How Much Income Inequality is Fair?

Surprising insights from Game Theory and Statistical Mechanics

Venkat Venkatasubramanian

Samuel Ruben-Peter G. Viele Professor of Engineering Center for the Management of Systemic Risk Columbia University, New York, NY 10027

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, even desirable and necessary for capitalist societies to work productively. As different people have different 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. A simple example illustrates this point. John is hired as a temporary worker for one hour and makes $100. Lilly is hired for two hours in the same job and makes $200. Is there inequality in their incomes? Of course, there is. But is the inequality fair? Yes, of course. Lilly earned more because she contributed more. Their incomes are not equal, but equitable. Their economic rewards, after accounting for their contributions, are the same.

In this simple case, it was easy to ensure equity. But how do we accomplish this, in general, in a free market society consisting of millions of workers of varying degrees of talent, skill, and capacity for work? Is there a measure of fairness that can guide us to accomplish this? Is there an income distribution that ensures equity? Given the complexity of the problem, one might anticipate the answer to be no. But, surprisingly, the answer is yes.

This central question about fair inequality has remained unanswered in economics and in political philosophy 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, such as the ones by Rawls and by Nozick, which 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. In a recent book, I have 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 rests on two surprising conceptual insights. One is that the concept of entropy from statistical mechanics is the same as potential from game theory, and that these represent fairness in economics and in 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 free-market economy. We prove that the fairest inequality of pay is a lognormal distribution under ideal conditions.

Comparing this theory’s predictions with the inequality data from different countries, we find more surprises. One is the finding that for the bottom 90% of the population, Scandinavia has achieved income shares that are close to the ideal values for the past 25 years. What is even more surprising is that these societies did not know, a priori, what the fairest distribution was, and yet they seem to have “discovered” a near-ideal outcome empirically on their own. It is no big surprise to learn that the United States is at the other extreme with markedly unfair distribution of income. Most other Western democracies are in between the two extremes of Norway and the United States.

It is quite intriguing that while this theory argues the libertarian case for the ideal free-market and proves its moral justification in mathematical terms, the theory’s predictions nevertheless result in a free-market society that looks more like Scandinavia, often favored by egalitarians. Thus, this theory seems to provide the elusive middle ground that can serve as the intellectual basis to advance the current debate on extreme economic inequality.

Professor Venkat Venkatasubramanian is Samuel Ruben-Peter G. Viele Professor of Engineering in the Department of Chemical Engineering, Professor of Computer Science (Affiliate), and Professor of 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 is understanding 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-book-how- 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 music, and cricket.