At least since Edmund Burke, the right has looked askance at mixing mathematics and politics. The French revolutionaries and philosophes, with their elegantly geometric counties and their 10-hour days and their Year Zeroes, were trying to squeeze the unruly contours of human nature into their godlessly oversimplified concepts. But out of the crooked timber of humanity, many conservatives insist, nothing precise was ever calculated.

　　Recently in these pages, Professor David Schaefer repeated this argument while critiquing a new book, Neil S. Siegel’s The Collective-Action Constitution. He concluded his critique with a biting aside: “We should indeed feel grateful that [the Constitution] was designed not by devotees of game theory, but by men whose experience and education had equipped them with a realistic understanding of human nature.” I politely protest. We game theorists have long been proud to claim James Madison as one of our own.

　　In reply, I would make a plea to non-mathematical humanists: give game theorists a chance. We are not your enemies. Many of us are, in fact, your allies, if only you will have us.

　　Humanists, including it seems Professor Schaefer, often believe that mathematics is about numbers. Human nature and human societies defy quantification, and so, they conclude, mathematical tools must be inappropriate for their description. This conclusion is false. Statistics, of course, measure the world with numbers—but other branches of mathematics, including game theory, are much more about logical relationships. Often, the only numbers we use are 0, 1, and, on a bad day, 2. We don’t need much more. A case in point: in A Beautiful Mind, after fruitlessly working numbers on chalkboards and trying to quantify pigeon perambulations, John Nash finally invents the Nash Equilibrium while staring, not at equations, but at a beautiful blonde. Are we game theorists really so different from the rest of you?

　　Ironically, when arguing against game theorists, humanists often deploy arguments long ago perfected by—you guessed it—game theorists. That’s precisely why conservatives and classical liberals need us.

　　Many of game theory’s most famous results are impossibility results: not idealistic descriptions of how to achieve desired outcomes (as in the book Schaefer reviews), but blunt truths about what humans cannot achieve. Impossibility theorems ought to be the foundation of conservative and classical liberal philosophy. From Burke to Babbitt to Buckley, most conservatives have spent their time athwart history yelling stop. Our entire mission, for 250 years, has been to tell the utopian dreamers that their crazy ideas will not work, that we would all be far better off reforming at the margins than inventing a new humanity.

　　Game theory has shown, I think quite conclusively, that the purpose of government cannot be to find and execute a general will, because a general will cannot exist.

　　Arrow’s Theorem and its heirs are the most famous of these impossibility results. In his introductory of Political Games, Macartan Humphreys summarizes these results bluntly: “There is no general will.” Political philosophers have quibbled, quarreled, and ignored these results for seven decades, but their logic is inescapable: there is no such thing as a general will. It is not logically possible to reliably aggregate people’s desires into a single, collective “will.” And that means there is no such thing as an objective, rational, “collective” weighing of costs against benefits when people disagree, and so it is a simple absurdity to call ours a “collective-action” constitution, especially when discussing “goods” (like abortion rights) which we certainly do not hold in common. 

　　Professor Schaefer wants to make this critique, but he struggles to do so. The book suffers from “very strained reasoning,” he claims, but to justify this claim he resorts to a string of rhetorical questions, e.g. “What could it mean to ‘assign values’ to the costs and benefits of [for instance] different abortion ‘regimes’?” Had he come armed with a little game theory, he could have swatted down the idea of a collective-action constitution for what it is: a merely cosmetic exercise to disguise a tired, sagging progressive agenda with mathematical mascara.

　　Above, I wrote that game theorists have long claimed Madison as a kind of patron saint. William Riker, who brought game theory firmly into political science, seems to have begun this reverence. In his celebrated Liberalism Against Populism, Riker exalts James Madison as “the original American spokesman for liberal democracy,” and he contrasts Madison’s restrained vision of republican democracy (constructing a government to limit tyranny) with more expansive, Rousseauistic visions (“computing” and implementing a “general will”). As his title might suggest, Riker’s project, which he executed decisively, was to prove that the latter view of democracy was logically untenable, and that game theory should force us to embrace, instead, the classical liberal view. 

　　Game theory has shown, I think quite conclusively, that the purpose of government cannot be to find and execute a general will, because a general will cannot exist. Rather, we must judge governments by the liberties they tend to secure. If this sounds familiar, it should—it is essentially Federalist #51. Our glorious Constitution was crafted by proto-game theorists, men whose experience and education had equipped them to structure coalitional dynamics to frustrate factional ambitions and protect the liberties of all. 

　　Nor are game theorists mere creatures of politics. Michael Chwe, for instance, has applied our methods to understand great literature in his Jane Austen, Game Theorist. Here at Law Liberty, others have been known to take a similar approach. As these writers demonstrate, game theory can help us understand the very things that make us human. Ultimately, we game theorists are often humanistic lovers of liberty, people striving for humility and irony and a deeper understanding of the world. When we consider politics, we take James Madison as our north star. I trust that political theorists would not wish to be judged by the latest Rawlsian rehash. Please do us the same courtesy, and don’t judge us by warmed-over progressivism thinly veiled with a few cant phrases about “collective action.” In short, dear lovers of liberty, the problem is not all game theory, but bad game theory.