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

Michael Ossipoff email9648742 at gmail.com
Thu Sep 6 19:10:52 PDT 2012

```Jameson:

You wrote:

[referring to the easy successful defection with MJ in the ABE
(Approval Bad-Example)]

> 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.

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.

> 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.

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.

> 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.

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.

>, 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. For one thing, tie-proneness isn't
considered a good property. For another thing, A's win probability
will be 1/2, even if A has many more voters than B has.

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.

(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.
>

```

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