# Department Seminar: Venkat Venkatasubramanian

### How Much Income Inequality is Fair?

*Surprising insights from Statistical Thermodynamics and Game Theory*

**Abstract**

Extreme economic inequality is widely seen as a serious threat to the future of stable and vibrant capitalist democracies. In 2015, the World Economic Forum in Davos identified deepening income inequality as the number one challenge of our time. Yet some inequality is inevitable. As different people have different talents and skills, and different capacities for work, they make different contributions in a society, some more, others less. Therefore, it is only fair that those who contribute more earn more.

But how much more? In other words, at the risk of sounding oxymoronic, what is the fairest inequality of income? This critical question is at the heart of the inequality debate. The debate is not so much about inequality per se as it is about fairness. But this question has remained unanswered in economics for over two centuries. Mainstream economics has offered little guidance on fairness and the ideal distribution of income in a free-market society. Political philosophy, meanwhile, has much to say about fairness yet relies on qualitative theories that cannot be verified by empirical data. As we take steps to address extreme inequality, we need to know what the desired target inequality is -- and for this we need a quantitative, testable theory of fairness for free-market capitalism. I recently proposed such a normative theory, an unorthodox, transdisciplinary theory that integrates foundational principles from disparate disciplines into a unified conceptual and mathematical framework that includes the key perspectives on this question -- the perspectives of political philosophy, economics, game theory, statistical mechanics, information theory, and systems engineering.

My theory, which I call statistical teleodynamics, rests on two surprising conceptual insights. One is that the concept of entropy from statistical mechanics and information theory is the same as potential from game theory, and that these represent the concept of fairness in economics and philosophy. The other is that when one maximizes fairness, all workers enjoy the same effective utility at equilibrium in an ideal free-market society, thereby providing the moral justification for the very existence of the free-market economy. We prove that the fairest inequality of pay is a lognormal distribution under ideal conditions. This result is the economic equivalent of the Gibbs-Boltzmann exponential distribution in statistical thermodynamics. Statistical teleodynamics is the generalization of statistical thermodynamics for rational agents, with the surprising connection that economic utility is similar to chemical potential.

I will compare my theory’s predictions with empirical data on global income inequality trends provided by Piketty and others. Our analysis suggests that the Scandinavian countries, and to a lesser extent Switzerland, Netherlands and Australia, have managed to get close to the ideal income inequality for the bottom ~99% of the population, while the U.S. and U.K. remain considerably less fair at the other extreme. Other European countries such as France and Germany, and Japan and Canada, are in the middle. I will conclude by summarizing the theory’s policy implications and future directions.

**Bio**

Professor Venkat Venkatasubramanian is Samuel Ruben-Peter G. Viele Professor of Engineering in the Department of Chemical Engineering, Industrial Engineering and Operations Research (Affiliate) at Columbia University in the City of New York. He earned his Ph. D. in Chemical Engineering at Cornell, M.S. in Physics at Vanderbilt, and B. Tech. in Chemical Engineering at the University of Madras, India. Venkat worked as a Research Associate in Artificial Intelligence in the School of Computer Science at Carnegie-Mellon University. He taught at Purdue University for many years, before returning to Columbia in 2011. At Columbia, Venkat directs the research efforts in the Complex Resilient Intelligent Systems Laboratory. He is also the founding Co-Director of the Center for the Management of Systemic Risk, a transdisciplinary center focused on understanding how complex systems fail in order to prevent or mitigate such failures in the future, with faculty from a number of departments at Columbia University.

By inclination, education, and experience, Venkat is attracted to fundamental questions that are at the intersection of different disciplines. A leitmotif in his work understands emergent phenomena in self-organized complex systems, particularly using artificial intelligence, statistical mechanics, game theory, and systems engineering concepts and techniques. Venkat’s research contributions have been in the areas of process fault diagnosis and risk management, materials design and discovery using informatics, pharmaceutical engineering, and complexity science. Venkat has a new book out, How Much Inequality is Fair? Mathematical Principles of a Moral, Optimal, and Stable Capitalist Society, published by Columbia University Press (http://cris.cheme.columbia.edu/prof-venkatasubramanian-publishes-his-new... much-inequality-fair-mathematical-principles-mora ).

Prof. Venkatasubramanian received the Norris Shreve Award for Outstanding Teaching in Chemical Engineering three times at Purdue University. He won the Computing in Chemical Engineering Award from AIChE and is a Fellow of AIChE. In 2011, the College of Engineering at Purdue University recognized his contributions with the Research Excellence Award. He is a past-President of the Computer Aids for Chemical Engineering (CACHE) Corporation. He currently serves as an Editor for Computers and Chemical Engineering. Venkat’s non-academic interests include comparative theology, classical