# New book on how much inequality is fair?

Venkat Venkatasubramanian, Samuel Ruben-Peter G. Viele Professor of Engineering, Department of Chemical Engineering, has a new book, How Much Inequality Is Fair? Mathematical Principles of a Moral, Optimal, and Stable Capitalist Society, recently published by Columbia University Press.

The book addresses a question Venkatasubramanian has long pondered–what level of inequality is fair?–and synthesizes fundamental concepts and techniques from economics, political philosophy, game theory, information theory, statistical mechanics, and systems engineering into a mathematical framework for a fair free-market society. The key to this framework, which Venkatasubramanian calls "statistical teleodynamics," is the insight that maximizing fairness means maximizing entropy, making it possible to determine the fairest possible level of pay inequality. The framework thus provides a moral justification for free-market capitalism in mathematical terms.

"To address inequality, we need to know what the goal is," says Venkatasubramanian, who is also the co-director of the Center for the Management of Systemic Risk and a member of the Data Science Institute. "For this, we need a quantitative, testable theory of fairness for free-market capitalism."

Venkatasubramanian also compares his theory's predictions to actual data on inequality from various countries–showing, for instance, that Scandinavia has near-ideal fairness, while the United States is markedly unfair–and discusses the theory's implications for tax policy, social programs, and executive compensation.

How Much Inequality Is Fair? is the culmination of a 34-year quest that Venkatasubramanian began in 1983 when he was a graduate student wondering about the generalization of statistical thermodynamics. He was curious whether there could be a similar statistical mechanics-like framework for millions of interacting rational agents (people, software, etc.) that make decisions, comparable to the one for molecules.

After three decades, his exploration has resulted in this new theory of statistical teleodynamics, and answers a major question in economics that has challenged economists and political philosophers for more than 200 years. Venkatasubramanian solved the last piece of his puzzle two years ago in collaboration with Jay Sethuraman, professor of industrial engineering and operations research at Columbia, and Yu Luo, then his doctoral student.

The book is available at Columbia University Press and on Amazon.

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