[EM] please read quick question about Condorcet

[Forest Simmons]

On Thu, 18 Mar 2004, James Green-Armytage wrote:

>
> Hi folks,
> 	I was just wondering what sort of Condorcet tally methods have been
> proposed to process ballots that are not only ranked, but where some
> preferences are indicated as being stronger than others. For example, a
> vote may look like this:
>
> Kucinich > Nader >> Dean >> Kerry > Edwards >> Clark >>> Lieberman >>>>
> Bush
>
> 	For example, I have heard of one where, if there is a majority rule
> cycle, the lowest-priority preferences on each ballot are changed to
> equalities. I'm wondering if anything else has been proposed along these
> lines.


Despite the many doubts expressed by various list members there are a wide
variety of methods that make effective use of the various preference
strengths.

We have been reminded of several of them in the last few days, most
recently by Chris Benham.

Here's another one which was my first suggestion for the use of dyadic
ballots, which I called "Dyadic Approval."  At that time I offered it as a
compromise between normal Approval and traditional Condorcet methods.

A pairwise matrix is constructed from each ballot as explained below, and
then the sum of the pairwise matrices is processed according to the rules
of Ranked Pairs, Beat Path, or any other Condorcet method that takes a
pairwise matrix as input.

Suppose that ballot B shows a preference of candidate i over candidate
j. Let M be the maximum strength of any preference on the dyadic ballot B,
and let m be the maximum strength among all preferences straddled by
candidates i and j.  Then the entry in row i and column j of the pairwise
matrix for ballot B is m/M.

Why not just use top strength for all preferences?  Because on dyadic
ballots only one preference of top strength is allowed, and on each side
of a preference of strength k only one preference of strength (k-1) is
allowed. [This constraint yields the binary structure of the ballot.]


If my ballot reads  Nader > Kucinich >> Kerry > Bush,

then my ballot will count as full preferences, both Nader and Kucinich
over both Kerry and Bush; along with half preference of Nader over
Kucinich and Kerry over Bush.


On the other hand if my ballot reads  Nader > Kucinich >> Kerry >>> Bush,

then my ballot will count as full preferences Nader over Bush, Kucinich
over Bush, and Kerry over Bush; as two-thirds preferences, Nader and
Kucinich over Kerry; and as one third preference, Nader over Kucinich.


After this suggestion Martin Harper came up with another method based on
dyadic ballots.  He called his method "Universal Approval."  I won't take
the time to describe it here, since it can be located in the archives by
searching the rare title "Universal Approval" along with the name Martin
Harper.  Martin's introduction included proof sketches of some of the nice
properties of Universal Approval.


Forest


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