[EM] Strategy-resistant monotone methods

[Kevin Venzke]

Hi Kristofer,

Thanks for the additional details.


----- Mail original -----
De : Kristofer Munsterhjelm <km_elmet at t-online.de>
À : Kevin Venzke <stepjak at yahoo.fr>; EM list <election-methods at electorama.com>
Envoyé le : Dimanche 7 février 2016 16h52
Objet : Re: [EM] Strategy-resistant monotone methods
>>>
>>> The best simple linear method I could find was this:
>>>
>>> f = fpA - fpC
>>>
>>> i.e. a candidate's score is the number of first preferences he has,
>> 
>>> minus the number of first preferences for whoever is beating him pairwise.
>> 
>> I think it's clear why this works: the candidate C who beats A doesn't get
>> "credit" for all C>A votes but only those dedicated to C as first preference.
>> So, the effect of strategic B>C>A votes (where sincere is B>A>C) is limited
>> to causing a cycle.
>
>Right, it feels a bit like a restricted tactical position in chess,
>where you know what you need to accomplish, but you can't get your
>pieces around in time. In other words, there's not enough freedom for
>the strategic voters to do everything they want to do at once.
>
>So intuitively I can see how it works. But I was hoping it'd be possible
>to derive some kind of theory of methods resistant to strategy, and that
>intuition doesn't seem to help us much; unless the best way of making a
>method resist strategy is reducing the freedom in a way analogous to the
>above.

That's an interesting way of looking at it. I'm not sure if we could easily
generalize this reduction of freedom concept though.

I see the issue much more simply, that the effect (or perhaps "independence")
of lower preferences needs to be kept low, on the assumption that they might
be mischief votes. (The possibility that they might NOT be mischief votes 
usually limits my enthusiasm for these efforts!)

In this scenario, when you have decided in advance that it's going to be a
Condorcet method, you necessitate that some mischief is going to be possible.
That's inherent to Condorcet, and the nature of the vulnerability is
basically the same no matter what you do. So all you can do is try to reduce
the damage done within the method of cycle resolution.

>Similarly, I get the impression that C,IRV works in part for the reason
>above (e.g. mutual dominant third and burial resistance) and in part
>because it's so chaotic. Because it's chaotic and has an exponential
>amplification in the worst case, an attempt at strategy can backfire
>quite easily.


Well, I would have said that C,IRV works because IRV works. (I think it's in
general pretty promising to take a burial-resistant non-Condorcet method and
use it to complete Condorcet, if one wants burial resistance.) And IRV works
because you can't use lower preferences for mischief.

I guess that doesn't cover all the bases, only burial. I doubt push-over is
really a big deal; in my own simulations I don't recall any sensible methods
with lots of push-over incentive.

As far as compromise, putting Condorcet on the front end helps C,IRV, I am
sure. Though IRV itself need not be terrible; the IRV exclusion rule is

often very reasonable, particularly when the model doesn't do anything to

create a "center squeeze" likelihood. IRV can somewhat "correct the course" 

through eliminations, reducing the need for favorite betrayal.

(I would be curious to see though, if the fact is that you're getting most
of your compromise-related performance simply from using Condorcet.)

I think the generalization (describing why things work, wrt burial anyway)
is LNHelp, except that in your experiment there is no truncation, so the
criterion is more like "shuffling lower prefs around doesn't help higher
ones," which is quite demanding, and will probably lead you towards FPP and 
IRV. It is nice to see that your generator didn't actually resolve to simple
FPP though.

Kevin