IMC, I2C and LIIA criteria (was Re: [EM] Markus: RP & BeatpathWinner/CSSD)

[Steve Eppley]

On 12 Mar 2003 at 11:55, Markus Schulze wrote:
-snip-
> As far as I have understood Young correctly, his LIIA is intended to
> be a weakening of Arrow's IIA. Therefore, in my opinion, it makes sense
> to ask whether in simulations compliance with LIIA really leads to fewer
> violations of IIA.
-snip-

As I recall, Young claimed Local Independence of Irrelevant 
Alternatives (LIIA) is a "slight weakening" of Arrow's IIA.  
Obviously Young exaggerated, since LIIA + Clone Independence is 
clearly significantly stronger than LIIA.  Therefore, since LIIA 
compliance was the primary reason Young advocated Kemeny-Young, he 
ought to prefer a method like MAM (or perhaps a "margins" variation) 
if MAM's satisfaction of LIIA + Clone Independence were brought to 
his attention.

Immunity from Majority Complaints (IMC) is stronger than LIIA, but is 
not intended as a weakening of IIA.  Therefore it does not make sense 
to me to test IMC as if it were a weakening of IIA.

As for your conjecture that MAM and BeatpathWinner would probably 
perform about the same in a simulation that adds a randomly ranked 
candidate (or, equivalently, a simulation that retallies after 
deleting a random loser, which might be easier to write), I guess I'd 
be willing to make a small wager that MAM would do slightly better 
than BeatpathWinner, based on the other random voting simulations 
that show MAM winners beat BeatpathWinner winners pairwise more often 
than vice versa. (For the results of my simulation comparing of MAM 
winners and BeatpathWinner winners pairwise, follow the link from 
www.alumni.caltech.edu/~seppley.)

-- Steve Eppley