# [EM] MJ: Worse Chicken Dilemma than Approval or Score, elaborate bylaws, computation-intensive count.

Jameson Quinn jameson.quinn at gmail.com
Thu Sep 6 19:40:20 PDT 2012

```2012/9/6 Michael Ossipoff <email9648742 at gmail.com>

> Jameson:
>
> You wrote:
>
> [referring to the easy successful defection with MJ in the ABE
>
> > This defection would "work" in Score (or probabilistic approval) as well.
> > That is, if the B voters commit to defect, the A voters have a choice of
> > making N high enough to elect B (submit to the extortion) or not
> (retaliate
> > spitefully).
>
> No, and I told why not in my post that you're replying to.
>
> Forest Simmons, some months ago, suggested an anti-defection strategy
> that I call Strategic Fractional Rating (SFR). I've mentioned it a few
> times here. I've described it in detail.
>
> The idea is, if you're an A voter, you try to give to B just enough
> fractional rating so that, under whatever assumptions or guesses
> you're making about the faction-sizes, if the B faction is larger than
> the A faction, you're giving B enough to win, but not if the B faction
> is smaller than the A faction. I posted some formulas for doing that,
> given various kinds of assumptions about the faction-sizes.
>
> It's an art of guesswork. It isn't reliable. But the B faction
> presumably doesn't have a better estimate of the faction-size numbers
> than the A voters do, and therefore the defection-deterrence of SFR is
> genuine.
>
> ...and it isn't available in MJ, for the reasons that I described in
> my previous reply to you.
>

Yes it is. Because with approval-style votes, MJ gives approval results. So
if it's possible under approval, it is possible under MJ.

And in scenarios like the one you gave, where the median of the unified
minority candidate (C) is known (0 in your case), it doesn't require votes
of max or min; it can be done just as well with votes of min or min+1.

>
> SFR could be done unilaterally, or could be done by agreement--an
> agreement that doesn't depend on trust, but only on the other
> faction's self-interest.
>
>
As in MJ.

> > In general, scenarios with solid blocs of voters are convenient for
> > illustrating the possibility of a pathology, but not good for comparing
> the
> > likeliness of that pathology.
>
> The simple solid blocs examples are sufficient to demonstrate the
> existence of the problem. It's a well-known problem, and we needn't
> wonder about how likely it is. It's a well known and well established
> aspect of human nature. It isn't a new theory or a speculation.
>
>
> > For that, you need a more sophisticated model,
> > like http://rangevoting.org/MedianAvg1side.html. This shows median doing
> > better.
>
> Several people at EM have discussed and demonstrated why Approval soon
> homes in on the voter median, and then stays there.
>

Did you even read that page? Because that's a non-sequitor response to that
page, as far as I can tell. You're just repeating prior assertions.

> In fairly recent postings, I've told some reasons why the Chicken
> Dilemma won't be as much of a problem when looked at over time (as
> opposed to in one single particular election) in Approval or Score.
> But sometimes one wants to avoid the Chicken Dilemma in one particular
> election. That's when SFR is more important. But it's helpful in
> general too--and unavailable for MJ.
>

Wrong.

>
> > In practice, in MJ both factions could rate each other's candidate at 1
> (the
> > second-from-bottom rating). This would mean that any further defection
> would
> > be risky
>
> No it wouldn't. If the A voters rate B at 1 (out of 100), and the B
> voters rate A at 0, then here are the MJ scores:
>
> A: 0
> B: 1
> C: 0
>
> (...for the reasons described in the post before this one, the post
> that you're replying to)
>
> B wins by defection.
>

This defection is dangerous: if both sides do it, C wins. And it is not a
temptation as with score or approval: unlike score or approval, it is
impossible for defection short of that required to give C a chance, to give
A or B an advantage. THAT is why defection (and thus the chicken dilemma in
general) is MORE of a problem for score/approval than for MJ.

>
> Sure, if the A voters and the B voters both give eachother's candidate
> a point, then the winner will be A or B. But that just means that
> there isn't a problem if no one defects. The Chicken Dilemma is about
> what happens when someone _does_ defect.
>

Yes. When some ONE. Not when some entire faction, as in your example.

>
>
> >, and yet the correct candidate (A in this case) would win
> > naturally.
>
> No, if the B voters defect, then B will win, because the B voters have
> taken advantage of the A voters, even if the A voters are more
> numerous than the B voters.
>
> And, besides, if the A voters and B voters give 1 point to eachother's
> candidate, the result will be a 1 to 1 tie between A and B. The winner
> will be decided by a coin flip.

You don't understand MJ or CMJ. They both have "tiebreaking" procedures
that would naturally give the right result.

> For one thing, tie-proneness isn't
> considered a good property.

In CMJ, the "tiebreaker" is an integral part of the process, such that the
tie is broken before it even exists. There is no sense in which CMJ can be
called tie-prone.

> For another thing, A's win probability
> will be 1/2, even if A has many more voters than B has.
>

Wrong.

>
> If you want to talk about co-operative trust (as you were doing),
> then, in Score, each faction could agree too trustingly and ethically
> give eachother's candidate max minus one. Then, they're helping
> eachother nearly maximally against C, and yet whichever of {A,B} has
> more voters will be the winner.
>
> That's another thing that won't work in MJ.
>

Um, yes it will.

> (But now we aren't talking about the Chicken Dilemma. I'm discussing
> the kind of trust and ethical voting that you were assuming for MJ)
>
> Here's the posting that Jameson was replying to:
>
> >> Michael Ossipoff
> On Thu, Sep 6, 2012 at 11:45 AM, Jameson Quinn <jameson.quinn at gmail.com>
> wrote:
> >
> >
> > 2012/9/6 Michael Ossipoff <email9648742 at gmail.com>
> >>
> >> On Thu, Sep 6, 2012 at 9:49 AM, Jameson Quinn <jameson.quinn at gmail.com>
> >> wrote:
> >>
> >> > MJ's chicken dilemma is incontrovertibly less serious than Score's,
> and
> >> > arguably less than Approval's.
> >>
> >> Maybe that depends on one's arbitrary choice among the sets of elaborate
> >> bylaws.
> >>
> >> But let's take an obvious and natural interpretation, and try it in
> >> the original Approval bad-example:
> >>
> >> Suppose a majority rate A at 0, and the rest rate A at s100. What's
> >> A's median score? Well, if the right number of those zero-raters had
> >> been a little more generous, and had given A a millionth, and one had
> >> given A 1/2 of a millionth, you could establish A's median at 1/2 a
> >> millionth.
> >>
> >> Therefore, if a majority of the voters rate A at an extreme, then it's
> >> obviously fair and right to call that extreme hir median.
> >>
> >> What if a not quite a majority rate B at zero, and a sub-majority rate
> >> B at max, and the rest rate B at N?
> >>
> >> An argument similar to that above shows that B's median should be taken
> as
> >> N.
> >>
> >> Now, let's try that in the original, standard Chicken Dilemma:
> >>
> >> Sincere preferences:
> >>
> >> 27: A>B
> >> 24: B>A
> >> 49: C
> >>
> >> Actual MJ ratings:
> >>
> >> 27: A100, BN, C0
> >> 24: B100, A0, C0
> >> 40: C100, A0, B0
> >>
> >> What are the candidates' MJ scores, by the above interpretation? Who
> wins?
> >>
> >> MJ scores:
> >>
> >> A: 0
> >> B: N
> >> C: 0
> >>
> >> B wins. The B voters' defection has worked. The B voters have easily
> >> taken advantage of the A voters' co-operativeness.
> >
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20120906/2c659ccd/attachment-0004.htm>
```