Brookings: Experts - H. Peyton Young

Gaming Performance Fees By Portfolio Managers

Dean P. Foster and H. Peyton. Young — Mon, 01 Nov 2010 00:00:00 -0400

Editor's Note: A PDF of the full paper can be downloaded at The Quarterly Journal of Economics website.

ABSTRACT

We show that it is very difficult to devise performance-based compensation contracts that reward portfolio managers who generate excess returns while screening out managers who cannot generate such returns. Theoretical bounds are derived on the amount of fee manipulation that is possible under various performance contracts.We show that recent proposals to reform compensation practices, such as postponing bonuses and instituting clawback provisions, will not eliminate opportunities to game the system unless accompanied by transparency in managers' positions and strategies. Indeed, there exists no compensation mechanism that separates skilled from unskilled managers solely on the basis of their returns histories.

Authors

Dean P. Foster
H. Peyton Young

Publication: The Quarterly Journal of Economics: Volume 125, Issue 4

Why Geithner’s Plan is the Taxpayers’ Curse

H. Peyton. Young — Wed, 01 Apr 2009 12:00:00 -0400

View the full paper upon which the op-ed below is based »

People who outbid others in auctions sometimes pay too much, a phenomenon known as the winner’s curse. Yet the plan outlined last week by Tim Geithner, US Treasury secretary, for pricing the toxic assets clogging up the financial system provides private investors with an unusually strong incentive to overpay: the government is proposing to pick up most of the tab if the assets turn out to be worth much less than was spent on them. Indeed, the more aggressively investors compete in bidding for these assets, the worse off the taxpayers will be. I call this the taxpayers’ curse.

A simple example will illustrate the problem. Suppose that a given bundle of mortgage-backed securities would be worth $20m (€15m, £14m) if you could be sure that all the mortgages will be repaid in full, but they might also turn out to be worthless. No matter how much you pay for them, the US government agrees to absorb any losses beyond approximately 15 per cent, while you get to keep half of any gains. In return, you only have to put up about 7.5 per cent of the purchase price. How much will the assets sell for? That depends on two things: how aggressively others bid and how much uncertainty there is about their ultimate value.

For simplicity, assume the assets could be worth $20m or zero with equal probability. Assume that yours is the winning bid at a price of $10m. Under Mr Geithner’s plan, you put up $750,000 for an equity stake and the government puts up the remaining $9,250,000: a loan for $8,500,000 and $750,000 for an equal share of the equity. There is a 50 per cent chance that you will get your money back in full and make a profit of $5m (in which case the other $5m in profit goes to the Treasury).

Of course, it is equally likely that the assets will turn out to be worthless, but in that case all you lose is your initial payment of $750,000, and the Feds are on the hook for the rest. That works out to an expected profit of $2,125,000 for an investment of $750,000, a return of 283 per cent.

If this seems too good to be true, it is: competition from other bidders will probably drive the bid price much higher. This would be unfortunate, however, because $10m is already the expected value of the asset. For example, a bid price of $14m would still be a bargain, because the investor’s expected profit would be approximately $1m on an initial investment of approximately $1m, which represents a 100 per cent return. Meanwhile, the taxpayers can expect to lose nearly 40 per cent of their money.

This is the singularly perverse feature of the Treasury proposal: the greater the competition among the bidders, the worse off the taxpayers and the more distorted the so-called “market” prices that result. More generally, one can work out the amount of price distortion and the expected returns to the taxpayers as a function of the variance in the realised values of the asset and the expected returns demanded by investors. For example, if there are two equally probable outcomes, one 50 per cent above the mean and the other 50 per cent below the mean, taxpayers can expect to lose money unless private investors make more than 180 per cent in expectation.

Some might argue that this is the price we must pay to get the financial system back on its feet but, in my view, it is much too steep. The problem is not merely the size of the bill, which could run into the hundreds of billions of dollars. The real difficulty is that the scheme perpetuates the very practices that got us into this jam in the first place. Over the last several decades, Wall Street wizards have developed products that most people cannot understand, including quite a few players in the financial markets themselves. The result has been mispricing and excessive risk-taking throughout the financial system.

It is truly dismaying that the Obama administration, which publicly champions greater transparency, should put forward a proposal whose main object is to subsidise the banks without appearing to do so. Instead of making the prices of toxic assets more transparent, it is likely to inject a new level of price distortion and uncertainty into the markets, while putting taxpayers at great risk. It may also allow banks to claim that assets remaining on their books after the auction should be priced at the same inflated level as the assets sold off.

A more straightforward plan would be strongly to encourage banks to auction off tranches of toxic assets without providing subsidies to the purchasers. This would involve fewer gimmicks and produce prices that more nearly reflect the assets’ true economic value. If these auctions do not generate enough activity to clean up the banks’ balance sheets, the government will have to seize control of insolvent institutions temporarily and sell off their bad assets over a period of time, as happened in the wake of the S&L debacle of the 1980s.

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H. Peyton Young

Publication: Financial Times

Living on the Hedge: A Forum on the Private Investment Fund Industry

Thu, 12 Feb 2009 08:30:00 -0500

Event Information

February 12, 2009
8:30 AM - 12:45 PM EST

Falk Auditorium
The Brookings Institution
1775 Massachusetts Ave., NW
Washington, DC

Wall Street hedge funds and their larger-than-life managers have captured Main Street’s imagination, as well as investor dollars. On February 12, the Brookings Institution hosted a forum to explore the role of hedge funds in the ongoing financial crisis, as well as their uncertain future in the evolving regulatory environment.

Glenn Hutchins, Brookings trustee and co-chief executive of Silver Lake, provided welcoming remarks. Senator Jack Reed, member of the Senate Banking, Housing, and Urban Affairs Committee and chairman of the Subcommittee on Securities, Insurance, and Investment, offered introductory remarks. Robert Greifeld, CEO of the NASDAQ OMX Group, offered the keynote address. Brookings Senior Fellow Martin Baily moderated a discussion on the hedge fund industry, and Brookings Senior Fellow H. Peyton Young gave a presentation on the importance of transparency.

James Chanos, Glenn Hutchins and Sebastian Mallaby at forum.

