Friday, October 21, 2011

Occupy Wall Street, Social Unrest and Income Inequality


We are seeing the specter of instability in the growing protests of income inequality, economic distress of the middle class, and economic and political power of the very wealthy. There is Occupy Wall Street in the U.S., and similar protests ranging across the globe. In parts of Europe there is rioting in the streets, in parts of China protests have turned deadly.

A microcosm for these protests can be seen in Israel, which is among the first of the countries to stage such protests. In a one of my recent posts, "Workers of the World, Goodnight!", I recount my experience in the egalitarian Israel of the early 1980s, and contrast that with the Israel of today, where a handful of families basically have a controlling interest in the economy proper, and where the concentration of wealth at the top makes the U.S. look like a commune. This transformation over the past few decades tells us something about the roots of social unrest that have spread recently from Occupy Wall Street to other countries. The Israeli society that I saw three decades ago was one that faced the unrelenting specter of war. During times of crisis, of war or natural disaster where there is a randomness to existence that extends beyond wealth to issues of life and death, people choose to be more egalitarian. People know they might end up with the short end of the stick with the next roll of the dice, and that whatever they acquire will likely be transitory. So they first and foremost focus on keeping a social system and its support structure in place.

Unerring stability leads to the opposite course. For example, in the medieval societies where position remained unchanged for decades, even centuries, where land, the key source of wealth, passed inexorably from one generation to the next, where class distinctions dictated the path of your life and that of your children, an egalitarian notion was not even in the realm of consideration. There were the rich and there were the poor. It was as simple as that.

Absent a policy of income redistribution, capitalism plus stability leads to income disparities. Take stability out of the equation, and the distribution will narrow. Israel is more stable thanks to the efforts of the broad base of society, most notably through their military commitment And so Israeli society as a whole maintains the environment that allows the remarkable income disparity to occur. Because of this, Israeli society as a whole questions the social structure that gives rise to this disparity. They have a hand in creating that stable society, and could theoretically choose instead to move more toward one of instability. In the extreme case, doing so might be their best course.

A Reworking of Rawls' Theory of Justice
In The Theory of Justice, Rawls performs the thought experiment of developing a political system where those determining this system are operating under what he calls the veil of ignorance. The veil of ignorance prevents the contractors – those who are going to enter into the political contract that they have a hand in developing – from knowing their place in the resulting society. They do not know their assets, their endowments of intelligence and strength, even many of their preferences and values. They do not know their place in society, they do not even know the civilization and culture that has been achieved.

The veil of ignorance is an important vehicle for the development of his political theory. The exercise is trivial without it. If one's endowment is known at the time political system is being crafted, then obviously the endowed will push toward a winner-takes-all system while those on the other extreme will push for an aggressive redistribution of wealth.

The epistemological constraint imposed by the veil of ignorance creates the circumstances for the contractors to act in accordance with Rawls' fair principles, which include: The contractors cannot choose to advantage just themselves (since they do not know where they will fall in society); they cannot choose to risk massively disadvantaging others (because these others will defect); and they cannot risk massively disadvantaging themselves (because they must consider their descendants and their own capacity to stay true to the principles they choose). Thus, even if the contractors do not affirmatively seek fairness, their circumstances lead what they choose to end up being fair.

From their perch in the original position behind the veil of ignorance, Rawls' contractors seek to temper the worst possible outcomes. We might think of this as the contractors choosing a basic structure for society in which there position will be randomly assigned, or even where there is a chance that their enemy will assign them their place. Rawls offers several reasons why this is the natural result. First, the parties cannot rationally take risks because the veil of ignorance makes probabilistic calculations impossible. Second, the contractors are choosing the political system not only for themselves, but for their progeny, and with such high stakes, they will want to guard against throwing their progeny into a purgatory. And third, although the contractors do not know their preferences or what they will consider good and desirable, they do know that there will be some notion of the “good and desirable” that will motivate them, so they seek to secure circumstances that will allow them to pursue this.
We can take Rawls' construction to explore the implications of instability in a capitalist society. Suppose that the contractors are told that whatever system they put forward will be beset by occasional exogenous shocks that destroy wealth. The social and political system may continue through these shocks, but there is nothing they can do to affect the occurrence of the shocks or their result.

