Irrationality in Economics

New ideas in economic theory that replace hyper-rational agents with mostly-rational ones.

1. Introduction

Economic theory purports to model the behaviour of rational agents – consumers, investors, and firms. As such, its predictions and its recommendations inform legal reasoning, government policy, and business decision-making. The basic assumption of economic rationality, as depicted by most of the mathematical models taught in undergraduate courses, is that the rational agent picks her actions so as to maximise her personal utility, at least in equilibrium. Alas, people do not really behave this way. Although economists since Adam Smith have recognised that man is not a wholly rational animal, it is only in the last half-century our wide-spread irrational behaviour has been researched extensively and thus influenced theoretical constructs. Modern experiments demonstrate, for example, that people turn down personal gains in the name of fairness, use heuristics infested with significant biases that result in incorrect or inconsistent conclusions, and fail to master complex tasks.

Economists have tried to mend the gap between the idealistic assumptions and messy reality, so far basically unsuccessfully. An easy way out would be to claim that economic theory has only a normative-prescriptive value – that it instructs people in how to behave economically, but it does not describe how people actually behave. This position, however, is not really available to economists: economic theory would then lose all its power to inform, as mentioned, a large array of important decisions made by governments, financial authorities, firms, and individuals; it would not fulfil its purpose as a social science. This point is articulated by the president of the European Economic Review, Jean Tirole (2002):

Social scientists (be they economists, sociologists, psychologists, political scientists or others) should not content themselves with observing and portraying human behavior; they also have a social responsibility to suggest and guide policies that promote economic development, reduce inequality, make product and financial markets function better, improve macroeconomic performance, and so forth. To this end, they need a parsimonious framework that has predictive power and normative content.

To describe human behavior with fidelity is to implement the heuristics, biases, dispositions, and emotive constraints people have into economic models while still maintaining their normative value. Thus today’s economists are faced with the gargantuan task of quantifying the ways in which people are less than rational, and recommending what to do about it. Many also choose to explore traditional models more fully rather than throw away what works pretty well.

Nevertheless, some improvement to economic theory has been made through understanding of cognitive heuristics. So-called “behavioural finance” gained voice in a front-page 2004 Wall Street Journal article, and applications of cognitive principles to the design of torts, contract law, tax structure, central banking policy, and other areas are similarly drawing interest. (e.g.: Jolls, Sunstein, Thaler, 1998; Gabaix, 2004; Nau, 1999; Bertrand, Mullainathan, Shafer, 2004)

In this chapter we will look first at the traditional model of economic man, starting with the so-called “neoclassical” theory of economics, a theory conceived by John Von Neumann and Oskar Morgenstern (1944) and now presented in textbooks on price theory (at IU, the intermediate microeconomics class). After understanding that model thoroughly, we will outline the behavioural research that casts dispersions on it. Following the evidence contra “homo economicus”, we will sample a few of the attempts made so far to describe what people actually do. The new models tweak the old model to allow for one kind or another of less-than-perfectly-rational behaviour.

2. Traditional Economic Man

The traditional model has three components: first, the notion of utility and the principle that agents maximise it; second, the application of consistent time discounting; and third, differing attitudes toward uncertainty.

2.1 Utility

The economic conception of rationality hinges on the concept of utility. Although its roots lie in Bentham's 19th-century conception of pain and pleasure as the “sovereign masters” that “point out what we ought to do, as well as determine what we shall do”, in modern economics utility has acquired a strictly behavioural meaning. (Kahneman, Tversky, 2000) That is, utility is inferred from a subject's actions: if, at the same price, the subject chooses X over Y, we infer that she values X more. Briefly put, utility is preferences demonstrated by decisions.

Here we have made a strong yet tacit assumption, namely that the choices people make are to be considered rational. Economists almost always temper this assertion with qualifications like “in equilibrium, with perfect information”, meaning that when agents have had enough time to ponder and practice, and when they have all the facts, the decision they make for themselves is the right one. At the least, economists will say that economic models represent either a) a good approximation of baseline behaviour, b) the study of incentives, or c) a metaphor helpful in designing policy.

Let's be more accurate in describing economists' conception of rationality, so we can better understand exactly what they are asserting (as well as to what extent their strong assumptions might be justified in the name of parsimony). Modern economists formulate their ideas mostly in the language of mathematics. Stating their ideas only in English will never be quite correct.

Mathematically, then, a person’s utility is seen as a function of her choices – that is, every action results in some number of “utils”. The figure below sketches some amounts of utility an agent might receive from various activities. The domain here is the set {Beach, Park, Stay Home, Roller-Coasters} and the range is a real number. A day at the beach may yield 5,000 utils and a day at the park 3,000.


Under this mathematical view, a utility function is a mélange of a person’s personality, mood, and intrinsic nature.  It describes her preferences in both real and counterfactual situations.

2.1.1 Cost-Benefit Analysis

Every decision comes with both benefits and drawbacks – expressed economically as utility gained and utility foregone (the jargon for which is “opportunity cost”). Since agents are limited by things like finite life-span (you can’t live everywhere or have every career), their wage and wealth (you can’t buy everything), the difficulty of obtaining natural resources (oil must be found and drilled to), weather (affects crop yields), facts of physics (you can’t fly), and other agents (who may already occupy a coveted position), they pick the highest-utility option from only a limited set of choices. The limitations imply that doing one thing always implies giving up the chance to do another – and foregoing utils (maybe just a few) from an action not taken.

