# [EM] More on Gerrymander prevention

Joe Weinstein jweins123 at hotmail.com
Fri Mar 22 18:42:41 PST 2002

```First, I want to thank Forest for a number of recent instances where -
likely better and certainly more rapidly than I could myself - he has
explained and clarified my proposals.

In my opinion - see example below - the practical merit of a districting
scheme generally can NOT reduce to only a purely geometric quantity (such as
average perimeter).

By the way though, even if pure geometry was all we cared about, we would
still have to incorporate population equality of districts as a
side-constraint.  But it would be easier to avoid use of side constraints,
and instead to incorporate population equality, in terms of a measure of
inter-district inequality in population, directly into the merit measure.
Namely, let total merit - or rather demerit - be a weighted sum of two
summands:  average perimeter, and variance among district population sizes.

However, additional 'demerit' summands will generally be needed in order to
ensure that intRA-district communications and commonalities are relatively
strong compared with intER-district communications and commonalities.

Here's a simplified example of what's at stake.  Consider a rectangular
state, with borders in the cardinal directions, and longer N-S than E-W.
The state is uniformly populated except for an unpopulated narrow strip of
high mountains which runs N-S so as to bisect the state into equal-size E
and W zones.  The state is to be divided into two districts.

Use only of equal population and minimum perimeter criteria would call for N
and S districts, whose straight E-W border will bisect the state.  However,
the facts of geography, as they play out in ease of communication, would
argue strongly for E and W districts which coincide with the geographic E
and W zones.

By the way, equal population and minimum perimeter (and maybe also
ease-of-communication, if not weighted too strongly) criteria together will
sometimes give results which will surprise some of us and delight others.

Consider the case of a square state (again, E-W and N-S borders), this time
quite flat, with a main city midway between E and W borders, and just 1/4
the way from the S border to the N border.  The city has half the
population, and the remaining land is uniformly populated.

An optimum two-district scheme will make the city one district and the
countryside another district.  The countryside district is not simply
connected, and thus violates Forest's proposed star criterion. That
criterion would be met, and the scheme then apparently optimized subject to
it, by shifting a few people on the north side of town into the rural
district and adding to the urban district a narrow strip running southward
to the state border, and widening as it does so.

The fun - i.e. clash between star and minimum perimeter criteria - is only
beginning.  Consider the case of a square flat state with four equally
populated corner cities, together adding up to half the population, with the
remaining land uniformly populated.  Disregarding the star criterion, an
optimum districting will give a rural district, plus an urban district
comprising four widely separated connected components - the cities.

Joe Weinstein
Long Beach CA USA

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