
> 
... 
> 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 ?

It seems logically consistent to count A >>>>>> D, as long as that is
a qualitative assessment, and not a quantitative one. I think that a
pairwise tabulation method will automatically take that into account, though.

=====
------- Roy One --- royone at yahoo.com --- Speaking for myself -------
PCs are great game machines. Macintoshes are great publishing tools.
      If you actually want a computer, get a Unix workstation.
   (It's nice that they put a game machine in every office here.)

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