In the example above, going to the beach might cost $200 plus 8 hours in the car, whereas going to Bryan Park might cost only $30 plus 15 minutes in the car. Choosing the beach will preclude choosing other utility-bearing options like sleeping the night before the trip or buying $200 worth of other stuff, while choosing the park will preclude fewer options – buying $30 worth of other stuff and whatever one does with 15 minutes. The choice from the set {Beach, Park, Stay Home, Roller-coasters} will affect a wider set that encompasses choices the agent will face tomorrow and thereafter.


The simplest analysable case under this conception of rational choice is where an agent has to choose how many X1 to buy and how many X2 to buy on a limited budget. (Using a fixed budget obviates the need to consider the dynamic problem of how to allocate time between leisure and work, which choice in turn determines the budget for buying other stuff.)


Here the thick black line represents the limitations of the budget, demarcating the feasible and the infeasible. Since the agent has only a certain amount of money to allocate between X1 and X2, after a point (near the constraint), buying more X1 precludes buying some X2 and vice versa. Her rational choice is thus conceptualised as being the most satisfying, given both the costs and the benefits of the choices at hand.

2.2 Constraints on the Utility Function

The neoclassical model delimits rationality by imposing a few constraints on the way someone’s utility function should behave. Below are two properties which any rational utility function should exhibit:


­–More is better than less. Having more of any good is better than having less – or at least, no worse. Even if you would throw up from eating 10 hamburgers, possessing that many should not make you worse off because you can leave however much you don’t eat on the table, throw it away, or give it to someone else.

The first taste is the sweetest. The second car doesn’t increase utility as much as the first one did. The third car increases utility even less. So-called diminishing marginal utility in each good explains why people buy many different things, rather than just a lot of one really good thing. (viz., “If I Had A Million Dollars” by The Barenaked Ladies: “If I had a million dollars / We wouldn't have to eat Kraft Dinner // Of course we would, we'd just eat more.”)  The drop in incremental utility from just one good makes agents spend their money on other things to obtain a more valuable balance.

2.3 Many Decisions, Many Dimensions

Economic agents are usually choosing between more than two options. Even though it is impossible to draw 2000 dimensions, you can still visualise the massive list of options agents are faced with in an everyday consumption-budgeting problem by thinking of a table with 2000 columns and enough rows to fill in the relevant variation in each column.

If the number of choices were large, a case-by-case search through the resultant utilities would take a computer a long time—longer than humans are observed to, or would want to, spend thinking about simple decisions. This observation is at the heart of one of the early sources of scepticism about any actual agent's ability to perform the global calculations required for homo economicus rationality. (Nobel laureate Herbert Simon's paper A Behavioral Model of Rational Choice.  [1955])

2.4 Decisions Under Uncertainty

Besides maximising utility in cut-and-dried allocation problems, homo economicus also makes rational (consistent and logical) choices when the outcome is unknown.  Thus the second element of his exposition concerns beliefs and expectations.  Although economists to the present day still lack a persuasive tool for describing rational behaviour under cognitive limitations, they have long had one for describing rational behaviour in the face of uncertainty. Of course economic agents are frequently faced with imperfect information. Apple doesn't know exactly how long the iPod will remain in vogue, and likewise an Apple employee doesn't know how long her wages and stock options will skyrocket. Governments that tender bids from engineers, software developers, or efficiency consultants receive good information about price but noisy information about work quality. Grocery shoppers guess at the freshness and taste of produce as do consumers of white goods about their durability and efficacy.

Fortunately for economic thinkers, a thorough theory of probability is available. One may summarize an economic agent's imperfect information as a probability distribution, for example as below:


An important feature of probability theory is that it allows the use of conditional statements, such as “Given what I know and have heard of the firm's past performance, what is the likelihood of their workmanship being of a certain level of quality?” If Q is work quality and I is the information the government has, then mathematically we can write

Pr[Q = {bad, medium, good, excellent},    given I]                        =          ?

. An answer might be, like in the graph above,

Pr[Q = {bad, medium, good, excellent}, given I]     =        (20%, 40%, 30%, 10%).

What's really nice about being able to ask and answer questions this way is that probability theory (Finite Mathematics!) allows us to derive expectations and perceived risk. If bad workmanship were worth $100 to the government, medium worth $1,000, good worth $10,000, and excellent workmanship worth $100,000, then with the information given above, the government expects $13,000 of value from the firm. The government’s preferences (and willingness to pay) could depend just on that average, or on the entire spectrum of possible performance (3.9 stars, 2.28 stars, etc.).

Having quantified the agent's perceptions of benefit and risk in this way, we can apply the same theory from above to expected utility rather than to utility itself. The government's choice set for outsourcing its software development is {Firm A, Firm B, Firm C}, each member of which comes paired with information – which leads to an expectation of performance quality from each, and thence to preferences and choices by the government.

From these theories were launched some of the richest and deepest predictions of economics, as well as some of its most important applications in financial markets. These same rich predictions also form the basis of many of the psychological experiments that were used to “disprove the rational hypothesis”.

