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

[Steve Eppley]

On 11 Mar 2003 at 20:55, Markus Schulze wrote:
> IMC, I2C, and LIIA sound interesting. But do they really say anything
> about how often an additional candidate changes the result of the
> elections? Or are they just curiosities? 

That's a false dichotomy.  These three criteria, and others such as 
monotonicity, Pareto, etc., are not about adding an additional 
candidate.  But that does not imply they are just curiosities.  They 
are "consistency" conditions whose violation may disturb some voters, 
perhaps causing them to change the voting method, or perhaps 
undermining the mandate of the winner.

There's no need to repeat the justifications for IMC and I2C here 
since they are posted in my web pages.  Follow the link to "Immunity 
from Majority Complaints" at the www.alumni.caltech.edu/~seppley web 
page.

>                                  In so far as you have already
> programmed some simulations, I would like to ask you to make some
> simulations where the number of candidates is increased from N to N+1.
> I guess that the numbers of situations where the additional candidate
> changes the winner without being elected won't differ significantly
> for the two Condorcet methods.

I don't know if I'll have time, but in case I do, can you provide a 
clearer specification of the problem?  Should we assume the 
additional candidate is inserted randomly into each voter's ranking?  
If so, why?  If not, then how should the candidate be added?  

Is the purpose of this simulation to test which method satisfies 
Arrow's IIA as much as possible? 

-- Steve Eppley