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Transcript (.pdf)

Event Materials

Participants

Panelists

Glenn Hutchins

Co-Chief Executive, Silver Lake
Trustee, The Brookings Institution

The Honorable Jack Reed (D-RI)

United States Senate

Moderator: Martin Baily

Senior Fellow and Director, Initiative on Business and Public Policy, The Brookings Institution

William Ackman

President, Pershing Square Capital Management

James J. Angel

Associate Professor of Finance, McDonough School of Business, Georgetown University

Moderator: Sebastian Mallaby

Paul A. Volcker Senior Fellow for International Economics and Director, Maurice R. Greenberg Center for Geoeconomic Studies, Council on Foreign Relations
Columnist, Washington Post

James Chanos

President, Kynikos Associates
President, Coalition of Private Investment Companies

Andrew W. Lo

Harris & Harris Group Professor, Sloan School of Management, Massachusetts Institute of Technology

Glenn Hutchins

Co-Chief Executive, Silver Lake
Trustee, The Brookings Institution

Robert Greifeld

Chief Executive Officer, NASDAQ OMX Group

The Not-So-Real-McCoy: Fake Alpha and the Need for Hedge Fund Transparency

Dean P. Foster and H. Peyton. Young — Wed, 17 Dec 2008 12:00:00 -0500

The current shakeout in the hedge fund industry is capturing headlines, as managers who suffered large double-digit losses in 2008 are likely to have little choice but to shutter their funds. But even if the past year’s turbulent financial markets had been more forgiving, the business would be facing a serious challenge from another source. Hedge funds’ fee structure, combined with an almost total lack of transparency, makes the industry vulnerable to invasion by low-quality entrants who could undermine returns and trigger a collapse of confidence. The trouble is that when hedge fund investors are not allowed to look “under the hood,” it can take a very long time for them to determine whether a manager is consistently generating true alpha or is simply having a run of good luck. Even worse, this information gap provides an opportunity for outright charlatans to enter the market — looking just like the real McCoys — without getting caught.

In this article we show how easy it is to generate “fake alpha” when investors can’t see what you are doing, and how much money you can make in the process. Although this potential problem has been discussed in the academic literature and is understood by some sophisticated players in the industry, how serious it is and how difficult it will be to fix is less widely appreciated. The problem can’t be rectified simply by tinkering with the hedge fund fee structure. It is not enough to defer performance fees for managers or require them to hold an equity stake, nor will it work to levy monetary penalties on managers who underperform. Returns can, in effect, be manipulated using a certain options trading strategy. We argue that the only solution is far greater transparency and that the industry itself has a strong interest in providing it.

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Authors

Dean P. Foster
H. Peyton Young

Publication: Institutional Investor

The Hedge Fund Game

Dean P. Foster and H. Peyton. Young — Wed, 24 Sep 2008 15:09:38 -0400

This is an updated version of a paper published Novermber 2007.

Abstract

We show that it is extremely difficult to devise incentive schemes that distinguish between fund managers who cannot deliver excess returns from those who can, unless investors have specific knowledge of the investment strategies being employed. Using a ‘performance‐mimicking’ argument, we show that any fee structure that does not assess penalties for underperformance can be gamed by unskilled managers to generate fees that are at least as high, per dollar of expected returns, as the fees of the most skilled managers. We show further that standard proposals to reform the fee structure, such as imposing high water marks, delaying managers’ bonus payments, forcing them to hold an equity stake, or assessing penalties for underperformance, are not enough to separate the skilled from the unskilled. We conclude that skilled managers will have to find ways other than their track records to distinguish themselves from the unskilled, or else the latter may drive out the former as in a classic lemons market.

Introduction

Hedge funds are largely unregulated investment vehicles that have become increasingly important in global financial markets.1 Currently there are nearly ten thousand funds that collectively have over two trillion dollars under management. Although hedge funds pursue a great variety of investment strategies, they have two key features that we shall focus on here. One is the fee structure: the great majority of funds have a two‐part structure consisting of a management fee plus a performance bonus that gives the manager a percentage of any excess returns he generates over and above some benchmark rate. Management fees are typically between 1% and 2% and the most common bonus is 20% (Ackermann, MacEnally, and Ravenscraft, 1999). A second key characteristic shared by many (though not all) hedge funds is lack of transparency: they need not, and often do not, disclose their positions or trading strategies to investors; all they are required to provide is regular audited statements of gains and losses.

These two features – fees based on excess returns and lack of information about how the returns were generated – create incentives for manipulation, as a number of authors have pointed out (Starks, 1987; Carpenter, 2000; Ackermann, MacEnally, and Ravenscraft, 1999; Lo, 2001; Hodder and Jackwerth, 2007). One problem is that the convexity of the fee structure encourages managers to employ strategies with high variance, especially as the date for meeting certain targets is approached. A second problem is that substandard returns in later periods do not offset the earnings from excess returns in earlier periods unless the contract contains clawback provisions, which are fairly unusual. Furthermore it is quite easy to ‘game’ standard measures of performance, such as the Sharpe ratio, Jensen’s alpha, and the appraisal ratio (Goetzmann, Ingersoll, Spiegel, and Welch, 2007; Guasoni, Huberman, and Wang, 2007).

This paper was featured in an article in The Financial Times, March 18, 2008.

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Dean P. Foster
H. Peyton Young

Understanding Strategic Learning through Game Theory and Agent-Based Modeling

H. Peyton. Young — Sun, 13 Jul 2008 12:00:00 -0400

The Question

When can rational players learn to play Nash equilibrium starting from out‐of‐equilibrium conditions?

The “classical” case

The number of players is small
The rules are common knowledge
The payoffs, or at least the distribution of possible payoffs, is common knowledge
Everyone is rational

Even in this high rationality world, learning is difficult because it is interactive: each player’s learning process complicates what has to be learned by everyone else.
Kalai and Lehrer, Econ, 1993 Jordan, GEB, 1991, 1993 Nachbar, Econ, 1997, 2005

In fact, the learning behavior of a Bayesian rational agent can be so complex that it is essentially unlearnable by other rational players.

Theorem:
There are simple games of incomplete information (e.g., matching pennies with uncertain payoffs) such that, for any prior beliefs, Bayesian rational players will fail to come close to Nash equilibrium play with probability one.
Furthermore at least one of the players will almost surely fail to learn how to predict the behavior of his opponent even approximately.
Foster and Young, Proceedings of the National Academy of Sciences, vol. 98, 2001.

Third World Congress of the Game Theory Society Info

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Investors Need More Hedge Fund Transparency

H. Peyton. Young — Mon, 14 Jan 2008 10:51:24 -0500

(A letter to the editor)

Sir, Raghuram Rajan argues that bankers' compensation schemes are flawed because they encourage excessive risk-taking (Bankers' Pay is Deeply Flawed, January 9). A similar argument holds for hedge fund managers, who are typically paid 20 per cent of the excess returns they generate. The problem is that managers can generate "apparent" excess returns by taking on huge tail risks that are hidden from investors and the managers get paid handsomely before the fund blows up.