2.4.1                      Attitudes toward Risk

Economists have had a lot of fun wringing all the juice from the parsimonious “expected utility” conception outlined above. One favourite trick is to derive attitudes toward uncertainty from the shape of an agent's utility function. They classify agents in three categories: risk-seeking, risk-averse, and risk-neutral. Risk-seeking agents will pay for more variation in their payoffs. Risk-averse agents will pay for less. Risk-neutral agents make decisions based only on the expected value of the outcome.

Remember from before that as regards wealth w, “more is better” – that is, rational utility functions must display u(w+$1) ≥ u(w). But how much better more is, depends on the person. The three attitudes toward risk just outlined correspond to three types of increasing functions: convex, concave, and linear.


To see this, consider a linear increasing utility function like u(w) = w: for this person every $1 of wealth results in 1 util, at any scale. Contrast u(w) = w to a curved increasing utility function like √w, log w, or w². People with curved utility functions receive more or fewer utils from the tenth dollar gained than from the eleventh. This results in differing attitudes toward risk, here understood as the likelihood of ending up with high or low wealth. (These agents still experience diminishing marginal utility in any one good. Their utility from wealth overall cuts across all goods and is thus not necessarily subject to diminishing returns.)

In fact, most people are probably risk-averse, which explains why there are insurance markets. In other words, people generally prefer the guarantee of moderate wealth to a chance of having high wealth and a chance of having low. To understand how this creates a demand for insurance, imagine that there are some vandals smashing mailboxes in a neighbourhood. Out of 100 houses, they smash one mailbox each night at random. Mailboxes cost $20 and mailbox insurance costs $1. A risk-neutral person would not purchase mailbox insurance because a 1-in-100 chance of losing $20 means an expected replacement cost of only $20 / 100 =20¢. But a risk-averse person values certainty in addition to the expected outcome (.1% chance of losing $20),  so they might be willing to take out a policy for $1 that replaces their mailbox if it is smashed.   Accepting what sounds like a losing proposition in a statistical sense might seem more human if you think about health insurance, which covers potential costs of a higher order (ones that can bankrupt a person if paid or kill or disable him if unpaid) by charging premiums to the subscribers which exceed the average cost of treatment.  Maximising expected health-and-wealth while ignoring the risk of very low health might, in fact, be seen as irrational, especially from the evolutionary fitness of tsuchbehaviour.

Conversely to the above case, risk-seeking people place a comparatively high value on the prospect of being very rich. They are thought to be much less common, but neoclassical economists can point to gamblers and entrepreneurs as making decisions consistent with risk-seekingness. (Some prefer to believe that gamblers suffer from cognitive biases like belief in “hot dice” and that entrepreneurs are victims of their own egos.)

Most important for the present discussion is that when economists noticed behaviour deviating from what they expected – max E[wealth] – they did not respond by proclaiming the subjects irrational. Instead, when someone is “too cautious” with their wealth, economists (actually D. Bernoulli, 1738) inferred that the subjects merely had a comparatively high disutility to low wealth and that it was therefore rational for them to give up possible gains to protect against such a contingency. A problem for that theory is that some people buy insurance yet also gamble; economists seek a similarly cogent explanation.

2.5 Decisions Over Time: The Ramsey Savings Problem

One more piece yet remains to the exposition:  the homo economicus model makes even more sense when a time dimension is added. Agents possess not merely preferences about wealth but about when that wealth is acquired and spent over time. For instance, most of us would rather have money now than later. This so-called “time value of money” is represented by multiplying future utility by a fraction d (d for time-discounting) to represent its comparatively decreased value relative to having money now. d can be thought of as a “patience factor” special to each person: someone with d=½ is less patient than someone with  d = ¾. d can also be thought of as money lost on a potential investment. If an investor has to wait a year to receive a sum, he loses a year’s worth of returns from stocks and bonds he could have bought – so he prefers to have the money sooner rather than later.

A utility function that takes time preferences into account looks like

max {u(w1) + d·u(w2) +  d2·u(w3) + d3·u(w4) …}    by allocating total wealth among {w1, w2, …}

. wt represents spending at time t. Utility at each succeeding stage is discounted by d% more than the previous stage (e.g., 90%, 81%, 73%, ...). Since rational agents are supposed to make consistent decisions, as each stage t=1, t=2, etc. gets crossed off, the agent’s choices of future wt’s are supposed to remain the same. (Notice that u(·) is the same at each stage.)  In the end, time-dependent utility functions are usually seen to imply using financial tools like saving and borrowing to smooth consumption over time to a constant – borrowing to pay for education in early life, paying loans back and saving in middle life, and living from savings and interest when old.

Fully exploring this formulation is the basis for a first graduate course in economics. I bring it up only to paint a complete picture of how economists see a rational agent functioning: she allocates resources over time to the choices that maximise her utility, or at least her expected utility.

2.6 Homo Economicus - Theory Summary

Perhaps Jean Tirole summarises “our received economic paradigm” best in a 2002 presidential address to the European Economic Review, Rational Irrationality:

“Much economic analysis builds on a deliberately simple-minded description of human preferences and behavior, in which the individual is depicted as maximizing at each instant t over some action set At the expectation of the present discounted value of … utility … given the information It he has accumulated prior to date t:

max, at each time t:   E [ ut (ct)  +  d·ut+1 (ct+1)  +  d2·ut+2 (ct+2)  + …,   given It ],   by choosing actions from At.

Economists have of course long been aware of the crudeness of this representation; but they have argued that its parsimony is also its strength.”

