IIA performance (was Re: [EM] IMC, I2C and LIIA criteria)

[Markus Schulze]

Dear participants,

I agree that randomly generating pairwise matrices instead
of randomly generating voter preferences could drive the
disagreement among Condorcet methods up. However, I see no
reason why the tendency of the simulations shouldn't be
the same. Norman Petry's simulations were motivated by the
fact that for Smith//MinMax, Ranked Pairs, and the beat path
method only the order of the strengths of the pairwise defeats
is relevant; the actual strengths of the pairwise defeats are
quite irrelevant.

Steve Eppley wrote (14 March 2003):
> That property doesn't sound like a good proxy for IIA; else it
> would be an indicator that Minmax is the best method.  Minmax
> fails clone independence and local independence of irrelevant
> alternatives, which are satisfied by MAM, so it seems silly to
> argue that Minmax is a good IIA benchmark.

The MinMax method has the property that an additional candidate
can change the result of the elections without being elected
only when he pairwise beats the original winner. In my opinion,
this property is less arbitrary than Young's LIIA. However,
to answer the question which weakening of Arrow's IIA is less
arbitrary, I suggested to use random simulations.

Steve Eppley wrote (14 March 2003):
> Markus' message had nothing more to say about MinMax (which is not 
> the same as Smith//MinMax, which Markus went on to discuss but which 
> doesn't share that property).  So I don't see the relevance of that 
> property to the discussion of MAM vs. BeatpathWinner.

In those situations where the MinMax winner is not the Smith//MinMax
winner (i.e. where the MinMax winner is not in the Smith set), of
course, both the Ranked Pairs winner and the winner of the beat path
method differ from the MinMax winner. Therefore, these situations
have no influence on the signification of Norman Petry's simulations.

Steve Eppley wrote (14 March 2003):
> One might also consider testing IIA performance by checking how often 
> deletion of the last-place alternative causes the winner to change.  
> An argument for this test is that the last-place alternative ought to 
> be the "least relevant" alternative.  Two arguments against this test 
> are (1) being ranked last by a method is not necessarily the same 
> thing as being least relevant, and (2) IIA says nothing about "least 
> relevant" alternatives.  MAM would trounce BeatpathWinner on this 
> test, since MAM satisfies LIIA and BeatpathWinner does not. (A 
> corollary of LIIA satisfaction is that MAM's winner will not change 
> if the last-place alternative is deleted.)  I assume Markus will 
> argue that this is not a reasonable test of IIA performance.  :-)

Of course, such simulations wouldn't bring any light to the question
whether compliance with Young's LIIA really leads to fewer violations
of IIA.  :-)

Markus Schulze