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 _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com
