[EM] Arrow's axioms

[wclark at xoom.org]

Kevin Venzke wrote:

> But if CR can't meet IIA in a meaningful, practical sense,
> I don't see the argument in favor of CR over ranked methods.

The deeper points to consider are that CR isn't the only rating method,
and ratings aren't the only alternative to rankings.

Forest Simmons outlined several examples of such alternatives in this
recent post:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-March/012298.html

I'm currently playing around with models for Normalized Pairwise Ratings
(what I was previously calling "Cardinal Condorcet") in which pairwise
comparisons between candidates are made and a winner determined as in
regular Condorcet -- except that rather than comparing the number of
ballots in which A was ranked/rated higher than B, the ratings themselves
are first normalized for each ballot (so that the higher-rated of the two
candidates is given the maximum value) and then these normalized values
are summed.

This removes the incentive to simply rate each candidate at the minimum or
maximum value, since the normalization transformation effectively does
this already.

For example, if I voted as follows (on a 0-1 scale:)

A:1.0
B:0.8
C:0.0

Then my normalized pairwise ratings might be:

A vs. B: 1.0 vs. 0.8
B vs. C: 1.0 vs. 0.0
C vs. A: 0.0 vs. 1.0

(The B vs. C comparison illustrates the lack of incentive to strategize by
rating at the extremes.)

Regular Condorcet would treat the A vs. B comparison as if the ratings
were 1.0 vs. 0.0, which doesn't accurately reflect the real strength (or
in this case lack of strength) of my preference for A over B.

I suspect that some modified version of Normalized Pairwise Ratings might
turn out to be equivalent to the Dyadic Approval method Forest describes
in more detail here:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2001-April/005741.html

and which is further discussed (in relation to CR) here:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2001-August/006564.html

-Bill

-- 
Ralph Nader for US President in 2004
http://votenader.org/