Take the two extremes of possible shocks: complete stability versus unrelenting instability. In the first case one's position and wealth are secure. Once you have it, you can't lose it. And if you don't have it, you can't get it. In the other extreme, society is essentially beset with economic revolution, and fortunes are made and lost.

Now back up and suppose that the contractors placed in the Rawlsian veil of ignorance know a little bit more than he allows, in particular, that they know what their initial state will be in terms of position and wealth when the political system is first set, and they also know the degree of instability that will surround that system. What happens when we add this additional knowledge to Rawls' original position?

The greater the instability, the less value there will be in their knowledge of their initial state. In the limit, the additional information of one's initial state means nothing, because everything will become randomized in short order. So we are pretty much back to Rawls' assumption of a veil of ignorance in terms of each person's initial state. Things do not exactly reduce to Rawls' argument, however, because we have an additional piece of information, namely that no matter what system we put in place, it cannot prevent the frequent and arbitrary change in each person's conditions. In this situation, there will be a move toward an egalitarian solution; those who know they will be at the top when the game begins will join those on the bottom rung to vote for an egalitarian system.

Indeed, on an inter-temporal basis an egalitarian system is inevitable in the roll-of-the-dice extreme, in the sense that over the many rolls of the dice sometimes one person will be on the top, sometimes another, and everyone will face the same distribution of wealth. If people are not myopic, that is, if they look at the results of this extreme as it plays out over a long period of time, they will find that the greater the instability – the more frequently the dice are tossed – the lower the dispersion of wealth will be. Indeed, for all practical purposes there will be no private property, because period by period the property will be sold off based on the reshuffling of fortunes. It is “here today, gone tomorrow”.

On the other hand, if there is no instability, and people know their initial states, if everything is set in stone and one's initial state will persist forever, then obviously the rich will vote for a system where the winners keep everything they get, while the losers in the lottery will vote, as they will always, for sharing the wealth.

(Note: We don't need a literal lottery; we can have hard work and talent take a part in getting people where they are, and that each time the world essentially starts over hard work and talent play a part in how wealth gets redistributed. But we need to recognize that luck also plays a role, and so we can still invoke the image of a lottery or a roll of the dice. And, as Rawls asserts, inborn talent comes from the luck of the draw. The joke that someone's best career move was in choosing their parents applies to more than inherited wealth).

Instability and Egalitarianism
This might help provide a context for some of the current debate on wealth, income distribution, and taxes, and the related protests arising throughout the world. Instability helps overcome one of Rawls concerns, and a concern, not always well articulated, that must be in the minds of the protesters and others among the “99 percent”: That the political system, though just, can gradually move toward a result that, ex post, is at variance with the principles that society initially agreed upon.

Rawls concedes that even if everyone acquires their property justly in accordance with the political system and all distributions are done freely in accordance with the agreed concept of justice, it is still possible that over time disparities in wealth may occur that undermine the values from overarching first principle. He states:

Even though the initial state may have been just, and subsequent social conditions may also have been just for some time, the accumulated results of many separate and seemingly fair agreements entered into by individuals and associations are likely over an extended period to undermine the background conditions required for free and fair agreements. Very considerable wealth and property may accumulate in a few hands, and these concentrations are likely to undermine fair equality of opportunity, the fair value of political liberties, and so on.

This gives rise to a possible social contract. Faced with a knowledge of their current state, the people can design a political system that is unstable, thus giving them at shot at the lottery in the future. Or they can move toward one that maintains stability, and in doing so establish the rich more securely. For the people to choose the latter route and participate in a government that entrenches the rich, they will demand an egalitarian structure similar to what they would under the Rawlsian veil of ignorance.

Conclusion
We cannot separate the issues of income distribution from the social system. As a starting point, a wide income distribution requires a developed society. This is somewhat of a tautology, because a distribution suggests a population to distribute, but income distribution is not very meaningful in a family clan. It is hard to be very rich when you are all tilling the land and are all facing risk of starvation. But even more than that, a wide income distribution requires a stable society, which means laws to maintain property rights, a government that is not confiscatory in taxation, and a military that protects the society from attack. It is impossible to discuss the economics without considering the social contract. That is why it is called political economy.

