To judge this book, let us return to the Madisonian Constitution, which has one central feature not discussed or even mentioned by Posner and Vermeule. For Madison, the main danger addressed by the Constitution is not executive tyranny but majority tyranny. Any government has to worry most about the abuse of power by those with whom power is placed — and in a republic, that is the people. Madison’s fear, stated very prominently in Federalist No. 10, is about majority faction, not usurpation by a minority or a single executive. He and Alexander Hamilton wanted a strong executive that would show its strength by standing up to the people, avoiding (in the phrase of Federalist No. 71) “servile pliancy” to their random wishes. For them, the sort of executive we today consider strong, in the image of Andrew Jackson and Franklin Roosevelt, is actually weak because it excites and furthers the majority’s possibly tyrannical desires.

In fact, the people today both love and hate the administrative state, and together our two parties register that ambivalence. With regard to welfare, Democrats are for it, Republicans against it; with regard to national security, the situation is reversed. We do have two recent examples of presidents who have stood up against majority opinion: George W. Bush with his surge in Iraq and Barack Obama with his health care plan. But Posner and Vermeule would say, with reason, that both the surge and the health care plan extended the administrative state. For them, democracy consists in giving the people what they want, and the test of a good president is his credibility with the majority, not his responsibility to the law or the Constitution.

Madison, be it noted, was one of the first to define “responsibility” in a republic as the virtue of officers of government toward the people. But Posner and Vermeule have no room for this kind of virtue in their model, no room for human responsibility. They assume that politicians, obeying the tenets of game theory, automatically follow the cues of public opinion, and for that reason their thinking is actually much more mechanistic than Madison’s.

My advice to the authors is, first, to toss out Schmitt from their construction; they don’t really believe (or know) him. Then they should reconsider whether formal institutions like the separation of powers in the Constitution are as insignificant as they say. True, the president manages his news conference to sustain his credibility, but reporters come to it because he is the president, not because he is a rational actor.

Posner and Vermeule belong to the school of legal realism, now dominant in law schools, which believes the law is always the consequence of some power greater than the law, in their case the rational calculation of benefit and cost. Like most economists, they can see no reason for resisting such calculations.

Yet Posner and Vermeule still claim to hold to the rule of law. They do not object to being called professors of law. Students listen to them and readers buy their books because they teach the law, not because they are professors of executive domination, servants of the administrative state. It seems that the rule of law cannot be sustained without the formality and the majesty of a system of law that people ­respect.