[EM] Manipulability stats for (some) poll methods

[Chris Benham]

Kristofer,

>
> 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. 

As the nominator of Smith//DAC I strongly request that in that case you 
list it as Smith//DSC  and accept that the Smith//DAC poll candidate 
hasn't been simulated. It has a  strong truncation incentive, and 
forcing full strict ranking destroys most of its point.

BTW there is no justification for Smith//DSC versus Smith,DSC.

Also with the voters fully strict ranking, the three versions of Raynaud 
become the same thing and those three "winning votes" Condorcet methods 
become the same thing as Margins.

But nonetheless some of this is interesting, thanks.

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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