Condorect sub-cycle rule
djmarsay at dra.hmg.gb
Fri Oct 10 08:27:08 PDT 1997
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
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+
Sorry folks, but apparently I have to do this. :-(
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