I know that you messed up on some decisions. I sure have.

This book is about decisions and elections. It is about decisions in the family, in economics, in engineering, in politics, and in every day life. Decisions are necessary, but even with the best of intentions the outcomes can go astray; they can be dreadfully wrong. Even worse, surprisingly often these “bad outcomes” occur for reasons so subtle that most of us may never realize that a mistake has been made. This can hurt. Realistically, if we fail to recognize that unanticipated, undesired outcomes can occur, we run the risk of inadvertently choosing badly.

In this book, by explaining what can go wrong and why, I describe central difficulties which can infect our decision processes. Examples and new explanations are used to introduce basic results and recent conclusions. The topics are purposely chosen to encourage the reader to further explore why it is so easy for “bad” outcomes to occur in politics, economics, law, engineering, and just about anywhere decisions are made.

This issue of trying to understand what can go right or wrong with decisions is not new; it has been a central concern for centuries if not millennia. Yet, this important topic was not embraced by academics until 1770 when the French mathematician Jean Charles de Borda introduced the issue to the French Academy of Science. Borda did so in a particularly pragmatic and personal manner.

Are all methods unfair?

How frustrating. Sen's and Arrow's results appear to establish the discouraging conclusion that “no method is fair.” To explain, both of these theorems use assumptions so fundamental that, presumably, all acceptable decision procedures should satisfy them. The theorems of Arrow and Sen, however, prove that this never can happen. Consequently, any procedure — no matter whether it is intended to assist in economics, voting, or ordinary daily decisions, and no matter how carefully it may have been designed — is condemned to abuse at least one of these basic conditions.

These theorems appear to force us into an uncomfortable situation. Either we must accept and use flawed election and decision methods fully aware that that the outcome may violate the group's true intent, or we must embrace a dictator. This does not offer much of an encouraging choice.

Although this dismal and gloomy “paradox or dictator” interpretation is almost universally accepted, I emphatically disagree with it. As I show, what spares us from this uncomfortable dilemma is that, when the various axioms are combined with one another, they need not mean what we commonly thought they did. What we encounter is an effect somewhat similar to what parents quickly learn about their charming four year old child. Individually, each little darling can be attractive and predictable; the parents can rightfully brag about how their child plays quietly in a productive manner.

Introduction

Rarely does a result so spectacular and fundamental come along that it forces us to revamp how we view a subject. This happened in 1951 when Kenneth Arrow published his Ph.D. thesis as the book Social Choice and Individual Values.

The effect of Arrow's stunning, seminal contribution was to create serious doubt about commonly accepted beliefs concerning decision procedures. This sense of doubt is so pervasive that it affects even the economic and political decision approaches so commonly used in our democratic societies.

Arrow accomplished all of this by listing properties sufficiently basic and natural that it is reasonable to expect them to be satisfied by all decision and election methods — particularly those employed by a democracy. Arrow's punch line was that requiring decision procedures to fill these conditions exacts a heavy cost. Once there are three or more alternatives, these requirements can be satisfied only by a dictator.

A dictator! What a predicament. By contradicting expectations and common sense, by showing that basic properties mandate a dictator, his conclusion raises serious doubts about fundamental democratic principles. As it is to be expected, Arrow's “dictatorial” assertion has been associated with all sorts of dire Draconian consequences.

More responsible commentary emphasized how Arrow's seminal result speaks to the basics of choosing. In a fundamental sense it addresses the quandary raised in the last chapter about selecting a decision procedure. This is because Arrow's result ensures that all non-dictatorial decision procedures are plagued with basic flaws.

Introduction

We now understand these problems from Arrow's and Sen's theorems, Simpson's Paradox, gambling, economics, inefficiencies of complex, decentralized systems, and on and on. The paradoxical behavior reflects the inadvertent loss of crucial but available information about how the disjoint parts are related. Worse than being “lost,” this information can be purposely dismissed whenever we use or design procedures — whether decision, economic, or statistical — which emphasize the “disjoint parts” over the “whole.”

As illustrated, by understanding why problems occur, a wide selection of unexpected examples from a variety of areas can be discovered. Quite frankly, by now, we should view with suspect any conclusion from any subject area which involves the surgical separation of “parts” from one another. Definitely worry when this separation is advertised in terms of noble intents such as “efficiency” or preserving the “integrity of the outcome.”

A more ambitious goal is to find resolutions. At least in principle, we know how to do this; reintroduce the lost information. But, how? To provide guidance in doing so, I tackle the obvious challenge of showing how not to, and then how to, circumvent the fundamental difficulties imposed by Arrow's and Sen's theorems.

To start, recall that Arrow's theorem requires a sufficiently heterogeneous society; this causes the Arrovian procedures to lose information about the rationality of the voters. So, to find a useful resolution, maybe we should design ways which avoid highly heterogeneous settings, or which require — in a “to-be-determined” manner — the decision process to use the previously dismissed information.

