[EM] Reply to Joe

[Michael Ossipoff]

Dear Joe,

You’d said:

Calling something "bias
free" does not shed extra light without more insights.

I replied:
What kind of insights does Joe want?

You reply:

By way of analogy, the kind of insight that Huntington offered in showing 
that Huntington-Hill minimized differences between 16 measures involving 
a(i) where a(i) is the number of seats given state i and p(i) is its 
population, in a relative sense under transfer of a seat between a pair of 
states. For Webster, the absolute difference a(i)/p(i) - a(j)/p(j) is 
optimized while for Dean p(j)/a(j) - p(i)/a(i) is optimized. For me, this 
gives an insight into the difference between Huntington-Hill and Dean. (See 
page 102 of Balinski and Young.)

I reply:

Ok, you want insights about transfer properties, or maybe about some other, 
unspecified, kind of properties. If you can find a way to combine unbias 
with transfer properties that you like, then be my guest. But it seems to me 
that that unbias is incompatible with transfer properties.

So, as I’ve said before, when you choose transfer properties, you choose 
bias. Can you imagine yourself trying to justify intentional systematic 
biass?

You said:

Here is your definition:
1. We’re talking about a hypothetical country that has arbitrarily many 
states.
2. “The largest states” means an arbitrarily large number of states at the 
top end.
3. “The smallest states” are defined similarly.

I reply:

Well, that’s part of my definition. It’s my definition of some terms in my 
definition.

Let me improve it just a little. I specify that the “small states” and the 
“large states” have no states in common. And, where I said “on average”, I 
mean averaged over the states and averaged over many apportionments.

You continued:

Suppose the "the largest states" which are equal or nearly equal in 
population have 12 percent of the total population, and the "smallest 
states" which are equal or nearly equal in population have 88 percent of the 
population.

I reply:

How would that be a problem for my definition? I’m not saying the large 
states shouldn’t have more seats; I’m saying they shouldn’t have, on 
average, more s/q.

You continue:

Also consider many other variants of this type of situation, both in the 
presence and absence of giving states some initial distribution of seats, 
say 1, as required by the Constitution.

I reply:

Did I guarantee that my methods remain unbiased when there’s a 1-seat 
minimum, or a larger minimum?

You continued:

The house size is a variable here.

I reply:

Yes, I didn’t specify a particular house-size.

I didn’t say that my methods were unbiased when there’s a seat-minimum. You 
know,.the 1-seat minimum is perfectly compatible with unbias: Just increase 
the house-size so that every state actually qualifies for a seat, by the 
method in use. Congress could do that, or it could even be part of a 
method’s rules, when Congress adopts a method.

You haven’t complied with my request to name another bias definition, and to 
tell how it justifies giving the large states more s/q than the small 
states. Shall we take that to mean that you don’t have such a definition?

You continue:

I am not trying to give any particular method a "free pass." I am trying to 
understand complex phenomena.

I reply:
Then forgive me for wronging you, because that’s sure what it sounds like.

Mike