Implicit Expected Utility Theory For Decision Making and Choice

ABSTRACT - Recent studies on expected utility theory and consumer unconscious information processing are reviewed, along with the rationality hypothesis. A new hypothesis is proposed, the implicit economic cognition hypothesis, suggesting that decision-making is not only based on cognitive processes, but also on unconscious and affective processes. Implicit expected utility theory is thus proposed with the intent to extend the bounded rationality hypothesis and prospect theory, with additional components of unconscious, affective, and guessing processes. These mental processes, backed up with their mathematical models, can be adopted from a multinomial decision process model. Two experiments are designed to investigate the price bubble-crash phenomenon and unconscious and affective processes in financial investment markets.

Citation:

W. Fred van Raaij and Gewei Ye (2002) ,"Implicit Expected Utility Theory For Decision Making and Choice", in AP - Asia Pacific Advances in Consumer Research Volume 5, eds. Ramizwick and Tu Ping, Valdosta, GA : Association for Consumer Research, Pages: 343-348.

Asia Pacific Advances in Consumer Research Volume 5, 2002      Pages 343-348

IMPLICIT EXPECTED UTILITY THEORY FOR DECISION MAKING AND CHOICE

W. Fred van Raaij, University of Tilburg, The Netherlands

Gewei Ye, Ohio State University, U.S.A. and University of Tilburg, The Netherlands

ABSTRACT -

Recent studies on expected utility theory and consumer unconscious information processing are reviewed, along with the rationality hypothesis. A new hypothesis is proposed, the implicit economic cognition hypothesis, suggesting that decision-making is not only based on cognitive processes, but also on unconscious and affective processes. Implicit expected utility theory is thus proposed with the intent to extend the bounded rationality hypothesis and prospect theory, with additional components of unconscious, affective, and guessing processes. These mental processes, backed up with their mathematical models, can be adopted from a multinomial decision process model. Two experiments are designed to investigate the price bubble-crash phenomenon and unconscious and affective processes in financial investment markets.

PART I: THEORETICAL INVESTIGATION

Decision-making and choice are the basic behaviors constituting most human social and economic activities. Decision-making and choice theory are like social physics: search for universal mathematical laws of social and economic behavior. It refers to models in which individuals seek to satify their needs and preferences from the consequences of their actions, given their beliefs about events, which are typically summarized by utility functions and probability distributions. This approach includes most standard models of mathematical economics, finance theory, statistical and behavioral decision theory, behavioral economics and behavioral finance. It also influences other areas such as marketing, operations management and accounting. Unfortunately, our current understanding of decision making and choice is like our understanding of physics in the mid-17th century. The quest is for a few universal mathematical laws that describe all facets of social and economic choice behavior so that predictions of choice would be reliable with the mathematical laws of choice. However, this gives us opportunities to search for the mathematical laws to interpret and predict choice behavior, like the predictions made with Newton’s laws for motion in physics.

Rationality hypothesis and expected utility theory

Although Daniel Bernouli (1738) proposed the theory of expected utility as a basis for decision-making under risk, using a logarithmic utility for wealth, his use of expected-value operation in conjunction with a utility function is largely ignored for 200 years until it re-emerged in modern financial economics, behavioral economics, and information theory. In the 1940’s, von Neumann and Morgenstern resurrect utility theory by axiomatizing the concept of expected utility as part of a new game-theoretic foundation for economics. Soon thereafter, Nash (1950/51) proposes an equilibrium concept for non-cooperative games and a non-cooperative model of the bargaining problem which became the standard tools of game theorists. Besides the interactive decision theory, namely the game theory, the expected utility theory forms the foundation of the rationality hypothesis for behavioral decision theory, decision analysis, and so on.

In the 1960’s and 1970’s, the model of subjective expected utility is elaborated and applied to problems of Bayesian inference, decision analysis, equilibrium in markets under uncertainty. The subjective expected utility model belongs to the camp of rationality hypotheses as well.