Prof Rajan suggests that the problem can be fixed by deferring performance bonuses until investors can be reasonably sure the excess returns are real. Unfortunately, this can take so long that it is not a practical solution. Consider the following example: using options, a manager can generate annual returns that exceed the S&P 500 by 5 per cent while exposing the investors to a 5 per cent chance each year of losing all their money.

Suppose that the manager's bonus is deferred for 10 years and that his deferred bonus equals 20 per cent of the cumulative excess return, assuming the fund does not blow up before then. The probability of this outcome is about 60 per cent and the cumulative excess return is over 60 per cent times the 10-year return of an ordinary S&P 500 index fund. Even for a modest-sized fund this represents a huge deferred bonus, and the manager has a 60 per cent chance of realising it even though the excess returns are faked.

Even with longer deferral times and claw-back provisions, it is very difficult to fix the problem by redesigning the incentive structure. A better remedy is for investors to insist on greater transparency so they know what risks are lurking in the tails.

Authors

H. Peyton Young

Publication: The Financial Times

Hedge Fund Wizards

Dean P. Foster and H. Peyton. Young — Wed, 19 Dec 2007 09:43:49 -0500

Scarcely a day goes by without another story of some large hedge fund blowing up due to bad bets. While many of the latest hedge fund casualties are linked to the subprime mortgage crisis, investors should not be lulled into thinking that the problem will be solved once the mortgage mess is mopped up.

Hedge funds are risky for another reason. It is extremely difficult to tell, based on past performance, whether a fund is being run by true financial wizards, by no-talent managers who happen to get lucky or by outright scam artists.

To illustrate how easy it is to set up a hedge fund scam, consider the following example. An enterprising man named Oz sets up a new fund with the stated aim of earning 10 percent in excess of some benchmark rate of return, say 4 percent. The fund will run for five years, and investors can cash out at the end of each year if they wish. The fee is the standard '2 and 20': 2 percent annually for funds under management, and a 20 percent incentive fee for returns that exceed the benchmark.

Although he has no investment track record, Oz has a smooth manner, a doctorate in physics and many rich acquaintances. He raises $100 million and opens shop. He then studies the derivatives market and finds an event on which the market places fairly long odds, say 9:1. In other words, it costs $.10 to buy an option that pays $1 if the event occurs and $0 otherwise. The nature of the event is unimportant: it might be a large fall in the stock market, Florida getting hit by a Category 5 hurricane or Russian President Vladimir Putin dying before the end of the year.

Next Oz writes some covered options on this event and sells 110 million of them in the derivatives market. This obligates him to pay the option holders $110 million if the event does occur and nothing if it does not. He collects $11 million on the options. To cover his obligations in case the 'bad' event occurs, he uses the investors' money plus the proceeds from the options to buy $110 million in one-year Treasury bills yielding 4 percent, which he deposits in escrow. This leaves $1 million in "pocket money," which he uses to lease some computer terminals and hire a few geeks to sit in front of them, just in case his investors drop by.

The probability is ninety percent that the bad event does not occur and Oz owes nothing to the option holders. With a gross return (before expenses) of $15,400,000, the investors are thrilled, and so is Oz. He collects $2 million in management fees (of which he has only spent $1 million), plus a performance bonus equal to 20 percent of the 'excess return', namely, 20 percent of $11,400,000. All in all, Oz nets over $3 million for doing absolutely nothing.

Oz can then repeat the same gambit next year. When the fund terminates after five years, the chances are nearly 60 percent that the unlucky event will never have occurred. Oz looks like a genius and gets paid like a genius.

While most hedge funds probably don't operate in such a nakedly self-serving way, the underlying logic of Oz's strategy is quite common: take a position that yields high returns with high probability and extremely poor returns with low probability, and keep your fingers crossed. Credit default swaps are one example, so are bets on interest rate spreads. Such strategies are risky but not fraudulent; the manager can always argue that his opinion about the odds differed from the market odds (he was simply engaging in arbitrage).

Eliminating such scams through regulation is not going to be easy due to the unusual nature of the product. Yet, some steps toward protecting investors can -- and should -- be taken.

All hedge funds should be required to register as soon as they are established and to report their returns on a regular basis. Such tracking would allow potential investors to study the records. New rules could also require managers to keep investors apprised of the fund's downside exposure. Alternatively managers could guarantee that losses not exceed a certain level, similar to a car manufacturer offering a warranty.

Although individual hedge fund managers may drag their feet, it is actually in the industry's best interest to encourage greater regulation and transparency. Otherwise, a rising tide of failed funds could cause a collapse in investor confidence, putting both the good and the bad wizards out of business.

Authors

Dean P. Foster
H. Peyton Young

Publication: Washingtonpost.com

Agent-Based Modeling and Spatial Population Dynamics Workshop

Fri, 07 Dec 2007 12:00:00 -0500

Event Information

December 7, 2007
12:00 PM - 5:00 PM EST

Stein Room
The Brookings Institution
1775 Massachusetts Avenue, N.W.
Washington, DC 20036

The Brookings Center on Social and Economic Dynamics and the Metropolitan Policy Program jointly hosted an NICHD funded Agent Based Modeling and Spatial Population Dynamics Workshop at the Brookings Institution. Researchers from across the country attended the workshop to discuss current projects, to gain insight into agent-based modeling, and to unearth issues for future research collaboration.

The workshop began with an introduction by Brookings scholars' Joshua M. Epstein and Audrey Singer, followed by background presentations on current agent-based modeling and migration research. During the afternoon, participants engaged in a moderated discussion focusing on outstanding spatial problems in demography, as well as, research opportunities for collaboration between agent-based modeling and migration analysis. The discussion generated many fruitful questions and potential for future work.

Agenda

Complete List of Participants

Presentations

Introduction to Agent-Based Modeling
Michael Macy (Cornell University)
Observations on Agent-Based Modeling and Applications for Demography
Robert Mare (UCLA)
Brief Presentations on Current Joint Work
Chris Fowler and Mark Ellis (University of Washington)
Steve Manson (University of Minnesota)
Dan Brown (University of Michigan)

Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence, and Social Learning

H. Peyton. Young — Wed, 31 Oct 2007 14:09:46 -0400

New ideas, products, and practices take time to diffuse, a fact that is often attributed to some form of heterogeneity among potential adopters. This paper analyzes the effect of incorporating heterogeneity into three broad classes of models -- contagion, social influence, and social learning. Each type of model leaves a characteristic ‘footprint’ on the shape of the adoption curve that amounts to a restriction on the pattern of acceleration with very few restrictions on the distribution of parameters. These restrictions provide a basis for discriminating empirically between different models, and have potential application to marketing, technological change, fads, and epidemics.

