Here’s a paper by Stephen Coate and Brian Knight. The abstract:
This paper investigates the problem of optimal districting in the context of a simple model of legislative elections. In the model, districting matters because it determines the seat-vote curve, which describes the relationship between seats and votes. The paper rst characterizes the optimal seat-vote curve, and shows that, under a weak condition, there exist districtings that generate this ideal relationship. The paper then develops an empirical methodology for computing seat-vote curves and measuring the welfare gains from implementing optimal districting. This is applied to analyze the districting plans used to elect U.S. state legislators during the 1990s.
This is clever, no doubt about it. I never would have thought there would be a way to come up with an optimal seats-votes curve based on maximizing welfare gain. On the other hand, I can’t say I really believe it. It just seems contrary to the basic idea of representative democracy to say that the optimal partisan bias is nonzero. It just seems too sensitive to the assumptions of the model. But here it is–your opinions may differ from mine. As I said, the paper is impressive as an intellectual endeavor!
Just a couple other comments:
1. It’s funny how sensitive I can be, as a political scientist, to very slightly different phrasings used by others. In particular, we always say “seats-votes curve,” but Coate and Knight say “seat-vote curve.” And we would say “Democratic voters,” but Coate and Knight say “Democrat voters.” For another example, they give ideologies of 0 and 1 to Democrats and Republicans, whereas we would use -1 and 1 (so that 0 is the center). None of this matters, of course, it’s just funny that I notice these things at all.
2. Regarding the presentation of results: in addition to the automatic point that the tables should be graphs, let me point out that there is no good reason to list the states alphabetically (better would be to list in decreasing order of population, or in order of Republican vote, or whatever), also with judicious rounding and formatting, about 6 of the tables could be combined into 1 table, much easier to read, with many columns.
3. Finally, the empirical seats-votes curves in Figure IV don’t look plausible to me. I’d suggest using the model of our AJPS 1994 paper (which we actually applied to state legislatures in our APSR 1994 paper!).