There are many social contracts that are possible. Although we have been focused on the trade off between income inequality and stability, Rawls considers social systems without using the degree of stability as a policy lever, so to speak. A society might decide to have system that is both stable and egalitarian, such as what we see in Scandinavia. The discussion is not one of capitalism versus socialism. We can take unfettered, eat-what-you-kill capitalism as a starting point. The knob that is being turned is the level of social stability. From their perch in my version of the veil of ignorance those who are wealthy in the initial state will choose to construct a society that has less inequality so that the knob can be turned to the “do not disturb” setting.

The Securities and Exchange Commission disclaims responsibility for any private publication or statement of any SEC employee or Commissioner. This post expresses the author's views and does not necessarily reflect those of the Commission, the Commissioners, or other members of the staff. Similarly, this post expresses the author's views and does not necessarily reflect those of the Department of Treasury or its staff.

Sunday, October 16, 2011

The iPhone, Siri, and the Turing Test


We can start counting the days until computers routinely win a Turing Test. It will happen for two reasons.

One reason, which is the basis for a post I wrote on the Turing Test earlier in the year, is that we are meeting the computers half way. The more we become twittering, texting beings, the easier it is for a computer to mimic us, because we are stripped of much of our human context and behave more like computers. 

The second reason is now readily apparent with the unfurling of the Apple iPhone4S and Siri, the digital assistant.  With the iPhone users accessing Siri to find restaurants, make appointments, and ask trivia-level questions (and with more areas of interaction added down the road),  Apple's servers are going to amass the queries of millions of people many times every day.  And as Google has shown with Google Translate, if a computer has enough raw material, it can pretty much figure this sort of thing out.

So as this database grows by orders of magnitude and the logic is refined accordingly, if a Turing Test is fashioned to distinguish a computer from a person in the day-to-day tasks of working with a personal assistant – in one room is hidden an iPhone, in another room a person, you interact with them as you would an executive assistant over the course of the day, and then at the end of the day you choose which one you think is the person – it is only a matter of time before the iPhone becomes indistinguishable from the human. In fact, to keep it from standing out, the iPhone will have to be dumbed down. 

In this respect, Apple's move toward a voice interface is brilliant. For one thing, no matter how well you do it, using a touchscreen on a phone is cumbersome. And although we have grown accustomed to it, as we have the desktop mouse and laptop touch pad, this isn't really the way we do things in life. Furthermore, hardware need only go so far. It is not like smart phone users are trying to model fluid dynamics. But while the hardware improvements at this point are marginal, for Siri it is open-field running. More and more sites can be added – travelocity, fandango, and what not – sites will be optimized for Siri and new sites will pop-up specifically for Siri. Logic and voice recognition will improve, and the move toward the iPhone as a conversational partner will accelerate. 

There already is an annual Turing Test underway, the Loebner competition, where a set of judges spend a few minutes conversing (via keyboard) with computers and with people, and then have to decide which is which. It is not a great test, because it is a competition rather than a normal human environment. The judges are trying to weed out the computer through types of questions and cadence of conversation in ways they wouldn’t in real life. A more reasonable Turing Test would be to invite a computer into a round of dinner conversations where the human subjects are not made aware that this is occurring. (They would all have to be remote conversations for obvious reasons). After the fact, subjects are told that some of their companions might have been computers, and only then are they asked to rank the guests by “humanness.”

A Personal Assistant Turing Test will be something like a mid-term. Computers may get to the final exam, but they will still have a ways to go. Free-ranging dinner conversation puts the bar high, because it brings in context and give and take.  The low bar, sort of the tests for remedial work, is one-liner text, or invective-laden argument, where the objective is to rant while ignoring anything the other person is saying. I go through a classic and humorous example of this in my other post. On the continuum from context-rich, intelligent conversation toward the increasingly vacuous – e-mail exchanges, online chat, and finally twittering – the digital assistant leans toward the latter. Its conversation is close to stateless, because each command is unanchored from all but the last inquiry and the information provided up to that point. One rung up is something like cocktail party chit-chat of the “do you know so-and-so”, “have you ever been to wherever” variety. For that, I think the iPhone and Siri will be able to shine. It can know just about everyone and everyplace.  

So if you love your iPhone now, just wait until you can chat with it over a couple of drinks.