1. Introduction

A basic puzzle posed by innovation diffusion is why there is often a long lag between an innovation’s first appearance and the time when a substantial number of people have adopted it. There is an extensive theoretical and empirical literature on this phenomenon and the mechanisms that might give rise to it.[1] A common feature of these explanations is that heterogeneity among the agents is the reason that they adopt at different times. However, most of the extant models incorporate heterogeneity in a very restricted fashion, say by considering two homogeneous populations of agents, or by assuming that the heterogeneity is described by a particular family of distributions.[2]

In this paper I show how to incorporate heterogeneity into some of the benchmark models in marketing, sociology, and economics without imposing any parametric restrictions on the distribution of the underlying parameters. The resulting dynamical systems turn out to be surprisingly tractable; indeed, some of them can be solved explicitly for any distribution of the parameter values. I then demonstrate that each class of models leaves a distinctive ‘footprint’; in particular, they exhibit noticeably different patterns of acceleration, especially in the start-up phase, with few or no assumptions on the distribution of the parameters. The reason is that the models themselves have fundamentally different structures that even large differences in the distributions cannot overcome. It follows that, given sufficient data on the aggregate dynamics of a diffusion process, one could assess the relative plausibility of different mechanisms that might be driving it with little or no prior knowledge about the distribution of parameters. While this type of analysis is not an identification strategy, and is certainly no substitute for having good micro-level data, it could be useful in situations where such data are unavailable.

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Publication: CSED Working Paper No. 51

Social Norms and Public Policy

H. Peyton Young — Wed, 31 Oct 2007 14:42:35 -0400

Why do medical practices vary so much between localities within the same state? Why do smoking rates among teens differ across age cohorts? Why do rates of voter turnout vary significantly between electoral districts that have the same socio-economic characteristics? Differences in social norms may help to explain these and other puzzling differences in group behavior that are not readily attributable to differences in income, tastes, and other individual characteristics.

Social norms are rules of conduct that govern interactions among individuals within a reference group. Norm violations often provoke disapproval and loss of esteem, which is the force that holds them in place [1]. Although social norms exert a powerful influence on people’s behavior in many arenas, they are difficult to measure directly and are often neglected in the design of policy. Standard policy analysis focuses mainly on individual responses to incentives, such as prices. If individuals are influenced by rules of conduct within their reference groups, however, policies must be designed to induce change at the group level, as well as, at the individual level. This requires a different set of tools than is provided by conventional policy analysis.

To analyze how norm shifts occur, and how policies can be designed to engineer such shifts, one must view individuals as embedded in a larger social system. Two factors of particular importance are: i) the social network, that is, the web of connections that describe who interacts with whom; and ii) the mechanism by which norms of behavior are enforced by the group.

Social norms are pertinent to many areas of policy, particularly health policy. Evidence is accumulating, for example, that obesity is spread in part by social contagion: if someone’s close friends become obese it is more likely that they will become obese also. Such effects are observed even after controlling for many factors that friends may have in common, such as income, education, ethnicity, even place of residence. Similarly, there is evidence that teenagers are more likely to take up smoking if their friends take up smoking; and adults are more likely to give it up if their friends give it up. These issues arise in many other areas of social policy, including teenage pregnancy, the willingness to get vaccinated, and the propensity to engage in criminal behavior.

The logic of these situations is that people want to conform to the customary practices and ideals of their reference group because they will be stigmatized if they fail to do so. This may or may not conflict with the choices they would make on their own, but there certainly are situations where perverse norms become entrenched that are quite detrimental to individuals’ welfare. Conventional policy interventions, such as taxing harmful practices or dispensing information about their negative consequences, will not have much impact unless they succeed in shifting the equilibrium at the group level. This may require targeted interventions that take account of the social network structure. In fact, when such interventions are correctly designed, they can sometimes “tip” group behavior into a new equilibrium even more rapidly than if norms were not a factor. Policy can use group norms to its advantage.

Agent-based models are especially well-suited to study these issues. Firstly, they are dynamic, and can simulate behavior both in and out of equilibrium. Secondly, the agents who populate the models are fully heterogeneous: they have a range of personal traits, differ in the amount of information they possess, have different positions within the social network, and so forth. The models are also explicit about the ways agents interact and respond to information, which may be highly rational, merely adaptive, or somewhere in-between. Recent advances in stochastic dynamical systems theory, some of them pioneered by members of the Brookings Center on Social and Economic Dynamics, allow researchers to study the long-run dynamical behavior of such models with great accuracy [2].

This general approach can be used to analyze such questions as how quickly norm shifts can spread through a society, and what types of interventions are most likely to trigger such shifts. The answers depend crucially on how agents use the information generated by other agents, and also on the topology of the social network [3, 4]. Empirical applications include a study of how new agricultural technologies diffuse [5], and how shifts in smoking behavior can be induced by targeted interventions [6].

Agent-based models also provide insights into the qualitative effects of social norms on group behavior. One of the most interesting is that norms often have a ‘patchy’ look; that is, they induce overly uniform behavior within a given community (in spite of individual differences among its members), yet they may also induce very different behaviors among communities (even though these communities are quite similar in a cross-sectional sense). This is known as the local conformity/global diversity effect [2].

Empirical support for this proposition can be found in a number of domains, including strong regional differences in medical treatments for a given condition combined with an excessive uniformity of practice within a given region [7]. This has implications for health policy, because it suggests that powerful professional norms can get in the way of delivering efficient medical care. It is therefore crucial to understand what holds such norms in place and how norms can be altered by targeted forms of intervention. This is one of many examples showing how policy analysis can benefit from models that incorporate social norms.

1. H. P. Young, “Social Norms,” forthcoming in The New Palgrave Dictionary of Economics, 2^nd edition. London: Macmillan.

2. H. P. Young, Individual Strategy and Social Structure: An Evolutionary Theory of Institutions. Princeton University Press, 1998.

