Condorect sub-cycle rule

David Marsay djmarsay at
Fri Oct 10 08:27:08 PDT 1997

Dear Markus,
			Thank you for your full response (3 Oct 97).
Sorry about the delay.

It seems to me that Condorcet had it about right, but left some 
confusion. I. McLean and F. Hewitt, Condorcet, Edward Elgar, 1994 p29 
cites: "From the above remarks, we can obtain the following general 
rule: each time we are forced to make a decision, we must take all 
the propositions with plurality support in succession, beginning with
those that have most support. As soon as these propositions give a
result, we should take that to be the decision, without taking into
account the less probable propositions which follow."
This seems to agree with your citation of Tideman.

You give some good reasons for thinking that this is a 'good' 
method. I am convinced, but obviously not everyone is.

May I suggest a GMC+ criterion , where the strength of a majority is 

A m-beats Z if there is a set of 
candidates A > B > C ... Z, where each pair-wise majority is of 
strength at least m.
X beats Y when, for some m, X m-beats Y but 
not Y m-beats X.
Now, >> satisfies GMC+ if X beats Y implies X >> Y. That is, >> 
agrees with 'beats'.

This is motivated by reading Condorcet (above). It implies MIIAC, 
GMC and Pareto. It remains to break ties of equal strength. This 
needs to satisfy GITC, but is perhaps not so important (cf your 
Levin/Nalebuff quote).

On its own, GMC+ implies GITC-:

If two candidates are twins and a candidate X wins, and when a twin 
is deleted a candidate Y wins, then neither X beats Y nor Y beats X.

I wonder if it wouldn't be easier to justify Condorcet using GMC+ 
than MIIAC+GITC+GMC+Pareto?

David Marsay

Sorry folks, but apparently I have to do this. :-(
The views expressed above are entirely those of the writer
and do not represent the views, policy or understanding of
any other person or official body.

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