[EM] LNHarm performance: CDTT and Schulze

[Kevin Venzke]

Hello,

I wrote a simulation to measure the rate of LNHarm failures under certain
circumstances. I've used it to compare a CDTT method, Schulze(wv), 
Schulze(margins), and Schulze(opposition).

The simulation works this way: There are five randomly-sized factions,
which each rank a random number of the 4 candidates. The first faction always 
first votes C>D, and then changes their vote to C>D>A. When this causes C or
D to lose, it's a Later-no-harm failure. If it causes one of them to win,
it's a Later-no-*help* failure.

The CDTT method used is CDTT,MMPO,FPP. In other words, a ranking is formed
according to MinMax(pairwise opposition), with its indecisions resolved using 
first preferences. Then the CDTT member appearing highest in this ranking is 
elected. I chose this method because I suppose MMPO performs better than
just FPP, but MMPO by itself is not decisive enough to make comparisons with
Schulze.

I used Schulze because I have and understand the source code for it. But
it might be an intuitive choice anyway for a method to compare with the
CDTT, since both use roughly the same code: You can find the CDTT set by
modifying Markus' code in a minor way.

There were 600,000 CDTT elections, and 200,000 each of the three Schulze 
variants. (You can guess how this happened.) So I've used division to bring all 
the results down to being out of 100,000.

Results:

CDTT,MMPO,FPP: 13.7 LNHarm, 1177.5 LNHelp.
Schulze(wv): 193 LNHarm, 750 LNHelp.
Schulze(marg): 306 LNHarm, 675.5 LNHelp.
Schulze(opp): 291.5 LNHarm, 838.5 LNHelp.

So, until now I've only been able to say that the CDTT "does well" by LNHarm,
despite not satisfying the criterion strictly. But now I have a number: In
these circumstances, the number of LNHarm failures was only 7.1% the number
occurring under Schulze(wv).

I'm not sure what to make of the LNHelp failure comparison; I'm inclined to
think that more LNHelp failures are good, since they give the voter more 
incentive to provide a full ranking.

I should also say that the Schulze(opposition) results might be hard to
compare with the others, since it was 20 times more indecisive than Schulze(wv)
or Schulze(margins). (The CDTT method was always decisive.)

I hope this is of some interest.

Kevin Venzke



	

	
		
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