[EM] Manipulability stats for (some) poll methods

[Chris Benham]

Kristofer,

How did Approval interpret these fully ranked ballots?

Chris

On 27/04/2024 9:06 pm, Kristofer Munsterhjelm wrote:
> 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
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