[EM] Regarding the districting solutions. My proposal in greater detail.

[Michael Ossipoff]

I looked up the proposed automated districting systems whose URLs were
posted by Ted. They answered my question: I'd asked "Why haven't they been
implemented?"

Ted seemed to be implying that I naively believed that no one has ever
discussed automated districting. Actually, it was discussed on EM some years
ago, and similarly complicated methods were suggested then too. But, more
relevantly, nothing that I'd said in my posting implied or suggested a
belief that automated districting had never before been proposed.

In fact, my own automated districting proposal is so simple and obvious that
of course it must have been the first one ever proposed.

Let me describe it in greater detail:

Band rectangle districting:

The state being districted is mapped, and it doesn't matter what map
projection is used. That map of the state will be divided into bands of
districts which are rectangular on the map. 

I'll refer to the (at least roughly) north-south direction on the map as
"vertical".

I'll refer to the (at least roughly) east-west direction on the map as
"horizontal".

Some sort of cylindrical projection would be good, because it would give
rectangular districts on the Earth. The sides would always meet
perpendicularly, but the horizontal sides wouldn't be straight lines on the
Earth (great circles). But all of the sides would be either north-south or
east-west. The sides would be parallels and meridians. 

A gnomonic projection would be good because it would give, on the Earth,
districts that are straight-sided, 4-sided polygons, though the sides would
generally not meet perpendicularly. When I say that, with the gnomonic, the
sides would be straight lines, I mean that they'd be great circles.

Of course if the state's population is P, and the number of districts
desired is N, then the population, D, of each district must be P/N.

Starting from the top of the map, draw a horizontal line that defines the
bottom of the topmost band. Position that line so that that 1st band will
contain an integer number of districts--the population in the band must be D
multiplied by an integer.

Of course there are more than one position for that line that will make the
1st band contain an integer number of districts. Choose the line position so
that the geometric mean of the rectangles' ratios of height to width is as
close as possible to unity. (or maybe, instead, so as to minimize the
maximum factor by which one of the rectangles differs from unity).

In that band, draw vertical lines to divide that band into rectangles with
population of D.

In the same way, choose where to draw the horizontal line that defines the
bottom of the 2nd band; and then divide it into rectangles, as above.  Same
for each successive band.

Because each of the districts is of the correct population-size, the state's
population will provide the right number of districts. 

The procedure is completed when the entire state has been districted, and
the desired number of districts have been drawn--two conditions that, of
course, will obtain at the same time.

[end of definition of band rectangle districting]

The districts are reasonably square, so that campaign travel distances won't
be unreasonably unnecessarily large. The rectangular districts fit neatly
together in bands. 

This automated districting method is much more briefly described than the
others, and it requires far less computation.

Mike Ossipoff