Thursday, October 13, 2011

A Crack in the Foundation: An error that has wended its way through economics for 77 years


This post is an introduction to a detective story about an error. An error that passed undetected by some of the greatest minds of the twentieth century, and led economics down a path that now must be cast into question. It is an error from 1934 Vienna that has lain hidden for the better part of a century, uncovered in 2011 in the academic halls of Imperial College of London. It is an error that is both obvious and startling after the fact, and is the result of a calculation that literally is off by an order of infinity.

A few weeks ago I attended a conference sponsored by the Santa Fe Institute, where I participated on a panel with Henry Kaufman, Bill Miller and Marty Leibowitz. The conference topic was Forecasting in the Face of Risk and Uncertainty. One of the presentations was by Ole Peters, from the Department of Mathematics at the Imperial College of London. His presentation compared time series analysis with ensemble analysis. Time series analysis takes one realization of a process and runs it over a very long time period and then looks at the distribution over the course of that run, whereas ensemble analysis creates many copies of the process and runs these over a shorter period, and then looks at the distribution of those results. Time series analysis is what you see over many years in one universe, ensemble analysis is what you see when you take many universes and integrate across them to look at the distributional properties.

Even if we use the same process for generating the paths as we do for the time series, these two approaches can lead to surprisingly different results for the ultimate distribution. This will always be true if a process is not ergodic, that is if it doesn't have the properties of creating a defined and unique distribution and leading to that distribution without regard to the starting point. Another way to think of an ergodic process is that over time it visits every possible state in proportion to its probability, and does so with the same proportions no matter where you start the process off. And one of the keystone processes analyzed in economics, the process of the inter-temporal compounding of wealth, is an example of a non-ergodic process. Peters presents a disarmingly simple example to show the difference between the time series and ensemble approaches for this process. Using a progression of simulated coin flips, he shows a case where the ensemble approach has a positive mean while the time series approach has one that is negative. On average people will make money while for the individual wealth will follow a straight line (on a log scale, at least) toward zero.

As Peters recounts in his presentation, economics has been almost unwavering in applying the ensemble approach. The reason is that in 1934 the Austrian mathematician Karl Menger wrote a paper that rejected unbounded utility functions. These unbounded functions include, for example, logarithmic utility, a particularly useful one because it corresponds to exponential growth, and thus is a natural for many time series processes (like compounded returns). Because his result is wrong, the motivation for focusing on the ensemble approach is ill founded. And, to make matters worse, in many important cases it is a time series approach that makes the most sense. After all, we only live one life, and we care about what is dealt to us in that life. If we enjoyed (and recognized that we enjoyed) reincarnation so that we could experience many alternative worlds – and better yet, if we experienced them all simultaneously -- perhaps it would be a different matter.

What is fascinating is that Menger’s paper has been cited widely by notable economists, including Samuelson, Arrow and Markowitz, Nobel laureates all. Peters recounts a number of these: In 1951, Arrow wrote a clearer version of Menger's argument, but failed to uncover the error while doing so. Ironically, by performing this service he helped propagate the development of economic theory along the wrong track. Arrow more recently wrote that "...a deeper understanding [of Bernoulli's St. Petersberg paradox] was achieved only with Karl Menger’s paper”. Markowitz accepted Menger's argument, stating that “we would have to assume that U[tility] was bounded to avoid paradoxes such as those of Bernoulli and Menger”. Samuelson waxed effusive regarding Menger's 1934 paper: “After 1738 nothing earthshaking was added to the findings of Daniel Bernoulli and his contemporaries until the quantum jump in analysis provided by Karl Menger”, and further that “Menger 1934 is a modern classic that stands above all criticism”. (And up until Peters’ paper, it seems it did indeed stand above all criticism, if there was any at all). That the paper was such a focus for so stellar a group of economists gives you a hint of its importance to the path economics has taken.

Not that the error is all that obscure, at least with the benefit of hindsight and a clear exposition. It boils down to Menger saying that the sum of a quantity A and a quantity B tends to infinity in the limit. Menger shows that A tends to infinity, and then argues that because of this, it doesn't matter what is going on with B, because infinity plus anything else is still infinity. Unless, of course, it happens that B is tending toward negative infinity even faster. Which, it turns out, is the case. So the sum, rather than having infinity as its limit, has negative infinity as its limit!