It is this dismissal of valuable but available information, this loss of connections, which makes the area of economics so rich in problematic examples. What makes these peculiarities from economics particularly frustrating is that, as with the Arrow and Sen assertions, it could be that the needed information is explicitly assumed or provided. But, it may be that relevant data is not being used to determine final outcomes and conclusions. Instead, economic procedures may ignore crucial aspects of the information.

As a slight digression, let me mention a positive development. Although the “parts-whole” conflict is not mentioned, the field of economics is addressing some of these difficulties. In the late 1960s, an economist from the University of Minnesota, Leonid Hurwicz, raised questions about the various economic solution concepts. To roughly paraphrase his more precise technical comments, “OK, these are nice notions, but are they any good? If these concepts truly model economic environments, then how do people find the solutions? Presumably, individuals find the price equilibrium, or other economic concepts, by interacting. But, how? Who says what to whom?”

This search for the “Who does what? Who says what to whom?” connecting information gives birth to a wide range of notions. It is the origin of the “mechanism design” literature where the goal is to specify the interactions needed to achieve a specified purpose. The design, for instance, might involve appropriate incentives to make the system self-policing; people do what they are supposed to do primarily because it is in their best interest.

The state of Michigan consists of two peninsulas; the much prettier upper one separates Lake Superior from Lake Michigan while the lower one separates Lake Michigan from Lake Huron. The Upper Peninsula, where the residents proudly call themselves “Yuppers,” is a remote, heavily forested, beautiful area known for its excellence in fishing and hunting. Manufacturing never made it this far north and the days of active, productive mining are decades past. Today the main industries center around activities such as tourism, logging, and several prisons positioned in the midst of deep woods — locations carefully selected to discourage the “big city guests” from thoughts of prematurely leaving the facilities. The northern most region of this remote north territory is Keweenaw County. It is easy to find this region on a map — the Upper Peninsula resembles a left hand with its thumb jutting into Lake Superior; Keweenaw County is the thumb nail.

During the “Copper Rush” of 1848, an event which never could compete with the glamour of a 1849 rush in California for a different metal, Keweenaw County was an active mining region. Its furthest north city of Copper Harbor even had a fort built to provide protection against the never threatening Indians. With the days of copper mining decades behind us, “exploration” of the area now involves hiking, biking, kayaking, and cross country skiing. Rather than searching for the red metal, the richness resides in the beauty of the county's extensive wilderness and shorelines.

A NEUTRAL CONSTITUTION

In his short but sharp dissent in Lochner v. New York, 198 U.S. 45 (1904), Justice Oliver Wendell Holmes declared that a constitution is neutral on economic policy. He was wrong in general because some constitutions have gone very far toward embodying particular economic theories. Even the U.S. Constitution embodies a limited degree of laissez-faire, enough to give capitalism at least an advantage over any other economic organization of the society, if Adam Smith's theory is roughly right. What capitalism mainly needed was free markets, and the U.S. Constitution went very far toward providing that markets would not be trammeled by the states acting for narrow interests against farmers and producers in other states.

Holmes was right, however, in the sense that the Constitution of 1787 would allow various economic theories to prevail. One of three systems of economic organization favored by different groups was plantation agrarianism. Although not constitutionally bound to fail, plantation agrarianism failed economically on its own in the face of overpowering capitalism. But the framers of the Constitution did not intentionally put capitalism into the Constitution. They merely designed an economically almost neutral – at least neutral between plantation agrarianism and capitalism – national government, which was virtually all that capitalism needed. And they arguably did even that without much understanding.

Martin Diamond, the late political theorist, closed a famous essay by reflecting on the “profound distinction” that the essays of The Federalist “made between the qualities necessary for Founders and the qualities necessary for the men who come after” (1992, 35). Whereas the act of founding the American constitutional republic had demanded an exceptional exercise in reason, he observed, the conduct of politics thereafter would depend on nothing more exalted than the ordinary play of interest. Diamond's distinction nicely captures the idealized image of constitution making that many scholars still intuitively, and perhaps even uncritically, share. In this view, considerations of stability and justice alike should encourage constitution makers to transcend the particular interests they represent. If they cannot be expected to step behind a Rawlsian veil of ignorance, where they will be uninformed of the social position they will occupy in the new regime, they should at least recall (to borrow a phrase from John Marshall) that it is a constitution they are drafting, not some ordinary piece of legislation. The establishment of a successful constitutional regime thus demands substantial self-restraint; its authors have to expect more of themselves than they do of their successors, the “posterity” for whose benefit framers, in the heroic account, struggle.

A satisfactory political theory of constitutionalism can well agree, with Diamond, on the importance of the initial deliberative processes through which a constitution is adopted. But such a theory can hardly stop there. It also calls for a satisfactory interpretation of constitutional history.

