[EM] IIAC. Juho: Census re-districting instead of PR for allocating seats to districts.

[Michael Ossipoff]

Juho:

I again refer you to Balinski & Young, and to my web article on
Sainte-Lague. And I'll repeat what I mean by SL's optimal proportionality:

SL minimizes differences in seats per person (whether seats are being
allocated to districts or to parties).

Starting with a Sainte-Lague allocation, take a seat from one party or
district, and give it to another. That will always increase the difference
between those two districts' or parties' seats per person.

You described something about LR that you like better. Fine.You have a
different definition of proportionality. There's nothing wrong with that.

Here's why I prefer my (Sainte-Lague/Webster's) proportionality standard:

Seats per person is what it's all about. If we want perfect
proportionality, we'd ideally like seats per person to be the same for all
parties or districts.

SL minimizes _differences_ between parties' or districts' seats per person.
Why _differences_? For example, Hall's Folly (aka "Equal Proportions"), the
apportionment method currently in use for the House of Representatives,
minimizes the _factor_ by which seats per person differs among pairs of
districts. Aesthetically, divorced from congressional (or parliamentary)
voting considerations, Hall's standard would make a lot of sense. Hall
evidently wasn't interested in the matter of which proportionality standard
is relevant to voting in Congress.

Say some Yes/No question is being voted on in Congress. For apportionment
relevance, let's look at it as an issue between districts. District A and B
disagree on that issue. In a Congressional vote, seat _differences_ are
what matter. That's the number of congressmembers who'd have to be
convinced to change their vote. That's the number that adds up overall to
determine the outcome.

Disricts, with a right to equal seats per person, have a right to expect
differences in that fair ratio to be as small as possible. because
differences in seats are what counts.

Sainte-Lague/Webster minimizes differences in seats per person.

So, for Congressional voting, Sainte-Lague/Webster makes more sense than
Hall's Folly.

But, again, if you prefer some other standard, of course that's your
business. But you might want to compare your standard to what I've
described here. And you might want to read Balinski & Young (B&L).

> (Btw, was this the key property that makes LR unacceptable to you, when
> compared to SL?)

The property that makes LR unacceptable compared to SL is that LR
allocations have greater differences in seats per person.

That, and the paradoxes, which are avoidable in party list PR and district
seat apportionment.

Those, and also the fact that LR is a two-part method, involving two
entirely distinct successively-applied rules, the 2nd of which has nothing
whatsoever to do with proportionality, and only spoils the proportionality
achieved in the first part.

> The purpose of that question was just to check that
> you don't claim that SL would always give optimal results or better
results
> than other methods.

I claim that SL will always give optimal results, better results than other
methods.

Mike Ossipoff
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