We introduce the first family of district compactness measures that can incorporate a wide range of internal geographic features. The measures in this family are the probability that a district contains an admissible path between a randomly selected pair of people. The measure can account for...

Paul Milgrom [Milgrom, P.R., 1981. Goods news and bad news: representation theorems and applications. The Bell Journal of Economics 12, 380-391] showed that if the strict monotone likelihood ratio property (MLRP) does not hold for a conditional distribution then there exists some non-degenerate...