[EM] ruminations on ordinal and cardinal information

[James Green-Armytage]

Hi Russ,
	Some replies follow, on the subject of cardinal pairwise in comparison
with other ordinal/cardinal methods.
>
>
>What if the two measures disagree about who is defeated? In other words, 
>what if one candidate wins the pairwise race but the other wins the 
>approval race?
>
	The defeat (as determined by the ordinal information) does not change
direction. Nor is the strength of the defeat negative, because only the
votes in agreement with a defeat are looked at when calculating the
strength of the defeat (the winning rating differential). 
	If you're not clear about the rules of cardinal pairwise, please refer to
section 3 of my cardinal pairwise paper, and then let me know if you have
any questions. If you're wondering why it works this way, this is also
explained in the paper, starting in section 6.
http://fc.antioch.edu/~james_green-armytage/cwp13.htm
	Please read also this brief example-based post from 9/22/04, where I
explain the anti-strategic benefits of the "winning rating differential"
approach, as opposed to a "marginal rating differential" approach:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-September/013936.html
	Conveniently enough, this same example from 9/22/04 can be used to
illustrate the strategic vulnerability in your Condorcet-approval hybrid
method.
>
>Your method is interesting, and it may have good properties. However, I 
>don't like the idea of dropping defeats. I think dropping candidates 
>based on approval scores is much easier to explain to the public and is 
>perfectly legitimate. But at this point that's just my opinion.

	I suppose that it would be possible to use an alternate version of
cardinal pairwise that was based on candidate eliminations, but I suspect
that it would be somewhat incoherent, because the logic of cardinal
pairwise is very much grounded in the defeat-dropping principle. The idea
is that when there is a majority cycle, and you have to overrule one of
the defeats, you should overrule the one which voters place the lowest
overall priority on. This is very different from eliminating the candidate
with the lowest cardinal score, and I submit that it is much less
vulnerable to strategic manipulation than such an approach.

my best,
James