3. H. P. Young, “The Diffusion of Innovations in Social Networks,” in Lawrence E. Blume and Steven N. Durlauf, eds. The Economy as a Complex Evolving System, vol. III. , Oxford University Press, 2003.

4. H. P. Young, “Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence, and Social Learning.” CSED Working Paper #51. October, 2007.

5. H. P. Young, “The Spread of Innovations through Social Learning,” CSED Working Paper #43, December ,2005.

6. Social Influences and Smoking Behavior: Final Report to The American Legacy Foundation. February, 2006. www.brookings.edu/dynamics/publications.aspx

7. Mary A. Burke, Gary Fournier, and Kislaya Prasad, “Physician Social Networks and Geographical Variation in Medical Care.” CSED Working Paper #33. July, 2003.

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Obesity and the Influence of Others

Carol Graham, H. Peyton. Young and Ross A. Hammond — Tue, 21 Aug 2007 00:00:00 -0400

A much-publicized article in the New England Journal of Medicine reports that your chance of becoming obese is much higher if you have a close friend who is obese. Obesity appears to be socially "contagious." The finding is remarkable in that it departs from much standard wisdom about the supposed causes of obesity. Most experts tend to view it as a combination of genetic predisposition and economic choice. If high-fat food is cheap and readily available, people will tend to eat more of it. And if you have an inherited tendency to put on weight, you are more at risk of becoming obese.

Notice that this is an individual-level explanation, not a social one. In fact, many economists and public health experts are uncomfortable with the notion that social norms could strongly influence individual choices about such matters as health and well-being. This is partly due to an academic bias against any explanation that smacks of "irrationality," and partly due to the difficulty of disentangling social influences from other factors. Using sophisticated statistical methods, the new study goes a long way toward solving the latter problem. But it stops short of asserting that adherence to social norms is the mechanism through which the contagion spreads.

In fact, there is ample evidence from our and others' research that supports this explanation. A social norm creates an ideal image of behavior that acts as a constraint on what individuals might otherwise do. Psychological surveys have shown that different socio-economic and ethnic groups have markedly different notions of what constitutes an ideal body weight. In the U.S. and Britain, for example, obesity rates are much higher among lower income groups. The presumption is that if you depart from the ideal too much, you will feel badly about yourself and, furthermore, others will make you feel badly.

There is substantial empirical evidence for this 'stigma effect'. Our research, based on surveys of well-being, finds that in cohorts where obesity rates are high, obese people do not report being more unhappy than others, whereas in cohorts where obesity rates are low, obese people tend to be much unhappier than the mean (controlling for other factors such as age, gender and income). In other words, it makes you less unhappy to be obese if others around you are obese. Our research also finds a negative link between obesity and upward income mobility; if you are obese and work at Walmart, you are less likely to move on to a better job than if you are not. Thus higher obesity norms may be poverty as well as health traps.

One outstanding puzzle is how the current obesity epidemic got started. Why did it suddenly take off more or less simultaneously in different socioeconomic and ethnic groups in the early 1980s? "Junk" food was surely widely available long before then. Was it the result of a change in the cost of food, of marketing campaigns by fast food chains, or attitudes about exercise? And why have such significant differences in levels of obesity and stigma persisted among groups? Whatever the ultimate trigger of the obesity epidemic might have been, it seems very likely that social norms are playing a critical role in the way it continues to spread.

Because social norms and social networks seem to play such an important role, computer simulations of social systems can be a very useful tool for solving the puzzles surrounding the obesity epidemic. These simulations can help us understand how the structure of social networks affects the spread of norms and weight change. For example, the simulations we use in our research suggest that overall social norms about weight can shift dramatically as a result of even small changes by some members of the group. Simulation models can also suggest policies for interrupting the spread, for example by targeting individuals who act as role models in particular communities or by changing the mixture of social messages that reach a network.

The goal of studying obesity is, ultimately, to try to reverse its dramatic rise and to close these gaps in its incidence among groups. To do that, policymakers need to understand the processes that led to the increase and the disparities in the first place -- not just what factors matter, but how and why they matter. Much public attention has gone to the role of cheap "junk" food, for example. Much less has gone to explaining why some cohorts consume so much of it and become obese, while others do not and maintain completely different weight norms.

It is becoming clear that social influence matters in obesity. But more research is needed to uncover exactly how it matters. We are using novel techniques -- computer simulations and well being surveys -- to study the problem and how we might use social networks to help us slow or reverse the alarming increase in obesity. Should policies be targeted at network leaders, for example? Should the links between obesity and lower levels of income mobility be made more explicit as a possible incentive, or will that merely exacerbate low expectations and poverty traps? We do not know at this point. Until we understand the causes at work, we cannot design effective policies to intervene, and we will continue to spend large sums of resources on public health messages that are not reaching the right audience.

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Publication: The Washington Post

The Possible and the Impossible in Multi-Agent Learning

H. Peyton. Young — Sun, 01 Apr 2007 00:00:00 -0400

Abstract

Interactive learning is inherently more complex than single-agent learning, because the act of learning changes the thing to be learned. If agent A is trying to learn about agent B, A's behavior will naturally depend on what she has learned so far, and also on what she hopes to learn next. But A's behavior can be observed by B, hence B's behavior may change as a result of A’s attempts to learn it. The same holds for B’s attempts to learn about A.

This feedback loop is a central and inescapable feature of multi-agent learning situations. It suggests that methods which work for single-agent learning problems may fail in multi-agent settings. It even suggests that learning could fail in general, that is, there may exist situations in which no rules allow players to learn one another's behavior in a completely satisfactory sense. This turns out to be the case: in the next section I formulate an uncertainty principle for strategic interactions which states that if there is enough ex ante uncertainty about the other players’ payoffs (and therefore their potential behaviors), there is no way that rational players can learn to predict one another’s behavior, even over an infinite number of repetitions of the game (Foster and Young, 2001; for earlier results in the same spirit see Binmore (1987) and Jordan (1991, 1993)).

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H. Peyton Young

Publication: CSED Working Paper # 47

Innovation Diffusion in Heterogeneous Populations

H. Peyton. Young — Fri, 01 Dec 2006 00:00:00 -0500

Abstract

New products and practices take time to diffuse, a fact that is often attributed to some form of heterogeneity among potential adopters. People may realize different benefits and costs from the innovation, or have different beliefs about its benefits and costs, hear about it at different times, or delay in acting on their information. This paper analyzes the dynamics arising from different sources of heterogeneity in a completely general setting without placing parametric restrictions on the distribution of the relevant characteristics. The structure of the dynamics, especially the pattern of acceleration, depends importantly on which type of heterogeneity is driving the process. These differences are sufficiently marked that they provide a potential tool for discriminating empirically among diffusion mechanisms. The results have potential application to marketing, technological change, fads, and epidemics.

