# What is the Fairest Inequality of Income?

This week, our featured book is

How Much Inequality Is Fair?: Mathematical Principles of a Moral, Optimal, and Stable Capitalist Society.Today, we are happy to present a guest post from author Venkat Venkatasubramaniani.

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. As many political observers remarked, extreme economic inequality, and its associated social and political consequences, played a significant role in the outcome of the U.S. presidential election in 2016. Many in the United States feel that the nation’s current level of economic inequality is unfair and that capitalism is not working for 90% of the population.

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.*

Consider a simple example to illustrate this point. John performs an odd job for one hour and makes $100. Jane performs the same job, but works for two hours and makes $200. Is there inequality in their incomes? Of course, there is. But is the inequality *fair*? Yes, of course. Jane earned more because she contributed more. Their incomes are not equal, but *equitable.* Their economic rewards, after *accounting* for John’s and Jane’s *contributions*, are the *same — *both are paid at the *same* rate per hour of contribution, which is the basis for fairness here.

In this simple case, it was easy to ensure equity. The question is 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? The fairest outcome is the one where everyone’s economic reward, after *accounting* for his or her *contribution*, is the *same, *similar to the John-Jane example. So, for the general case, is there a measure of fairness that can guide us to accomplish this? Given the complexity of the problem, one might anticipate the answer to be no. But, surprisingly, the answer is yes. Furthermore, what that measure turns out to be is an even bigger surprise as we discuss below.

The critical question of “How much income inequality is fair?” has remained unanswered in economics for over two centuries, largely because this question seemed mathematically intractable. As a result, 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. This book offers 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.

While there has been exciting recent progress on the empirical front, as seen in the outstanding contributions of Atkinson, Piketty, Saez, and others, one doesn’t get the sense that the theoretical front in distributive justice is also making such ground-breaking progress, going beyond the transformational ideas of Rawls, Nozick, Dworkin, and others from the 1970s and 1980s. Empirical observations are obviously very important, but it is equally important to complement them with a theoretical framework that provides a deeper understanding and analytical insight. Many feel intuitively that the current level of inequality is unfair, is morally and economically unjustified, and is potentially destabilizing. Can we convert this *intuitive,* *qualitative* understanding into a more *formal* quantitative theory? That is, can we address this intuition *mathematically* and develop an analytical framework that can model and explore this understanding in more precise, quantitative terms? This is what I accomplish in this book.

One might be surprised to hear that the answer to the aforementioned question requires concepts and techniques from statistical mechanics, information theory, and systems engineering, disciplines that seem unrelated to, perhaps even incompatible with, economics and political philosophy. However, a free-market system is, after all, a system of millions of rational agents interacting and making decisions, thereby exhibiting many features of *stochastic dynamical systems* long-studied in these disciplines. As I demonstrate, these concepts and techniques are not only relevant, they are, in fact, quite *indispensable* to answer our question.

My theory integrates liberty, equality, and fairness principles from political philosophy with utility maximization by rational self-interested agents in economics, which dynamically interact with one another and the environment modeled by entropy and potential from statistical mechanics, information theory, and game theory, subject to the efficiency and robustness criteria from systems engineering. The framework unifies the concept of *entropy* from statistical mechanics and information theory with the concept of *potential *from game theory, and proves these represent the concept of *fairness* in economics and political philosophy. This surprising and deep insight is one of the two key concepts in our unified framework, which I have named *statistical teleodynamics*.

The concept of entropy is a hard one to grasp and is somewhat mysterious to many. Even 150 years after its discovery, it is still one of the most misunderstood, and often maligned, concepts in science. Its common association with randomness, uncertainty, and disorder – with doom, as the economics Nobel laureate Amartya Sen put it – has been a major conceptual stumbling block, for over a century, preventing its proper recognition and use in economics. By correctly interpreting entropy as a measure of fairness, I solve this conceptual problem and show how central entropy is to the functioning of an ideal free-market system.

The other key insight is that when one maximizes fairness, all agents enjoy the *same* *overall* or *effective* *utility* (after accounting for an agent’s contribution) at *equilibrium* in an ideal free-market society, which is our desired outcome. The theory proves that the fairest inequality in pay, achieved at equilibrium when entropy (i.e., fairness) is maximized, is a *lognormal* distribution in an ideal free-market. Even though an individual employee cares only about her utility and no one else’s, the collective actions of all the employees, combined with the profit-maximizing survival actions of all the companies, in an ideal competitive free-market environment of supply and demand for talent, under resource constraints, lead toward a fairer allocation of income, thereby maximizing social utility, guided by Adam Smith’s invisible hand of self-organization. Thus, the ideal free-market promotes fairness and social utility, and not just efficiency, as an emergent property. I call this the *fair-market hypothesis*. Since maximizing fairness leads to an *equitable outcome* for all workers, similar to our John-Jane example, my theory provides the *moral justification* for the free-market economy in *mathematical* terms.

Comparing this theory’s predictions to the actual inequality data of different countries, we find more surprises. One is the finding that for an overwhelming majority of the population (bottom ∼99%), Norway, Sweden, Denmark, and Switzerland have 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 ideal, theoretically fairest, distribution was, and yet they seem to have “discovered” a near-ideal outcome empirically on their own. One should take this as encouraging news for the other societies that may strive to accomplish this goal.

It is no big surprise to learn that the United States is at the other extreme with markedly unfair distribution of income, but my new inequality measure tells us by how much – the bottom 90% are making about 24% less than their fair share, which is a significant because it amounted to about $800 billion/year in 2010. The resulting reduction in aggregate demand could potentially reduce GDP growth by an estimated 1% every year. Most other Western democracies are in between the two extremes of Norway and the United States.

Since we now know what the fairest possible outcome is — the lognormal distribution — we have a target that can help us design better tax policies and executive compensation packages. For instance, even if the pre-tax income shares are not fair, we can design appropriate taxes & transfers such that the post-tax income shares are fair to all workers. Thus, instead of guessing what the different tax brackets should be, we now have a scientific basis for applying the fairness criterion across the compensation spectrum.

I also outline twenty one research questions, both theoretical and empirical, raised by my theory, which should be of interest to researchers, particularly young scholars, who are searching for interesting and important problems to work on.

Even though this theory answers a long-standing critical question in economics, and provides practical guidelines for designing tax and transfer policies, which are important contributions, the main intellectual appeal, I think, is that the theory breaks new ground on several fronts – in economics, in philosophy, in game theory, and in complexity science – by showing how the fundamental concepts and principles from seemingly different disciplines can be unified under a single conceptual and mathematical framework. This universality, I believe, is quite attractive.

Remember to enter our book giveaway by Friday at 1 PM for a chance to win a free copy!