Rational behavior, in the broad meaning of sensible, planned, and consistent behavior, is believed to govern most conduct in economic markets, because of self-interest and because of the tendency of markets to punish foolish behavior. The rationality hypothesis formed the cornerstone of economic theory as shown in Hicks and Samuelson’s classic theory of consumer demand.

However, Simon started to criticize the assumption in the 1950s, with the idea of bounded rationality. It suggests that the capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problems whose solutions is required for objective rational behavior in the real world (Simon, 1997). As a result, the rationality hypothesis for human decision making, which assumes perfect information and unlimited computational capacity, is questionable.

In our view, rational behavior is conscious choice behavior, but not all conscious behavior is rational. The decision maker is aware of the stimuli and consequences, is able to recollect the information needed for decision making, and is able to control his/her action and will to make the decision. There is other information pertaining to the stimuli and consequences that the decision maker is not aware of, unable to recollect and control, but this other information may contribute to the decisions being made. This part of decision making and choice behavior is implicit, unconscious, or affective, which has been recently understood by behavioral researchers. With this view, the bounded rationality hypothesis is actually challenging the conscious proportion of the decision-making process, which is certainly limited in computational capacity because a large part of the decision-making process may be unconscious, like the 'iceberg’ under the water as described with Freud’s psychoanalysis theory.

The classical expected utility theory can be presented with the following equation:

V(q)= E_i p_i $ u(x_i)

V(q): expected value function

q: prospects, a probability distribution=(p₁, p₂, ,p_n)

p₁, p₂, ,p_n: probabilities

x₁ x_n: consequences ordered from worse (x₁) to best (x_n)

u(x_i): utility function

Review the process flow of the information that is processed and the calculation of the expected value. The input for the utility function is the stimulus such as money and wealth, and output are consequences of the choice. If we use the information-processing framework (McFadden, 1999) to analyze the expected utility theory, only the inputs and outputs of the stimulus information are mapped, while the mental processes are largely ignored although there are attempts to remedy this (von Neuman & Morgenstern, 1941; Kahneman & Tversky, 1979).

Non-expected utility theory and unconscious information processing

In the 1980’s, theories of "non-expected" utility theory respond to the persistent challenge of the rationality hypothesis and try to explain cognitive anomalies from behavioral decision theory. The major contribution to the non-expected utility theories came from behavioral economics, for instance, "prospect theory" by Tversky & Kahneman (1992) and Kahneman & Tversky (1979). It postulates that choice is achieved by maximization of a weighted value function of gains and losses. The shape of the value function conforms to the asymmetry effect. The weighted value function is an outstanding departure from the subjective expected and expected utility functions. The formula for the value function is:

V(q)= E_iw_i $ u(x_i)

w_i=p(p_i): decision weights

x₁ x_n: consequences ordered from worse (x₁) to best (x_n)

q: a probability distribution=(p₁, p₂, ,p_n)

Where, decision weight is determined by a probability weighting function, n(p_i).

Review the process flow of the information that is processed and the calculation of the expected value. Although the decision weights replace the probability in the expected utility theory and psychological estimates on the probability is provided, how the information is processed in human mind is not represented in the value function. Meanwhile, the utility function, u(x_i), still uses the inputs and outputs, not mental processes, for representing mental judgments.

Behavioral economics and behavioral finance are terms adopted in the United States. The equivalence in Europe is Economic Psychology (Van Raaij, 1981). From the 1990’s till now, behavioral researchers and economists continue to explore non-expected-utility ideas, e.g., separation of risk and time preference, properties of the probability weighting function. In addition, the authors have proposed decision likelihood functions based on mathematical and statistical models (Ye & van Raaij, 2000, 2001a, 2001b). In this proposal, we argue that the decision likelihood functions can be an extension of the non-expected value function, V(q), which will capture mental processes including unconscious process instead of inputs/outputs for money and wealth, etc.

