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

Michael Ossipoff email9648742 at gmail.com
Thu Sep 6 07:28:01 PDT 2012

```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

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.

With Score, the A voters, by giving to B some fractional rating, could
have at least tried to give B just enough to win if B does better than
A, but not enough to win if B doesn't do as well as A. It's a
difficult estimate, but the A voters could make thereby make
successful defection more difficult. I call that Strategic Fractional
Rating (SFR).

With Approval, the A voters could do SFR probabilistically.

>> For computations in the count: I'd argue that it's actually easier to carry
> out in practice than Score. Even more so if you consider CMJ.

With Score, you add each ballot's rating of X to X's total.

With MJ, if one or two newly-counted ballots rate X above hir current
median, then you must raise X's MJ score to hir rating on the ballot
with the lowest X-rating above X's median (or maybe to the mean of two
such ballots?).

That means you have to go through the ballots again, to find the one
with the lowest X-rating above X's median.   ...unless you've sorted
all of the ballots, by their ratings, for each candidate.

You don't think that's a lot more computation-intensive than Score? (see above).

Michael Ossipoff

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