[EM] Manipulability stats for (some) poll methods

[Michael Ossipoff]

On Tue, May 14, 2024 at 08:58 Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 2024-05-03 23:18, Michael Ossipoff wrote:
> > 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.
> >
>

[…]

And another part of
> the problem is that, even if IRV and Benham are equally good at
> defending the honest outcome, IRV's honest outcome is much worse than
> Benham's to begin with.


Yes, then, as you suggest, “manipulability” doesn’t tell us anything of
interest. I agree.

Then how much do those manipulability numbers mean, in regards to the
strategic merit of the methods. Nothing?






> That Approval and Score are on the high end makes sense to me because
> strategy (watching the polls) is such an integral part of the greater
> dynamic. Anybody who looks at the polls and then focuses his cutoff to
> maximize the effect will have a good chance of changing the outcome, and
> reducing a fully ranked non-dichotomous ballot down to an approval-style
> ballot to begin with is somewhat of an art.


If “manipulation” consists of getting, by voting insincerely, an outcome
better than what a sincere ballot would get, then what do you mean by a
sincere ballot in Approval?

If there are more than 2 candidates, then, for a particular voter, there
might not even *be* a strongly-sincere ballot.

Then a weakly-sincere one? Every ballot that isn’t obviously suboptimal is
weakly-sincere. There are lots of weakly-sincere ways to make-out an
Approval-ballot.

So then, what does it mean to say that a voter in Approval has
“manipulated”?

Yes, the Above-The-Mean strategy is regarded as the only sincere strategy
in spatial-simulations. Is that accurate? Of course not.

Above-Mean is one strategy that you can use. It’s one among many. …& it’s
incorrect to say that any other way of voting is insincere. As I said, any
strategy not obviously suboptimal is weakly-sincere.

So spatial simulations plainly aren’t saying anything valid about Approval.

Does that bother the academics? Nah :-)



>
> Someone on reddit said: "I would never vote in an Approval election
> without reviewing all the polls…


Our elections have unacceptable candidates. Acceptability & unacceptably
are evident without polls.

Approve (only) all of the Acceptables.

But yes, of course, if someone believes that there are no unacceptable
candidates, then some (certainly not all) ways of choosing how to vote can
use poll information. e.g. the Best-Frontrunner strategy (…& no, the
Democrat & the Republican aren’t the frontrunners).

Better-Than-Expectation, too, is affected by predictive information.

Voting for the Acceptables, or ( if everyone is acceptable), for everyone
you like, or ( if you like or dislike them all), for those above the
biggest merit-gap, or above the mean, lor (if you don’t have an estimate
for the mean),voting for the best half of the candidates… etc.:  Those ways
of choosing how to vote don’t need polls.

About Beatpath, MinMax & Ranked-Pairs: Did you use wv or margins?

In roughly 1/3 of the elections, those methods were reported as having
someone gain from insincerity. That’s surprising if wv was used.





but wouldn't care in a Baldwin's
> election. It's not really about the raw complexity of the strategies
> itself, but their relevance."
>
> So what I would take from the manipulability values is that we should
> try to find a method that both has good honest outcomes, and is
> resistant to strategy away from those honest outcomes. IRV fails the
> former; the cardinal methods fail the latter.


…because manipulability, by itself doesn’t measure strategic merit.

>
>
> Someone might say "just sum up the utility of the worst candidate that
> could be elected by strategy, then". But I think that there's a drawback
> to strategy in itself. Intuitively "you shouldn't need to look over your
> shoulder all the time". Just the effort of adapting your vote to the
> strategy can deter.


I’ve suggested judging a method’s merit by the drastic-ness of the
defensive strategy that it can make necessary.

A simulation could compare the methods by how often that need occurs.

For Condorcet-versions, it would be enough to determine ratio of backfire
to success, for offensive-strategy.

 Academic authors have latched onto “manipulability”. That doesn’t make it
a useful measure.
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