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

[Markus Schulze]

Dear Steve,

you wrote (12 March 2003):
> 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.

The MinMax method has the property that an additional candidate can
change the winner without being elected only when the new candidate
pairwise beats the original winner. Random simulations by Norman Petry
in 2000 demonstrated that the winner of the beat path method is almost
always the Smith//MinMax winner. Therefore, I would give a small wager
that the beat path method does it better.

For example, when there are 15 candidates then the Smith//MinMax winner
and the winner of the beat path method are identical in 91.7% while the
Smith//MinMax winner and the Ranked Pairs winner are identical in only
41.8% of all situations:
http://groups.yahoo.com/group/election-methods-list/message/5948

Markus Schulze