1. Introduction

The diffusion of new products and practices usually takes time, and the proportion of people who have adopted at each point in time frequently, though not invariably, traces out an S-shaped curve. There is an extensive theoretical and empirical literature on this phenomenon and the mechanisms that might give rise to it. Different lines of explanation have been pursued in the various disciplines -- marketing, sociology, and economics – where innovation diffusion has been most intensively studied. A crucial feature of some of these explanations is that heterogeneity among the agents is the reason they adopt at different times. Nevertheless, most of the extant models incorporate heterogeneity in a very restricted fashion, say by considering two homogeneous populations of agents, or by assuming that the heterogeneity is described by a particular family of distributions.

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H. Peyton Young

Publication: CSED Working Paper #45

Social Influences and Smoking Behavior

Fri, 10 Feb 2006 00:00:00 -0500

The objectives of this project were to conduct a comprehensive study of social influences on smoking behavior using an agent-based modeling approach. The results of the research can be divided into three parts. The first part was devoted to understanding the physiological and psychological bases of nicotine addiction in order to integrate them into the model. This work is summarized in two papers, “Social Influence, Reactance, and Tobacco,” by Ross Hammond, and “Addiction and Cessation Functions in the Agent-Based Smoking Model” by Zirui Song. The second part of the research involved a statistical analysis of social network structures among teenagers, which function as conduits for initially taking up smoking and also for quitting based on targeted interventions. These findings are reported in the paper “How to Form a Network of Junior High School Students,” by Ben Klemens, and form an integral part of the computer models described below.

The third and principal component of the research was to construct agent-based computer models that can be used to simulate the impact of various types of policy interventions. This work was carried out by Robert Axtell, Joshua Epstein, Ross Jon Parker, and Peyton Young. The project produced two models that are designed to study different types of effects.

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Robert Axtell
Steven Durlauf
Joshua M. Epstein
Ross A. Hammond
Ben Klemens
Jon Parker
Zirui Song
Thomas Valente
H. Peyton Young

The Spread of Innovations through Social Learning

H. Peyton. Young — Thu, 01 Dec 2005 00:00:00 -0500

Presented at the CSED Seminar Series

Abstract

Innovations often spread by the communication of information among potential adopters. In the marketing literature, the standard model of new product diffusion is generated by information contagion: agents adopt once they hear about the existence of the product from someone else. In social learning models, by contrast, an agent adopts only when the perceived advantage of the innovation -- as revealed by the actions and experience of prior adopters -- exceeds a threshold determined by the agent's prior beliefs. We demonstrate that learning with heterogeneous priors generates adoption curves that have an analytically tractable, closed-form solution. Moreover there is a simple statistical test that discriminates between this type of process and a contagion model. Applied to Griliches' classic results on the adoption of hybrid corn, this test shows that learning with heterogeneous priors does a considerably better job of explaining the data than does the contagion model.

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H. Peyton Young

Publication: CSED Working Paper No. 43

Social Dynamics: Theory and Applications

H. Peyton. Young — Fri, 01 Apr 2005 00:00:00 -0500

Abstract

Agent-based models typically involve large numbers of interacting individuals with widely differing characteristics, rules of behavior, and sources of information. The dynamics of such systems can be extremely complex due to their high dimensionality. This chapter discusses a general method for rigorously analyzing the long-run behavior of such systems using the theory of large deviations in Markov chains. The theory highlights certain qualitative features that distinguish agent-based models from more conventional types of equilibrium analysis. Among these distinguishing features are: local conformity versus global diversity, punctuated equilibrium, and the persistence of particular states in the presence of random shocks. These ideas are illustrated through a variety of examples, including competition between technologies, models of sorting and segregation, and the evolution of contractual customs.

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H. Peyton Young

Publication: CSED Working Paper # 39

Ignorance Fills the Income Gulf

Carol Graham and H. Peyton. Young — Mon, 23 Jun 2003 00:00:00 -0400

At a recent Washington social gathering in honor of graduating seniors heading to elite colleges, the subject turned to the new tax cut. "Isn't it too tilted toward the wealthy?" one parent asked. Another retorted, "Why give tax breaks to the poor? All they will do with it is buy more Cokes or another pair of Nikes. We need to stimulate investment to create new jobs and wealth."

This is, of course, exactly the rationale the Bush administration used to justify the tax cut. Yet the remark is deeply troubling, in ways that go beyond the usual policy debates. As economic policy, it is simply wrong-headed. The economy is well below capacity and needs demand, not investment stimulus. An extra $30 billion a year in the hands of millions of lower and middle class families would buy a lot of Cokes and Nikes. Meanwhile $30 billion in the hands of a few investors may eventually lead to more jobs and investment, but that could be a long way off.

But are the people at the party right about what plain folks want? Perhaps they want better health insurance - or just some health insurance. They might need to spend the tax break on college for their kids. Indeed, in-state tuition at many state universities is going up by 10 to 20 percent in just one year. Yet these facts are simply not part of the current political debate. In part this is because those who frame the debate find these facts almost impossible to imagine. It's not that they are mean-spirited; on the contrary, they are well-meaning people who give generously to charitable causes. It's just that they find it hard to believe an extra $500 or $1,000 for the typical American family could make a real difference.

Ultimately what drives these attitudes is ignorance about how others actually live, a gulf between the haves and the have-nots in American society that seems to widen every year. It is not only ignorance on the part of the haves, however, that keeps this system in place. A surprising number of have-nots expect that they, or at least their children, will eventually be attending parties just like this one. An October 2000 Time-CNN news poll showed that 19 percent of Americans thought that they were in the high income group that would benefit from proposed tax cuts - defined as roughly the top 1 percent of the distribution.

The strong belief that the United States is the land of opportunity helps explain why support for income redistribution is low in America compared to Europe. A study by Roland Benabou and Efe Ok of Princeton University, for example, finds that the majority of Americans believe they will be above average (mean) income in the future, a Lake Wobegon fantasy if there ever was one.

To what extent is the United States the land of opportunity? How does the myth - which has clear effects on political attitudes - square with reality? Evidence suggests that mobility in the United States is not higher than in other countries in the Organization for Economic Cooperation and Development and indeed may be lower. A Stockholm University study finds more mobility in Sweden than the United States and that only South Africa and Britain have as little mobility as the United States. Indeed a recent Brookings Institution book records more mobility in a 10-year period in Peru than in the United States.

