[EM] Manipulability stats for (some) poll methods

[Kristofer Munsterhjelm]

Here are voter manipulability stats for some of the poll methods, using 
James Green-Armytage's spatial model with 4 dimensions, 4 candidates and 
99 voters. Each method is tested on 500k elections, with 32k attempts to 
strategize per election.

The manipulability value is the fraction of elections in this model 
where the method elected a unique winner, and voters who preferred 
somebody else to the current winner could get that somebody elected by 
changing their ballots. Note that it does *not* check strategic nomination.

I've prefixed entries that aren't actually part of the poll with an 
asterisk. I'll explain later why I've included them. Entries prefixed 
with a number sign are from JGA as my simulator doesn't support them.[1]

The simulator uses full ballots, so Smith//DAC is the same as 
Smith//DSC. If truncation would make the method more resistant, that's 
not reflected here.

0.698	*Borda
0.668	#Approval (from JGA)
0.545	Condorcet//Borda (Black)
0.480	Copeland//Borda (Ranked Robin)

0.417	Plurality
0.417	Smith//DAC
0.412	*BTR-IRV

0.350	Baldwin
0.333	Raynaud (Gross Loser Elimination)
0.333	Schulze(wv)
0.332	Minmax(wv)
0.321	Ranked Pairs(wv)

0.075	Woodall, Schwartz-Woodall
0.074	RCIPE
0.074	IRV
0.074	Benham

I've included Borda to show that my results are similar to James Green 
Armytage's. (Compare also the results minmax results.) In addition, I've 
included BTR-IRV to see how well it would do. Too bad it didn't do 
better, though...

My simulator show higher manipulability for IRV and the Condorcet-IRV 
hybrids than JGA's simulator did. I think this comes down to that my 
simulator is more thorough and thus is able to uncover more 
nonmonotonicity- and pushover-related strategies.

Finally, I'm working on the cardinal methods, but the devil's in the 
details so it's taking a lot longer than expected. More about that when 
I've solved it. But my preliminary tests put Smith-Range around 0.5 and 
STAR as worse than this. Unnormalized (fixed scale) Range, though not a 
poll method, even does worse than Borda. And if the preliminary tests 
give some indication, all the Range/Score-based methods do worse than 
Plurality.

-km

[1] Green-Armytage, James (2011). "Four Condorcet-Hare hybrid methods 
for single-winner elections". Voting matters (29): p. 7; 
https://www.votingmatters.org.uk/ISSUE29/I29P1.pdf