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

Jameson Quinn jameson.quinn at gmail.com
Thu Sep 6 08:45:57 PDT 2012

```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
>
> 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.
>

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 extorsion) or not (retaliate
spitefully).

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. For that, you need a more sophisticated
model, like http://rangevoting.org/MedianAvg1side.html. This shows median
doing better.

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, and yet the correct candidate (A in this case) would win
naturally.

>> 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).
>
> Yes, but that's totally the wrong way to do it. You don't keep a running
track of the median as you count, you simply tally each rating for each
candidate. (Note that part of the definition of MJ is that you use a
limited number of non-numeric ratings, so it's more like A-F than 100-0; a
manageable number of tallies.) Once you have the tallies, computing the
median (and the MJ or CMJ tiebreakers) is easy. And tallying is easier,
less error-prone, and more informative, than a running total as in Score.

> Michael Ossipoff
>
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