There are many factors determining mobility. Children from well-to-do households tend to fare better than children from poor households for a variety of reasons, including transmitted cognitive abilities and higher expectations, as well as better access to health and educational opportunities. The factors that are most influenced by policy, especially health and education, are becoming increasingly expensive, even out of reach for many families with the exception of the poorest ones that qualify for special programs. An Urban Institute book says that access to good schools is increasingly important for upward mobility - but is strongly linked to family income.

Policies that give tax breaks to the wealthy at the expense of support for basic social services such as affordable health insurance and public education risk undermining the foundation of the American dream. While the public may still believe that we live in the land of opportunity, the reality is one of increasing stratification of incomes and of opportunities.

We need a broader public debate about opportunity in our society and how it relates to current policy. It seems that the rich are as uninformed about the facts as the poor. Ignorance is not without cost, however. Antonia Fraser's biography of Marie Antoinette suggests that she was not the nasty person of popular imagination, but was quite generous and warm-hearted (if rather naive). What ultimately did her in was simple ignorance about how others live.

Authors

Publication: The Boston Globe

Dividing the House: Why Congress Should Reinstate an Old Reapportionment Formula

H. Peyton. Young — Fri, 31 Aug 2001 00:00:00 -0400

The dramatic changes in state populations revealed by the 2000 census will cause twelve seats to shift from one state to another in the House of Representatives in 2002. Although much attention is being devoted to redistricting within states, not enough is being paid to a fundamental flaw in the formula used to allocate the 435 seats among the states. This peculiar method, first adopted in 1941, violates the principle of one person, one vote by systematically giving more representation to residents of small states than to residents of large states.

Fortunately, the situation is easy to fix: a simpler formula, first proposed by Senator Daniel Webster in the 1830s and currently used in other representative democracies, treats small and large states even-handedly. Reinstating Webster's method now—well in advance of the next census—will restore the long-term balance between small and large states.

POLICY BRIEF #88

Every ten years, a new census leads to a constitutionally mandated reapportionment of the House of Representatives. Inevitably, this process has major political consequences, and the 2000 census is no exception. The new apportionment will cost the Northeastern states ten seats and give a substantial boost to the political fortunes of the South and the Southwest, as shown in figure 1.

Unfortunately, the process that governs reapportionment is fundamentally flawed. Through a strange combination of historical accident and political and mathematical intrigue, Congress is presently saddled with one of the most peculiar apportionment methods used anywhere in the world. Not only is it unnecessarily complex—involving square root formulas—it demonstrably favors small states at the expense of large states. Fortunately, there is an easy way to remedy the problem, as I will explain here.

Heading Off Politics as Usual

A number of political factors have converged to make the issue of equal representation particularly potent this year. There was extensive debate in the executive and legislative branches leading up to the 2000 census about how to correct for errors that tend to undercount minorities. Then there was the contested presidential election, which made Americans keenly aware that every vote really does count. Finally, there are questions of fairness in how district lines are being redrawn within the states.

These issues have fed public concern that the right to equal representation is perhaps being compromised. Given these perceptions, Congress would do well to reform the inequitable process by which seats are distributed among the states in the first place. Although Congress can take up this matter at any time, this seems like a particularly propitious moment, since it could correct a long-term problem in the system with no short-term political consequences, because no seats would shift this time around.

How could such a seemingly straightforward problem turn into such a quagmire? In particular, why not simply take each state's fraction of the total population, multiply it by the total number of seats (currently 435) to determine each state's seat quota (see figure 4), and then round the quotas to the nearest whole numbers?

To illustrate the difficulty, consider the example in figure 2, which represents a hypothetical federation of three states with a "house" of 21 representatives: inspection of the quotas shows that ordinary rounding will not work because all three states would be rounded down, and thus only 20 seats would be apportioned.

The earliest proposed solution to this difficulty came from Alexander Hamilton in 1792, who suggested rounding the quotas in the usual way, and if any seats are left over, giving them to the states with largest remainders. In figure 2, state B, with remainder .41, would receive three seats under Hamilton's method.

While that approach may seem straightforward, later experience would show that it was fraught with difficulties. At the time, Hamilton's nemesis, Thomas Jefferson, argued that the method was fundamentally wrong. Jefferson asserted that the correct approach was to choose a common divisor, divide it into each state's population, and drop the fractional part of the resulting quotient. The "trick" is to adjust the divisor so that the required number of seats is apportioned.

Jefferson's approach apportions each House size in an essentially unique way, because as the divisor is adjusted downwards (or upwards), exactly one state at a time gains (or loses) a seat, barring improbable ties.

In the 1790s debate, Jefferson prevailed over Hamilton—not because Congress recognized its mathematical subtlety, but largely because it gave one more seat to Virginia, which at that time was the most populous and most politically important state. Jefferson's method was used through the 1830s, even as it came under increasingly bitter attack in Congress because it blatantly favored large states. (If Jefferson's method were in use today it would give California 55 seats, even though California's current seat quota is only 52.45.)

The evident bias of Jefferson's reapportionment method ultimately led to its abandonment in 1840, when it was replaced by a method first proposed in 1832 by the brilliant orator Daniel Webster. Like Jefferson, Webster began with a common divisor, but instead of dropping the fractional remainder, he argued that fractions should be treated in the usual way: rounded up if the fraction was more than one-half, rounded down if it was less. As with Jefferson's method, there typically exists a range of divisors that apportions the required number of seats and does so in a unique way.

The "Alabama Paradox"

Webster and Hamilton's methods were used sporadically until 1900, when Webster's approach definitively replaced Hamilton's. The reason for rejecting Hamilton's method was its bizarre behavior when the size of the House changed. In the 1880s, for example, an increase in the House size from 299 to 300 seats would have caused Alabama's allotment to decrease from eight seats to seven.

To see how this can happen, consider the hypothetical three-state example described in figure 2 and suppose that the House size were increased from 21 to 22 seats. The quotas would be as follows: state A, 14.92; state B, 2.52; state C, 4.56. To apportion 22 seats, Hamilton's method would round two states up and one down (even though all remainders exceed 0.5). Since the state with the smallest remainder is B, it must be the one rounded down. In other words, in a 22-seat House, state B receives only two seats, whereas in a 21-seat House, it would receive three seats. This absurdity was dubbed the "Alabama paradox" and led Congress to abandon Hamilton's method—thus showing that intuitive mathematical principles can, at least occasionally, play a role in politics.

