The point here is not to predict how the court will actually rule in Dobbs. Cohen said he thinks that Roe v. Wade will likely be overturned, so there won’t be any voting paradox. Still, it’s cause for concern that it’s possible for this sort of thing to happen.
“If you got an opinion like we’re describing, you would have deep arguments among people who follow the court about whether Roe had been overturned” or just weakened, Cohen said. “How do you derive rules from Supreme Court decisions when there’s a voting paradox? Frankly, I think you would get people arguing all different sides.”
While a voting paradox in Dobbs may be unlikely, there have been documented voting paradoxes in other Supreme Court decisions, including those involving retired miners’ health benefits, state restrictions on truck length, a claim against a Cuban bank and gun rights. In an article for the Boston University Law Review in 2010, Cohen argued that voting paradoxes can arise whenever questions of precedent are at stake and thus “almost every case can result in a voting paradox.”
This issue comes up in any voting system in which voters rank their choices. One solution is to allow voters to express the strength of their preferences, not just how they rank them, but Arrow warned that it’s impossible to see inside people’s heads to compare what they mean by a given strength of preference. (In markets, as opposed to rank-order voting systems, people can reveal the strength of their preferences through how much they’re willing to pay for something.)
The Marquis de Condorcet, a French mathematician, discovered a version of the voting paradox in the 18th century. Charles Dodgson, better known as Lewis Carroll, the author of “Alice’s Adventures in Wonderland,” proposed a partial solution in the 19th century. Arrow generalized the result to all election systems in his doctoral thesis and a 1951 book, “Social Choice and Individual Values.” It’s now known as Arrow’s impossibility theorem. “Most systems are not going to work badly all of the time,” Arrow told New Scientist magazine in 2008. “All I proved is that all can work badly at times.”
The implications of Arrow’s work have troubled many political thinkers. The Stanford Encyclopedia of Philosophy says:
The tenor of Arrow’s theorem is deeply antithetical to the political ideals of the Enlightenment. It turns out that Condorcet’s paradox is indeed not an isolated anomaly, the failure of one specific voting method. Rather, it manifests a much wider problem with the very idea of collecting many individual preferences into one. On the face of it, anyway, there simply cannot be a common will of all the people concerning collective decisions that assimilates the tastes and values of all the individual men and women who make up a society.
Maxwell Stearns, a professor at the University of Maryland Carey School of Law who has written on social choice theory and the law, argues that the Stanford entry is a bit strong. (Stearns speaks with some authority: Arrow provided a blurb for one of his books.)
The possibility of paradox “doesn’t mean that these systems aren’t legitimate,” he says. He says lower courts are practiced at interpreting Supreme Court decisions with muddled messages. The losing side, he explains, “might say, ‘I lost this round, but I can’t say that it was unfair. There will be other rounds, and I might win those.’”