POLITICAL NUMERACY: Mathematical Perspectives on Our Chaotic Constitution (Norton 2002) ISBN 0-393-32372-2

Legal Times magazine called Political Numeracy “one of the ten best books of 2002”.

Here is an excerpt from their review:

Counting on the Constitution, by James H. Johnston, April 19, 2002:

Michael Meyerson of the University of Baltimore School of Law takes a refreshing new approach to the Constitution in "Political Numeracy." His book makes a compelling case for the proposition that the application of geometry, can add perspective to constitutional law.

Most lawyers are vaguely aware of at least some of the arithmetic problems in the Constitution. Does constitutional reliance on the principle of majority rule prevent state legislatures from diluting the voting power of minority populations by gerrymandering election districts? To what extent did the Founding Fathers intend the system of checks and balances and the Bill of Rights to control tyranny of the majority? Can the president avoid the constitutional requirement that treaties be approved by a two-thirds vote in the Senate by entering into "executive agreements" with foreign governments? What does the Constitution say about how to count votes in presidential elections? And then there is the fraction that Meyerson calls the "ugliest number in the Constitution," that slaves counted as three-fifths of a person.

But "Political Numeracy" isn't just about arithmetic. For example, according to Meyerson, mathematical proofs show there is no perfect way to pick the winner in a three-way race. His reasoning may be of comfort to supporters of Ralph Nader, whom some Democrats blame for handing George W. Bush the victory over Albert Gore in the 2000 presidential election. Meyerson delves into applications to constitutional law of more elegant mathematical concepts, such as game theory, Einstein's theory of relativity, topology and Godel's incompleteness theorem. Game theory, for example, says that individual states, left to their own devices, will pass protectionist laws to discriminate against commerce from other states. Thus the commerce clause of the Constitution can be viewed as being intended to prevent the states from playing such games while nonetheless allowing them to impose nondiscriminatory burdens on interstate commerce. (Those who liked the Oscar-winning film "A Beautiful Mind" will be interested to learn that its protagonist, mathematician John Nash, won his Nobel Prize for his contributions to the game theories that Meyerson discusses.)

The most thought-provoking chapter in this short book is "Constitutional Chaos." Meyerson looks at judicial interpretation of the Constitution as an exercise in chaos theory: "It certainly is plausible that constitutional jurisprudence, a discipline that considers whether rulings over time are consistent with 'a line of cases' or 'a pattern of decisions,' will benefit from asking whether we have something akin to a straight line or a fractal [an irregular geometric shape such as the branchings of a tree] and whether there is a chaotic or a predictable pattern."

Chaos theory may be used to describe situations where small and seemingly inconsequential changes in initial conditions have huge but unpredictable consequences later. (For those who have missed or forgotten the movie "Jurassic Park," the actor Jeff Goldblum portrays a mathematician who harps incessantly about chaos theory to refer to the nutty experiments in cloning on a deserted island that produce a lawyer-devouring Tyrannosaurus Rex and a bevy of hungry velociraptors.)

Chaos theory would suggest that, like the clones in "Jurassic Park," seminal constitutional principles from 1787 may evolve into very different forms by 2002. And so, Meyerson says, "A quantitative analysis of the Constitution is impossible to perform and meaningless to imagine. There is no mode to predict the next Supreme Court ruling or the outcome of the next election. Nonetheless, there is much that those studying the Constitution can learn from chaos."

To emphasize that he is not advocating mathematical perfection in the law, Meyerson concludes his book with a chapter entitled "The Limits of Mathematics."

"Political Numeracy" is more than just the sum of its parts. With this book, Meyerson adds two and two and gets five. For whether or not mathematics may be rigorously applied to constitutional law, it clearly provides intellectual exercises that lead to valuable new insights.

Michael Meyerson has produced an excellent little book that looks at constitutional principles from an interestingly different quasi-mathematical viewpoint. Yet he is well aware of the limits of math and logic in our political system — of the need sometimes to follow our hearts and consciences. He quotes the Rev. Martin Luther King's explanation for why "justice too long delayed is justice denied" in a letter to eight clergymen: "But when you have seen vicious mobs lynch your mothers and fathers at will and drown your sisters and brothers at whim ... when you find your tongue twisted and your speech stammering as you seek to explain to your six-year-old daughter why she can't go to the public amusement park ... then you will understand why we find it difficult to wait."

Publishers Weekly
February 18, 2002

University of Baltimore law professor Meyerson shows how a wide range of mathematical subjects, from Euclid's ancient axiomatic method to recent developments in chaos theory  can throw light on the Constitution and how the Supreme Court interprets it. Though he sometimes delves into fairly sophisticated math-game theory, transfinite arithmetic, Gödel’s Incompleteness Theorem — his sharp focus on essential insights should put all readers at ease. For example, he demonstrates how the comparison of infinite numbers illuminates different precious values- the author's life may be of “infinite value” to him, for example, and yet his children's lives are more valuable. Calculations are rare and only involve simple arithmetic. By disavowing claims that a focus on math can replace other perspectives, Meyerson highlights the valuable insights his methods can provide. His use of proportional analysis as a way of evaluating affirmative action is fascinating -not because he suggests an ultimate solution, but because the mathematical approach “infuses analysis with an awareness of the inevitable imperfections of one's own position.”  Such an awareness might encourage more reasoned debate. Some of Meyerson's topics — voting systems, reapportionment — have long been studied mathematically, but most get a novel treatment (for example, “our federalist system can be seen as a kind of fractal structure”). Particularly intriguing is the argument, based on chaos theory, which asserts that the nation is on a "very different constitutional path" than Madison and Hamilton would have ever imagined. Meyerson's insights vary in profundity, but all serve to stimulate awareness of a potentially rich new perspective.

Amazon.com

Editorial Reviews
There's more math in the Constitution than most people realize, from legislative majorities to congressional apportionment to what Michael Meyerson calls "the ugliest number in the Constitution" — the Founders' treatment of each slave as "three-fifths" of a person for the purposes of representation and taxation. Political Numeracy is a delightfully offbeat book, bursting with ideas that will appeal to the sort of person who had trouble deciding whether to major in math or political science: "Our federalist system can be seen as a kind of fractal structure," observes the author at one point. Meyerson, a law professor at the University of Baltimore, writes accessibly; it does not require a prior knowledge of fractals to follow his prose. Indeed, he even appreciates the severe limits of math: "It is utterly incapable of making the sorts of judgments and interpretations that lie at the heart of the Constitution." At the same time, he uses math to illuminate our understanding of that document. His discussion of the electoral college, for instance, shows why the result of the 2000 presidential election, in which the winning candidate won fewer popular votes than his opponent, should not be considered anti-majoritarian. Political Numeracy will appeal to fans of  The Armchair Economist by Steven E. Landsburg and other readers who like to look at old topics from new perspectives. — John Miller