It could be argued that, since the size of the U.S. House of Representatives is currently fixed at 435, the Alabama paradox is no longer relevant. But Hamilton's method also displays unacceptable behavior when the House size is fixed and the state populations change. In particular, a state with an expanding population can lose seats to a state with a declining population, a phenomenon known as the "population paradox." For both of these reasons, Hamilton's method must be deemed unacceptable.

Alternative Methods

But are there any more reliable methods? In fact, there is a large class of methods, of which Jefferson's and Webster's are particular examples, that avoid both paradoxes. All of them are based on the principle of the common divisor invented by Jefferson.

Using this method, each state population is divided by an adjustable divisor to obtain a quotient. The quotients are then rounded to whole numbers and one adjusts the divisor until the rounded numbers add up to the required number of seats. Any such rule is called a divisor method; the only issue is how to round the quotients to whole numbers. Webster's method—rounding each quotient to the nearest whole number—is the most logical.

In addition to the methods of Jefferson and Webster, three other divisor methods have been proposed over the course of U.S. history. John Quincy Adams argued in 1832 that all quotients should be rounded up instead of down, no matter how small their fractional parts. Conveniently, this would have saved a couple of seats for New England, his constituency. The same year, James Dean, a former professor of Webster's at Dartmouth, suggested a complicated method that entailed rounding up the quotient if it exceeds the harmonic mean of the two nearest whole numbers. Otherwise, he said it should be rounded down. (The harmonic mean of two numbers is their product divided by their average. So if a quotient is 2.45, it should be rounded up because it is more than 6 (the product of 2 and 3) divided by 2.5 (the average of 2 and 3).

Joseph Hill, a Census Bureau statistician, suggested an equally bizarre alternative in 1911 that was later refined by Harvard mathematician Edward Huntington, and which the House uses to apportion seats today. They argued that a quotient should be rounded up if it exceeds the geometric mean (or square root of the product) of the two nearest whole numbers. Using this method, a quotient of 2.45 would yield three seats. (The square root of 2x3=6 is 2.449 which is less than 2.450.)

The 50-state chart (figure 4) gives the 2000 apportionments by each of these five divisor methods (and also by Hamilton's method). An inspection of the table reveals an interesting pattern. Arranged in the order Adams, Dean, Hill, Webster, Jefferson, each divisor method progressively favors large states more and small states less. For example, Adams's method would give South Dakota, whose seat quota is 1.170, two seats.

From a policy standpoint, the crucial question is whether any of these methods treats small and large states even-handedly over a period of years. (Hamilton's method is even-handed, but it has proven to be so prone to paradox that Congress would likely never revert to it.) To examine this issue empirically, we can review the solutions that each of these methods would have given if they had been used from 1790-2000 (see figure 3).

To account for the constitutional mandate that each state, no matter how small, must get at least one seat, I omit the very small states with a quota of less than one-half in order to examine whether any bias remains after deleting these "very small" states.

The remaining states are then divided into three categories—large, middle, and small—with the middle category taking up the slack if the number of states is not divisible by three. For each method and each census year, I compute the per capita representation in the large states as a group and in the small states as a group. The percentage difference between the two is the method's relative bias toward small states in that year. To estimate their long-run behavior, I compute the average bias of each method up to that point in time.

The results are shown in figure 3. Only Webster's is close to being unbiased, while the method currently in place (Hill's) systematically favors the small states by 3-4 percent.

Given these findings, it is remarkable that the current method was adopted. That happened in part because some of the country's leading mathematicians—including John von Neumann, Marston Morse, and Luther Eisenhart—claimed that it was unbiased. In a National Academy of Sciences report to Congress, they claimed that Hill's method was preferable because it "stands in a middle position as compared with the other methods." In other words, the mathematicians argued that two methods favor small states more than Hill's method does, and two methods favor small states less. Using this reasoning, it was fortunate for them that Congress was considering an odd number of methods. Empirical evidence that was not considered by the mathematicians—such as the actual effect of different methods over the course of United States history—shows that on the contrary, Hill's method is biased and Webster's is not.

Politics versus Logic

Of course, politics also played a role in the outcome, as it always has: the switch from Webster's to Hill's method in 1941 gave one more seat to Arkansas and one less to Michigan, which essentially guaranteed one more seat for the Democrats (the majority party). It is also true, however, that the scientific arguments bolstered the Democrats' case.

Indeed, apportionment debates over the years exhibit an interplay between political and mathematical logic. Jefferson's method was ultimately rejected because of large-state bias, Hamilton's because of bizarre behavior when the House size grew. Changes in method had to wait, however, for the underlying problem to be articulated and for the congressional votes to be in place.

The current dilemma is clear—Joseph Hill's method favors small states over large ones. If Congress begins the task of changing the apportionment formula now, it will avoid a more complicated political fight when the next census rolls around. With Webster's method reinstated, the treatment of large states and small states will be brought into better balance and in the long run, all states will be fairly represented.

This Policy Brief is based on a new book, Fair Representation: Meeting the Ideal of One Person, One Vote (2nd edition) by M.L. Balinski and H. Peyton Young, published this year by the Brookings Institution.

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Fair Representation : Meeting the Ideal of One Man, One Vote

H. Peyton Young and Michel L. Balinski — Wed, 28 Mar 2001 00:00:00 -0500

Brookings Institution Press 2001 200pp.

The issue of fair representation will take center stage as U.S. congressional districts are reapportioned based on the 2000 Census. Using U.S. history as a guide, the authors develop a theory of fair representation that establishes various principles for translating state populations-or vote totals of parties-into a fair allocation of congressional seats. They conclude that the current apportionment formula cheats the larger states in favor of the smaller, contrary to the intentions of the founding fathers and compromising the Supreme Court's "one man, one vote" rulings.

Balinski and Young interweave the theoretical development with a rich historical account of controversies over representation, and show how many of these principles grew out of political contests in the course of United States history. The result is a work that is at once history, politics, and popular science. The book-updated with data from the 1980 and 1990 Census counts-vividly demonstrates that apportionment deals with the very substance of political power.

ABOUT THE AUTHORS

H. Peyton Young

Michel L. Balinski

Michel L. Balinski is the former director of the Laboratoire d'Econometrie of the Ecole Polytechnique in Paris, the founding editor of the journal Mathematical Programming. and is a noted authority on mathematical optimization and operations research.

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