Tom Knight <tk@csail.mit.edu> wrote:
If the region is borderless, how do I decide which district a new person belongs in?
By, for each district, summing the squares of the distances between the new person and every person in the district. Whichever district gives the smallest sum is the district the new person is assigned to. Of course there would be implicit borders, the boundaries between where a new person would be assigned to one district rather than another, but nobody needs to think in terms of them. Anyhow, these implicit boundaries would change whenever anyone moved, was born, or died. It might be interesting to study how such boundaries would move in response to such events, what kinds of shapes the boundaries would tend to have, and whether these boundaries can ever be counterintuitive or pathological. Not very practical in the US as it exists, since apparently the census department assigns everyone to a census block with explicit borders, rather than assigning everyone a point location. And not necessarily desirable even if possible, though arguably better than the current system which is vulnerable to gerrymandering. But then this is the math list, not the politics list. Interesting math problems can be inspired by all sort of things. Similarly, the question of what proportion of trees are visible in a forest, where there's a tree at every point x,y where x and y are integers and at no other points, where you're at the origin, and where a tree is visible iff there's no other tree directly between you and it, limit as the forest grows large, is of little relevance to actual forestry.