Modern commentators on the U.S. Constitution of 1787 generally share two broad but closely related sets of assumptions about its origins. First, we tend to ascribe a high measure of coherence and purpose to the original intentions and understandings upon which the framers and ratifiers of 1787–8 acted. We regard the Constitution not only as the bundle of bargains required to replace the “imbecile” union of the Articles of Confederation with an effective national government, but also as the expression of a deeper body of norms, values, and expectations that together constituted a coherent and integrated theory of a federal republic. This belief has in turn sustained seemingly endless searches for the true sources of these norms in different intellectual traditions, modes of thinking, or “discourses.” Second, in reconstructing this theory, scholars often emphasize the extent to which the Constitution was designed to establish a set of self-enforcing and self-correcting mechanisms that would preserve the general stability of the constitutional system against the vicissitudes of time and fortune. The constitutional scheme of checks and balances (embracing both the separation of powers and federalism) was contrived to maintain an enduring equilibrium while permitting gradual adjustments to take place (through either Article V amending procedures or judicial review) without blunt trauma. This scheme would neutralize the “mischiefs of faction” that so alarmed James Madison and other framers, thereby demonstrating that it was entirely realistic to extend the republican form of government to the dimensions of an expanding national empire of quasi-sovereign states.

Constitutional democracy can be modeled as a complex game involving two general stages of political decision making. One stage (sometimes labeled the constitutional phase or higher track) is a cooperative game in which moral (i.e., rational and fair-minded) players jointly agree to promote their common good by unanimously accepting a (written or unwritten) constitutional code. The code typically sets out fundamental political institutions (including legislative procedures, modes of election and appointment, amendment processes, and the like), delineates a system of checks and balances (though not necessarily one that undergirds an American-style separation of powers), and lists some basic rights of the people. Unanimous consent to some such constitution is effectively guaranteed through suitable definition of what it means to be a moral agent. For example, it might be supposed that, for this higher track of politics, any moral agent is an expected utility maximizer who imagines himself in a hypothetical position (or state of nature) behind a veil of ignorance, where he is uncertain as to his actual position in society and thus assigns equal probabilities to occupying each of the possible positions. Given these assumptions, moral agents will consent to a utilitarian constitution whose rules of conduct maximize the general welfare.

The second stage (also called the postconstitutional phase or lower track) is a noncooperative game in which the veil of ignorance is lifted and each moral player freely pursues his particularistic interests in competition with other people under the constitutional rules chosen at the first stage.

INTRODUCTION

In contemporary democracies electors can choose their representatives, reward them by reelection, or turn them out of office; no appeal can be made against a judgment as final or conclusive as an election. However, electors cannot bind representatives, once elected, in the choices they make as legislators. Representatives have a power constitutionally unbound from any promise they may have made during the campaign; a freedom that also entails a risk, because they may be punished at the next election, but only if the voters hold them to their promises. The ban on “imperative mandates” is one of the central tenets of modern representative government.

Rousseau famously held, not without reason, that the citizens of representative governments – which we call democracies with a small abuse of language – are, like the English, free only for one day, the day of the elections, and slaves the rest of the time. Unfortunately, Rousseau failed to suggest any clear or sensible alternative to that extreme and bleak verdict. Perhaps unintentionally, he eventually opened a path that leads nowhere, or rather, toward the utopia that some still vaguely call “direct democracy.”

In addition to the rejection of representative government, another aspect of Rousseau's theory of democracy deserves emphasis: its nonconstitutionalist thrust. Rousseau in fact did not distinguish between ordinary and constitutional laws. He had no conception of the supremacy or “superlegality” of the constitution; nor did he notice the critical difference, pivotal in any contemporary Rechtstaat, between the constituent power that establishes the constitution and the subordinated powers, such as the legislative, that carry out their constitutionally delegated duties.

Multiethnic nations (South Africa, Russia, Nigeria, Rwanda, the former Yugoslavia, to name a few) have sometimes found decentralized political arrangements attractive. Such arrangements – as long as they last – permit peoples who may differ greatly in their conceptions of a good public life to develop and maintain their own separate communities, within the context of a larger and more powerful political economy. Ethnically more homogeneous nations such as the United States, at the time of its founding, or Australia today, often find decentralized modes of policy formation and administration convenient as well. In such nations, geographic distances, diverse economies, regional disparities in preferences, and variations in local historical experience can make decentralized policy-making institutions more efficient and more responsive than national ones.

The advantages of decentralization are realizable, however, only if there are good reasons for the players – ordinary citizens as well as regional and central governments – to believe that others will generally abide by the terms of the federation. That is, all must believe that the regional governments will not try to take advantage of one another and that the center will not try to usurp power from the regions. Without such assurance, frequent disputes and suspicion of foul play would reduce the participants' enthusiasm for the federation, possibly motivating some participating governments to withdraw from the federation altogether. Decentralized political institutions must somehow induce participants to believe that all others will abide by the federation's terms and to act accordingly, by complying as well.