3. Are we really Homo Economicus?

Perhaps it comes as no surprise that humans do not perform in this “hyperrational” way. As mentioned, economists since Adam Smith have written on man's irrationality, from his behaviour in market frenzies and bubbles to his obtuseness in forecasting. However, it was not until the second half of the 20th century that a wealth of experimental evidence demonstrated systematic errors which seriously undermine the axioms of economic theory. This evidence is even more disturbing when combined with theory that shows that systematic errors by individual agents will not necessarily be solved by collective market wisdom.

3.1 Evidence of Irrationality

The body of evidence accumulated even just by the two most famous psychologists of the field, Nobel prize-winner Daniel Kahneman and Amos Tversky (who was deceased in 2002 and thus ineligible for the prize), is too large in scope to consider here. As John Conlisk wrote in 1996:

“There is a mountain of experiments in which people: display intransitivity; misunderstand statistical independence; mistake random data for patterned data and vice versa; fail to appreciate law of large number effects; fail to recognise statistical dominance; make errors in updating probabilities on the basis of new information; understate the significance of given sample sizes; fail to understand covariation for even the simplest 2x2 contingency tables; make false inferences about causality; ignore relevant information; use irrelevant information (as in sunk cost fallacies); exaggerate the importance of vivid over pallid evidence; exaggerate the importance of fallible predictors; exaggerate the ex ante probability of a random event which has already occurred; display overconfidence in judgment relative to evidence; exaggerate confirming over disconfirming evidence relative to initial beliefs; give answers that are highly sensitive to logically irrelevant changes in questions; do redundant and ambiguous tests to confirm an hypothesis at the expense of decisive tests to disconfirm; make frequent errors in deductive reasoning tasks such as syllogisms; place higher value on an opportunity if an experimenter rigs it to be the “status quo” opportunity; fail to discount the future consistently; fail to adjust repeated choices to accommodate intertemporal connections; and more.

In such experiments, the mental tasks put to people are often simple, at least relative to many economic decisions; whereas their responses are frequently way off. Most important, reasoning errors are typically systematic….The sheer number of experiments reporting biases is so great that a sizable number of books and long survey papers have been written just to review the evidence.”

A brief description of some of the jargon in Conlisk’s quote follows:

Intransitive Preferences. Preferring A > B and B > C, yet also C > A. If utility maps to a real number (or even to a ranking of choices), this should be impossible.

Statistical Independence. When two variables move without regard to one another.

Random versus Patterned Data. A completely random sequence shows no persistent relationship between pairs of entries – between neighbours, between entries separated by four, between randomly chosen entries – absolutely nowhere.

The Law of Large Numbers implies that large samples (over 50) closely resemble the populations from which they are drawn. It follows from the work of Chebyshev.

Statistical dominance. A bet that in every case returns a better outcome than another is said to dominate it. Imagine two gambles, one which pays $100 with 10% probability and $0 with 90% probability, and a second which pays $101 with 10% probability and $1 with 90% probability. The latter statistically dominates the former.  Likewise if the second pays $100 with 11% probability and $0 with 89% probability.

Updating probabilities on the basis of new information should be done using Bayes' Rule: 

A might represent the event where one has parachuted into enemy territory (A’ being friendly territory), and B the event where one has landed in mountainous terrain (B’ being flat terrain). Knowing the overall amount of mountainous terrain (Pr(B)) and the amount of territory occupied by enemies (Pr(A)) can be supplemented with information about the specific distribution of enemy troops in the mountains (Pr(B|A)) to figure out the current danger of being shot (Pr(A|B)).

Covariance. Covariance measures how often two unpredictable things move together. If the random variables are called X and Y,

Covariance        =          E[   (X − E[X])  ·  (Y − E[Y])   ]    =          E[X · Y]    E[X] · E[Y]

. Covariance is zero when and only when X and Y are statistically independent. Covariance is important in picking stocks (low covariance is better), in understanding voter response to policies (individuals that co-vary can be classified as a voting bloc), and in validating statistical studies (explanatory variables in a simple regression are assumed to be independent).

Sunk costs are costs which must be paid regardless of an agent's choices, and therefore shouldn't factor into a decision. For example, if you buy season tickets to the opera only to realise you really dislike the line-up, you should stop attending it and do something more fun, rather than “getting your money's worth” by viewing the rest of something bad.

Consistent future discounting. In the time-dependent utility subsection, I used a constant d, 0<d<1, to represent the agent's patience. Some experiments have shown d to vary. Some people are consistently impatient in the medium- and long-term but inconsistently impatient in the very short term. This behaviour is called “hyperbolic discounting”. For example, a person might prefer a candy bar now to two candy bars tomorrow, while at the same time preferring two candy bars in 101 days to a candy bar in 100 days. Hyperbolically discounted preferences result in “impulse buying”.

3.2 Mistakes Do Not Cancel in the Aggregate

Two traditional responses to the objections raised above are (1) people will behave more intelligently after having time to learn (in particular professionals are good at what they do), and (2) mistakes will cancel out in the aggregate through imperfectly-understood aspects of markets.

A simple rebuttal of (1) is that some important decisions do not admit repeated trials, such as picking a career or a spouse. A response to (2) came in 1985, when George Akerlof and Janet Yellen published a tight mathematical argument against it. Using the envelope theorem (which says that near-optimal behaviour is only negligibly worse to one's utility than exactly-optimal behaviour), they show that 1) sometimes individuals' deviations can result in a systemic deviation whereby even fully rational agents will face incentive to act in a way that would be suboptimal were every agent rational, and 2) this systemic deviation can be significantly large.

