[EM] Manipulability stats for (some) poll methods

[Kristofer Munsterhjelm]

On 2024-05-15 10:46, Michael Ossipoff wrote:
> 
> 
> On Tue, May 14, 2024 at 08:58 Kristofer Munsterhjelm 
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> 
> 
>>     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?

It tells you how often you have to be thinking about "playing the 
strategy game" to improve the outcome (or how often you may regret if 
you don't). In a low manipulability method, you don't have to start 
thinking about whether you should tailor your response to poll data, 
etc. as much.

There are two approaches here: you can make an apparently simple but 
highly manipulable method and then place the burden of voting "the right 
way" on the voters. Or you can take the spirit of the revelation 
principle further (it can never go all the way) and place that 
responsibility on the voting method itself.

IMHO, the more a voting method supports "just go there and submit your 
vote", the better it is, all else equal. As I have pointed out, it's not 
the full picture - you also need to know that the sincere unmanipulable 
outcome isn't going to suck. But that doesn't mean manipulability is 
meaningless.

>>     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?

For a near-dichotomous opinion (A > B > C >>>>>> D > E > F), the answer 
is easy. But for fully general opinions, you're absolutely right. You 
have to make some assumption on honest behavior.

But it seems like the ambiguity is fundamental to Approval. The strategy 
tester works by generating ballots for a sincere first stage and then 
seeing if coalitions can change the winner. The defining feature of the 
sincere stage is that nobody takes information about anybody else into 
account (and that it adheres to the model, e.g. spatially distributed 
utilities, impartial culture, whatnot).

So we need some way for the virtual zero info voters to transform 
utilities to Approval ballots. The virtual voters have to answer Robert 
Bristow-Johnson's question: "do I approve of my second favorite"? And 
it's not at all clear how they should do it.

This reflects a property of Approval itself. The Approval ballot asks an 
ambiguous question and it's up to the voter to interpret it.

Note that this ambiguity doesn't misclassify sincere ballots as 
insincere ones. In the second (strategic) stage, any voter is allowed to 
submit any ballot so long as it'll serve their purposes. What it does 
affect is the weighting (how often would this particular first-stage 
Approval election happen).

In practice, what the simulations do is use some kind of translation 
function. Both JGA and I use a mean utility cutoff. It would of course 
be possible to vary the "translation function" to see if the results are 
robust.

> 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.

It doesn't say that any other way of voting is insincere. It would just 
consider the other ways of voting to happen too rarely or too often 
given the spatial model.

Ultimately, we need a reasonable model of how sincere voters would vote 
in the absence of poll data. Just like we need a reasonable utility 
model to begin with (spatial vs IIA vs whatever). If the model is 
unreasonable, then the results will be wrong. (Just like a wrong utility 
model would produce wrong VSE or ranked method manipulability values.)

If it's impossible to create such a reasonable model because Approval 
voting in non-u/a settings is too intervowen with the wider "adapt to 
the polls" strategy, then there will be no meaningful results. But then, 
that would be telling in itself.

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

> 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.

Would running the simulations with different transformation functions 
corresponding to the approaches you listed help, or would you still 
consider the values to be meaningless?

> 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.

I used full ranking, so wv vs margins makes no difference - though my 
code is set to use wv.

>>     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.

That's not quite what I'm saying. Consider Random Ballot. It has zero 
strategic merit because strategy will never help you: if you're the 
fortunate voter whose first preference was picked, you can't do better 
than getting your honest first preference. And if you're not that 
fortunate voter, nothing you can do will make a difference.

So the strategy potential is zero, as would its manipulability be (with 
"who is the lucky voter" held fixed between the honest and the strategic 
round).

But its honest outcome, even in expectation, is really awful. If you add 
a variance penalty, it gets worse still. Nobody proposes Random Ballot 
as a single-winner method.

Manipulability rightly measures its strategic potential to be zero. But 
we need more information: how good its honest outcome is. Same here. 
That doesn't mean that manipulability is a useless strategy measure. It 
just means it doesn't answer the other question we're interested in.

-km