[EM] More on Gerrymander prevention

[Joe Weinstein]

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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