Since their argument relies on calculus, the science of the infinitesimal, it may have limited application in the real world of finite-sized mistakes. In addition, theirs is just one way to view suboptimal behaviour (as inertia which causes a deviation from the optimal decision) but nevertheless Akerlof's and Yellen's argument is extremely important in justifying the non-triviality of investigating irrational behaviour.

4. We Need More Than Evidence

Promising as the case against homo economicus is, lawmakers, financiers, and social scientists cannot advance much without a new, coherent theory that can “glue together” the disparate results showing that man doesn't maximise the discounted sum of expected utility, into a theory that shows what he actually does do.

4.1 New Theories

In searching for a new theory of economic behaviour, coherence is more important than answering all irrationality objections. A completely correct yet unsatisfactory new theory could simply list all experimental results to date and say “Man behaves like this”. What we seek should grow from a few axioms about human behaviour that also end up according with more experimental evidence than the neoclassical theory did.

Because of the disparate nature of these efforts, this last section will be rather disjoint. Jean Tirole has outlined several categories of new theories.

4.2 Tirole's Four Types of Departure from Homo Economicus

In Tirole’s 2002 presidential address, he covers four sorts of deviations from economic dogma, which call into question four assumptions inherent in the homo economicus model

max{At} E [ sum dt · ut (ct), given It],

which are optimisation (max); judgment (E); discounting (d); preferences (u).

4.2.1 Preferences – changing ut (ct)

This first class of models fiddles with the utility concept itself, proposing to include in it: anticipatory feelings or savouring of future consumption; self-image; altruism or spite; status concerns; guilt, shame, or pride. Utility may also centre around a reference point (as in drug use, where a greater high is always sought; or as in the endowment effect; or as in the sunk cost fallacy).

Tirole deprecates these because (1) new utility forms can be proposed ad hoc; (2) they can easily end up being imprecise; (3) changing the utility function may only paper over the deeper reason for behavioural anomalies:

“Clearly, we, as a profession, should not impulsively add a new element into the utility function every time we cannot readily explain a behavior or an apparent concern. First, we would lose parsimony and thereby predictive power. As Bob Frank (2001) puts it:

The problem here is that if analysts are totally unconstrained in terms of the number of goals they can attribute to people, virtually any behavior can be “explained” after the fact simply by positing a taste for it. A man drinks the used crankcase oil from his car, then writhes in agony and dies moments later? No problem, if we are free to assume that he really liked crankcase oil. As students of the scientific method are quick to emphasize, a theory that can explain everything ends up explaining nothing at all. To be scientifically valuable, a theory must make predictions that are at least in principle capable of being falsified.

And hence the dilemma confronting proponents of rational choice theory: versions that assume narrow self-interest are clearly not descriptive, whereas those to which goals can be added without constraint lack real explanatory power.”

Second, we would end up with potential contradictions. For example, the sensitivity to change suggests that the key to happiness is low expectations, an hypothesis that does not accord well with the benefits from savoring and/or with the demand for a positive self-image, which both suggest benefits from high expectations….

Third, and relatedly, we may need to dig deeper into the real motivation of behaviors. Are the extra ingredients really part of the preferences or are they purely instrumental? For example, the demand for self-esteem may come from the experience of reflexive consciousness, as when you lie awake in bed at night or look in the mirror glorying in your triumphs or thinking about your failures; alternatively self-confidence has an executive function. It drags you out of bed, makes you undertake things and gets you going. In the former case, self-esteem is a direct hedonic component of the utility function; in the latter case, it is not.

4.2.2 Discounting – changing sum dt ×

Some models question the time consistency assumption discussed in Section 2.5. Agents are given an additional taste for immediate gratification (“hyperbolic discounting”), placing extra weight on current consumption, at the expense of later consumption. In this sort of model, the agent maximises something that shouldn’t be maximised; in a sense it is a perfectly calculating being with irrational goals.

Such inconsistent preferences lead impatient agents into self-control problems, giving rise to a formal notion of willpower. *Description of hyperbolic-discounting agents ventures into language about “multiple selves”, e.g.: “self t will take decisions that are too short-termist from the point of view of previous selves, who do not suffer from the same instant gratification bias with respect to date-t decisions.”

4.2.3 Beliefs – changing E[ …   given It]

Models that address beliefs take into account well-known biases such as the gambler’s fallacy, hot-hand bias, belief confirmation bias, hindsight bias, projection bias, and others, by removing emotionally uncomfortable information from an agent’s information set (or editing that information to make it easier to face up to) – trying to mimic the blinders we put on ourselves. The math may get tough in these models because the blinders themselves are strategically placed by the agent and thus endogenous.

4.2.4 Optimisation – changing max{At}

A final group of models tries to quantify cognitive costs or the resulting heuristics. They may add random error to otherwise good choices, use a learning algorithm such as evolutionary learning, limit the number of strategic steps that may be backward-induced (as in a chess game), make adding actions to {A­t} be costly, or apply specific heuristic devices.

4.3 A Few Examples of Proposed Theories

Below are several examples of theories which have been proposed to explain deviant economic behaviour.

