[EM] Manipulability stats for (some) poll methods

[Michael Ossipoff]

Then Plurality is better than Black & Score; & Benham & Woodall are no
better than IRV; & IRV is 4 times better than the best Condorcet methods?

Of course JGA’s results lead to similar questions.

Doesn’t this bring into question the meaningfulness & usefulness of
manipulability as a measure of merit?

IRV has an incomparably worse strategy problem than the best Condorcet
methods.

Plurality is incomparably strategically worse than Approval.

Benham & Woodall, as everyone would agree, significantly improve on IRV.



On Sat, Apr 27, 2024 at 04:38 Kristofer Munsterhjelm <km_elmet at t-online.de>
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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