[EM] Michael O, who are you talking to or with?

[Michael Ossipoff]

I was replying to a message from Toby Periera, in which he quoted an
academic paper that reported & commented on Bias-Free (Ossipoff-Agnew).

I assumed that Pereira’s message was an EM post.

But, when you asked to whom I was replying, that probably means that
Periera’s message Sasha post, but was only an individual email me.

On Sun, Jul 21, 2024 at 18:23 robert bristow-johnson <
rbj at audioimagination.com> wrote:

>
>
> > On 07/21/2024 8:04 PM EDT Michael Ossipoff <email9648742 at gmail.com>
> wrote:
> >
> >
> > No, I didn’t assume that the probability-distribution for states’
> populations is uniform.
> >
> > I merely assumed uniformity for that distribution *within any particular
> interval between two whole numbers of quotas*.
> >
> > …& it wasn’t so much an *assumption*, as much as part of a useful
> operational definition for bias. …a bias easily defined, determined &
> avoided.
> >
> > (…explaining why I’d denied an assumption of special conditions.)
> >
> > Because in this topic, an interval between two whole numbers of quotas
> is often mentioned, it needs an abbreviation. I’ll call it an
> “integer-interval” (ii).
> >
> > Obviously it’s within a lower ii that that distribution varies most.
> >
> > The 0-1 ii doesn’t count, because , in House-apportionment, each state
> gets at least one seat.
> >
> > It doesn’t count in PR either, because SL specifies .7 (instead of .5)
> of a quota as the rounding-point in the 0-1 ii.
> >
> > That’s to discourage & thwart strategic-splitting. BF’s results are so
> close to those of SL, that the .7 rounding-point in the 0-1 ii should be
> used in BF too.
> >
> > …& so, the lowest ii in which the operational-definition makes a
> difference is the 1-2 ii.
> >
> > In that ii, the values of the BF & SL rounding-points differ by only
> about 2%.
> >
> > Obviously that % rapidly becomes drastically lower for higher ii s.
> >
> > …as also must the variation of the probability-distribution within an ii.
> >
> > As for my useful operational-definition of bias:
> >
> > 1.
> >
> > One justification for it is that the vagaries & continual variations of
> the probability-distribution for states’ populations isn’t the
> responsibility of an allocation-rule.
> >
> > …as is tacitly, performatively, agreed by every allocation-rule that
> doesn’t require recalculating an approximation to that distribution at each
> census.
> >
> > 2.
> >
> > But what would an alternative to my useful operational definition look
> like? A mess, that’s what.
> >
> > Obviously the probability distribution within each ii could only be
> *approximated* by a formula based on…what? The historical record of
> populations in that range?
> >
> > Why should old records be assumed relevant to today’s probabilities. We
> haven’t gotten away from assumptions—a futile goal.
> >
> > Or maybe an interpolation or least-squares approximation based on the
> new populations of the states.
> >
> > The operative word there is “approximation”.
> >
> > All that extra work for something that’s still only approximate.
> Exactitude hasn’t been gained.
> >
> > Arguably, in a particular ii, the approximation to the
> probability-distribution, a best-guess, is more realistic than a uniform
> distribution there.
> >
> > But the better likely-accuracy of that guess, doesn’t make it more than
> a guess.
> >
> > I didn’t stumble-upon BF as a useful, feasible avoidance of a usefully
> operationally defined bias.
> >
> > That was the purpose.
> >
> > But sure, any other interpretations or interesting aspects that I didn’t
> know about—yeah I stumbled onto that.
> >
> > Bias has very much been part of the merit evaluation & comparison of PR
> methods, & that was always so with House-apportionment as well.
> >
> > So that was my purpose.
> >
> > I hadn’t considered the interesting entropy consideration, so yes that
> was an accidental result.
> >
> > Entropy in PR had never occurred to me, but it’s the basis of a number
> of useful measures of inequality.
> >
> > The most relevant 1-number inequality-measure based on
> summed-aggregation is a generalized entropy called ge(-1).
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > ----
> > Election-Methods mailing list - see https://electorama.com/em for list
> info
>
> --
>
> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
> .
> .
> .
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
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>
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