4.3.1 Kahneman and Tversky: Prospect Theory

Heavyweights Daniel Kahneman and Amos Tversky didn't present their experimental evidence on betting behaviour without eventually (1979) offering a model to explain it all: they propose that in addition to risk aversion, people frequently exhibit loss aversion. Prospect Theory supposes that people’s utility derives from losses and gains, rather than from final wealth. People work from a psychological reference point and strongly prefer to avoid losses below it. They also have different risk attitudes toward perceived losses and gains – being risk-averse in gains but risk-seeking in losses. Finally, people misperceive probability, overestimating the likelihood of extreme yet unlikely events and underestimating that of “average” or “normal” events.


Like many theories, Prospect Theory has changed since its original form. Its current manifestation is “Cumulative Prospect Theory”, which answers some technical objections to the original theory (PT originally violated statistical dominance).  Cumulative Prospect Theory has been used to explain the “equity premium puzzle” (why stocks enjoy such high returns compared to bonds) and various betting anomalies.

4.3.2 Harbaugh: Alternative Social Theories

Indiana University Professor Rick Harbaugh is working on two alternative theories which give the same results as Prospect Theory but for different reasons.  In his working paper “Prospect Theory or Skill Signaling?” he shows that signalling games can also explain loss aversion, probability weighting, and framing effects:

 “Failure is embarrassing. In gambles involving both skill and chance, we show that a strategic desire to avoid appearing unskilled generates behavioral anomalies that are typically explained by prospect theory's concepts of loss aversion, probability weighting, and framing effects. Loss aversion arises because losing any gamble, even a friendly bet with little or no money at stake, reflects poorly on the decision maker's skill. Probability weighting emerges because winning a gamble with a low probability of success is a strong signal of skill, while losing a gamble with a high probability of success is a strong signal of incompetence. Framing matters when there are multiple equilibria and the framing of a gamble affects beliefs, e.g., when someone takes a "dare" rather than admit a lack of skill.

In another working paper, Harbaugh and Tatiana Kornienko offer a local-status explanation for anomalies explained psychologically in Prospect Theory:

 “People are sometimes risk-averse in gains but risk-loving in losses. Such behavior and other anomalies underlying prospect theory arise from a model of local status maximization in which consumers compare their wealth with other consumers of similar wealth. This social explanation shares key features with the psychological explanation offered by Kahneman and Tversky.”

4.3.3 Mogiliansky and Danilov: Quantum-like Reasoning

 [T]he classical theory of preference assumes that each individual has a well-defined preference order and that different methods of elicitation produce the same ordering of options... [but] observed preferences are not simply read off from some master list; they are actually constructed in the elicitation process.”

The above quote motivates Arianne Mogiliansky and Vladimir Danilov (who have given several talks to IU’s cognitive science programme). They want a theory which generates preferences as questions are asked of agents – and furthermore, they want the theory to explain inconsistent, non-commutative preferences.

To obtain this they invoke the formalism of quantum logic. Whereas physicists measure atomic states, Mogiliansky and Danilov measure psychological states - instead of a particle collider taking the measurement, a psychological experiment (like a questionnaire) or a decision situation does. Whereas measuring a particle’s position changes its momentum, in this theory measuring a person’s preferences in one decision situation changes her preferences about another decision situation.

Mogiliansky and Danilov noticed that economic experiments sometimes display a similar form. While asking someone the same question repeatedly yields the same answer repeatedly, throwing in a different question and then returning to the original might change the subject's original answer. So while someone’s preferences might be stable to repeated like measurements, they could be jarred loose, so to speak, by a different sort of measurement.


Figure 2 represents classical measurement along two dimensions, R and Q. s, representing the state of mind of the agent, is actually in the quadrant “positive R, negative Q”. It is our job to measure it. Figure 1 represents quantum-like measurement, in which one’s state of mind s is in a “superposition” of mental states – not actually in any state but suspended, so to speak, over them, ready to collapse upon one or another when faced with a decision. Asking the question R in this case leads to a negative answer; asking R again would cycle back to the same answer; asking Q would elicit an answer about Q but would return s to a superposition about R (neither in R+ nor R-).

Their idea is wholly unrelated to theories of the mind (such as Roger Penrose's) that use quantum-physical descriptions of brain matter.

4.3.4 Tirole: Willpower

Tirole sets agents in a game against themselves, trying to exercise willpower by way of internal commitments. Agents may choose not to exercise willpower at all, or may try to exercise willpower, knowing that they might fail – and that this failure might lead to future lapses, as once a personal rule is broken it is no longer salient.

Imagine that you are trying to quit smoking. On the first day you try to quit, you will be tempted – and your ability to resist will set a precedent for later. Should you fail once, the next day you will remember that and be more likely to lapse again. With concern for precedent in mind, you might relax your personal rule ex ante some days (such as at a bar) when you know exercising self-control will be too difficult.  In other words, by giving yourself a break from abstinence, you avoid damaging your “self-reputation” (or perhaps “self-respect”) and thus avoid setting a precedent of weakness.

Tirole aims to explain irrational over-control like greed, workaholism, and anorexia, as well as irrational under-control like heroin addiction or unsafe gambling. Moreover he is concerned with self-destructive behaviours like drinking the night before a test so as to avoid finding out how bad you do even when you really try.

