[EM] Fixing IRV

Richard Moore rmoore4 at home.com
Thu Aug 9 20:25:58 PDT 2001

Markus Schulze wrote:
>>>Some elimination methods are monotonic (e.g. Ranked Pairs). Some
>>>methods are not monotonic although they don't use eliminations
>>>(e.g. Dodgson).
>>Granted, but disproving the converse doesn't disprove the 
>>original statement.
> The negation of "No elimination method is monotonic." is: "There
> is a monotonic elimination method." And of course proving the
> negation is the same as disproving the original statement.

But, the *converse* of "All elimination methods are 
non-monotonic" is "All non-monotonic methods are elimination 
methods". You cited Dodgson as a counter-example of the 
converse, as a method that is non-monotonic but not an 
elimination method. And as I said, disproving the converse 
does not disprove the original statement.

> I guess that it will be very difficult to define "eliminating
> alternatives prior to selecting a winner" without making
> Riker's theorem trivial or even a tautology.

I for one don't see a tautology, but since tautologies are 
true by definition then if it were one we wouldn't even need 
to see a proof.

However, I see your point that "eliminating alternatives 
prior to selecting a winner" could be subject to 
interpretation (English can be a slippery thing). But to me 
it's pretty clear that this phrase would apply IRV (for 
example) but not to RP. Without the "prior" phrase, any 
method might be considered an elimination method, since all 
election methods eliminate alternatives.


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