4.3.5 Subjective Probability

According to the classical (“frequentist”) approach to determining expectations, as stated by Laplace (1812), the expected value (E in the homo economicus equation) is the number of favourable observations divided by the total number of observations, after many have been made.  While this approach makes sense for things which admit a large number of trials (dice, nuclear decay, ~1022 atoms involved in visible thermodynamic systems), it does less so with single-shot uncertain events (weather, the stock market, the results of a job application) or uncertainty that reflects our lack of knowledge (what’s the likelihood that Jupiter has a solid core, what’s the chance that Iraq has nuclear weapons, what was the chance that Iraq had them at date D given information ID).  Questions of the latter type are often relevant in economics.  Likewise, vague expressions like “I expect it will rain today” affect economically significant outcomes like soy production and the price of soy futures.

In 1954, L. J. Savage proposed “subjective probability” as an alternative to the frequentist interpretation.  The axioms of subjective probability are cast in terms of bets that a rational person would place, rather than as long-run propensities over repeated trials.  This means probability statements reflect knowledge rather than an objective probability. Prior knowledge and new information are used to compute Bayesian statistics, which find hold in the theory of quantum communication as well as in economic applications. Subjective probability and its relation to describing choice problems has developed under further mathematical, economic, and philosophical scrutiny to include imprecise probabilities, non-linearly weighted probabilities, and other ideas (Nau, 2006).

4.3.6 Satisficing

Satisficing refers to agents’ acceptance of “better solutions” rather than “best solutions” to their problems.  The idea is due to polymath Herbert Simon and has also propagated into the realm of computer programming, wherein algorithms look for good-but-not-necessarily-best solutions (e.g., Goodrich and Quigley, 2004).  One application in the theory of firms is to suppose that firms do not maximise profit, but rather keep it above a certain threshold.  This may be especially descriptive of organisations with poorly designed incentive systems, like some bureaucracies.

IU’s Robert Becker recently (2005) proved the existence of a Nash equilibrium based on better-response maps using a famous theorem by logician L.E.J. Brouwer.  The idea of satisficing has also been applied in ethics, wherein one’s culpability is tied to cognitive capacity for understanding and preventing wrongdoing.

5. Conclusion

This chapter presented 1) the traditional conception of rationality in an economic paradigm, 2) evidence that real economic agents don't behave as proposed in the theory, and 3) some new theories which present new conceptions of decision-making. The traditional homo economicus paradigm assumes that people maximise their expected utility given the information at their disposal. They value more over less, sooner rather than later, and a variety of goods over just a few. This is summarised in the formula

max{At} E [ sum dt · ut (ct), given It].

with At the available actions at time t, It the available information at time t, E expected value, d a patience or discount rate, and u(c) the utility from consumption.

People fall prey to a variety of errors in their decision-making, which leads economists to pursue a better descriptive theory of behaviour than the one just outlined.  Ideas on how people do behave abound and vary considerably. So far, none has gained as much foothold as Von Neumann and Morgenstern’s homo economicus model. Even lacking a single theory, however, experimental findings on heuristics, biases, and the like increasingly occupy the minds of those who rely on economic theory for their decision-making. Observations like mental accounting, loss aversion, and framing effects are being felt in a reworking of law, financial advice, and other economic realms.



1.      Elsevier.  European Economic Review 46 (2002) 633–655.  Rational irrationality: Some economics of self-management.  Jean Tirole. doi:10.1016/S0014-2921(01)00206-9

2.      Stock Characters.  As Two Economists Debate Markets, The Tide Shifts: Belief in Efficient Valuation Yields Ground to Role Of Irrational Investors:  Mr. Thaler Takes On Mr. Fama.  By JON E. HILSENRATH.  Staff Reporter of THE WALL STREET JOURNAL.  October 18, 2004; Page A1.,,SB109804865418747444,00.html
Copy for personal, non-commercial use:

3.      A Behavioral Approach to Law and Economics, Christine Jolls, Cass R. Sunstein, Richard Thaler.  Stanford Law Review, Vol. 50, No. 5 (May, 1998), pp. 1471-1550. doi:10.2307/1229304

4.      MIT OCW course: Psychology and Economics.  By Xavier Gabaix.  Spring 2004.

5.      A Behavioral-Economics View of Poverty.Marianne Bertrand, Sendhil Mullainathan, Eldar Shafir - American Economic Review, 2004 -

6.      Experienced Utility and Objective Happiness: A Moment-Based Approach. Daniel Kahneman. Princeton University
Chapter 37, pp. 673-692,  in: D. Kahneman and A. Tversky (Eds.) Choices, Values and Frames New York: Cambridge University Press and the Russell Sage Foundation, (2000).

7.      A Behavioral Model of Rational Choice. Herbert A. Simon. Quarterly Journal of Economics, Vol. 69, No. 1 (Feb., 1955), pp. 99-118. doi:10.2307/1884852.

8.      Why Bounded Rationality? John Conlisk.  Journal of Economic Literature, Vol. 34, No. 2 (Jun., 1996), pp. 669-700.

9.      Prospect Theory: An Analysis of Decision under Risk

Daniel Kahneman; Amos Tversky

Econometrica, Vol. 47, No. 2. (Mar., 1979), pp. 263-292.

Stable URL:

10.  Non-Classical (Quantum) Logic: Toward a Theory of Actualized Preferences (Type).  V.I. Danilov and A. Lambert-Mogiliansky.  April 12, 2005.

  1. Page name: Cumulative prospect theory.  Author: Wikipedia contributors. Publisher: Wikipedia, The Free Encyclopedia. Date of last revision: 13 November 2006 08:37 UTC. Date retrieved: 13 November 2006 08:42 UTC. Permanent link: Page Version ID: 87503891.

Weighting function in Cumulative Prospect Theory, drawing by Marc Oliver Rieger, --Rieger 13:39, 2 August 2006 (UTC)
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13.  J. von Neumann and O. Morgenstern (1944) Theory of Games and Economic Behavior. 1953 edition, Princeton, NJ: Princeton University Press.  Explained at

14.  Pierre de Laplace.  Théorie Analytique des Probabilités. 1812.

15.  Savage, L.J. (1954). The Foundations of Statistics. New York, NY: Wiley

16.  Robert Nau.  Arbitrage, Incomplete Models, and Other People’s Brains.  In Beliefs, Interactions, and Preferences in Decision-Making.  M. Machina and B. Munier (eds.),  Kluwer Academic Publishers, 1999.

17.  Robert Nau.  Extensions of the Subjective Utility Model.  October 2006 version.  Forthcoming in Advances in Decision Analysis: From Foundations to Applications. Ward Edwards, Ralph Miles, Jr., and Detlof von Winterfeldt (eds.).  Cambridge University Press.

18.  Akerlof, George A & Yellen, Janet L, 1985. "Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria?," American Economic Review, American Economic Association, vol. 75(4), pages 708-20, September.

19.  Harbaugh, Richmond.  Prospect Theory or Skill Signaling?  Working Paper.  October 2006 version.

20.  Harbaugh, Richmond and Tatiana Kornienko.  Local Status and Prospect Theory.

21.  D. Bernoulli, 1738, Specimen theoriae novae de mensura sortis, Papers of the Imperial Academy of Science of Saint Peterburg, vol 5, pp 175-192.  Translated (1954), Exposition of a new theory on the measurement of risk. Econometrica vol 22, pp 23-36.

22.  Robert Becker and Subir Chakrabarti.  Satisficing behavior, Brouwer’s Fixed Point Theorem and Nash Equilibrium.  Economic Theory, 2005, vol. 26, issue 1, pages 63-83.

23.  Roger Penrose.  The Emperor’s New Mind.  Oxford University Press, 1990.

24.  Satisficing Q-Learning: Efficient Learning in Problems with Dichotomous Attributes.  Michael A. Goodrich and Morgan Quigley.  Brigham Young University.  2004.







Further Readings

1.      Trygve Haavelmo.  Nobel Prize Lecture.  Econometrics and the Welfare State.  Lecture to the memory of Alfred Nobel, December 7, 1989.

2.      Harry Markowitz.  "Portfolio Selection," 1952 Journal of Finance.

3.      Olivia Mitchell and Steven Utkus.  Lessons from Behavioral Finance for Retirement Plan Design.  Pension Research Council Working Paper PRC WP 2003-6.


5.      Syllabus and Reading Links: Ph.D. Seminar on Choice Theory. Robert Nau. Fall Semester 2004.

6.      Nevins, Dan.  Of SEI Investments.  Goals-Based Investing: Integrating Traditional and Behavioral Finance.  Journal of Wealth Management, Volume 6, Number 4, Spring 2004.

7.      Ariane Lambert Mogiliansky & Shmuel Zamir & Herve Zwirn, 2003. "Type Indeterminacy: A Model of the KT(Kahneman-Tversky)-man," Discussion Paper Series dp343, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem.

8.      Vladimir I. Danilov and Ariane Lambert-Mogiliansky.  Non-classical measurement theory: A framework for behavioral sciences.



11.  Anscombe and Aumann’s Axioms of Subjective Probability.

12.  Daniel Bernoulli’s Contributions to the Theory of Expected Value.

13.  Stavros Drakapoulos. Satisficing and Sequential Targets in Economic Policy: A Politico-Economic Approach. Contributions to Political Economy, 2004, vol. 23, issue 1, pages 49-64

14.  Paul Mosley. Towards a "Satisficing" Theory of Economic Policy. Economic Journal, Vol. 86, No. 341 (Mar., 1976), pp. 59-72 doi:10.2307/2230951.

15.  Roy Radner. "Bounded Rationality, Indeterminacy, and the Managerial Theory of the Firm," in Z. Shapira, ed., Organizational Decision Making, Cambridge U. Press, Cambridge, 1997. [A shorter version published as "Bounded Rationality, Indeterminacy, and the Theory of the Firm," Economic J., 106, no. 438 (Sept. 1996), 1360-1373.]

16.  Christopher Tyson. Axiomatic Foundations for Satisficing Behavior.  Nuffield College Economics Working Papers Ref: 2005-W03.

17.  Mark Blaug. "Ugly Currents in Modern Economics", Policy Options, September 1997.

18.  Subjective probability and “objective” description of the physical world.


20.  anything by De Finetti, P.C. Fishburn, Irving Fisher, Frank P. Ramsey

21.  course: Experimental Economics, ECON E427

22.  course: Probability and Statistics, MATH M365

23.  course: Probability Theory I, MATH M463

24.  course: Finite Mathematics, MATH M118

25.  course: Calculus I, MATH M211

26.  course: Math & Logic for Cognitive Science, COGS Q250