The 1990s also saw the progress of exploring unconscious information processing in behavioral research, such as implicit attitude and memory, emotion, and automatic priming. The progress deepens our understanding on individual decision process that involves conscious, unconscious, and affective information processing. Consumer cognition is not only regarded as pure conscious or rational processes that constitute the rational judgment or choice, but also involving implicit social and economic cognition that is part of decision-making process. The behavioral studies that may be instrumental for a better understanding choice behavior are: (1) automatic and implicit memory processes (Jacoby, 1991, 1998; Ye & Yang, 1994; Ye, 1994). The process-dissociation procedure is a basic computational model that separates unconscious components from conscious components in experimental judgment or mental tasks such as cued recall, recognition, and word-stem completion measures. (2) Implicit social cognition (Greenward & Banaji, 1995; Greenwald, et al., 2002). A unified theory on implicit social cognition is to integrate the affective (attitude and self-esteem) and cognitive (stereotype and self-concepts) constructs. (3) Priming and the development in neuroscience (Schacter, 1987; Schacter et al, 2001; Ye & van Raaij 1997). Priming refers to a change in the ability to identify or produce an item as a consequence of a specific prior encounter. It is one of the important evidence of unconscious information processing and has been studied extensively in cognitive science and neuroscience. Studies using modern functional neuroimaging techniques have proven that the automatic and implicit cognition is accompanied with identifiable brain activities. (4) Affective responses (Van Raaij, 1989) and emotion-based choice (Mellers, 1999). Primary affective reaction contributes to the evaluation and choice. Also people are assumed to anticipate how they will feel about the outcomes of decisions and use their predictions to guide choice.

Along with behavioral researchers, economists have recently shown a keen interest on human or behavioral aspect of the choice process too. A new research domain, behavioral finance, is focused on this topic and received extensive attention in the United States (Shiller, 2000; Shleifer, 2000). In Europe, the Economic Psychology will re-emerge and join the exploration.

One of the renowned economists, Daniel MacFadden (1999), calls an agent (consumer) the K-T man if he/she exhibits cognitive anomalies where his/her behavior shows surprising departure from rationality. K-T stands for Kahneman and Tversky who pioneered the work of cognitive anomalies. One the other hand, he calls an agent (consumer) Chicago man if he/she conforms to the standard economic model of perception, preference, and process rationality. He is also encouraging that economists should evolve Chicago man in the direction of K-T man, adopting those features needed to correct Chicago-man’s most glaring deficiencies as a behavioral model, and modifying economic analysis so that it applies to this hybrid.

The classical rationality hypothesis with utility theories is looking at only the objective result of monetary choice. It seems that the decision makers are actually computer-like observers while making his/her own choice, without self-involvement. This research methodology departs from the actual choice scenarios and should evolve to a K-T man’s choice. With the information processing perspective, the decision makers are participating in making the choice with his/her own conscious, unconscious, and affective processes.

As the nature of choice process is better understood by behavioral researchers, such as the unconscious components of decision-making (Van Raaij, 1989; Roediger, 1990; Schacter, 1987, 2001; Ye, 2000; Ye & van Raaij, 1997, 2001a, 2001b), cognitive anomalies (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992), emotion-based choice (Mellers, 1999, 2000), the rationality hypothesis for choice should be revisited because it was based on limited knowledge of human information processing and choice process with a observer-type research methodology.

Implicit economic cognition hypothesis

As an advance for the rationality and bounded rationality hypothesis, we like to propose a new and integrated hypothesis for choice behavior. It involves rationality, K-T man’s properties, emotion, and unconscious information processing. This hypothesis is called implicit economic cognition. It suggests that people make their economic or social decisions based on factors of rational choice, unconscious and affective judgments, with or without their own awareness. These factors can be represented with conditional-probability parameters in the multinomial decision process (MDP) model that depicts the information processing and decision-making processes for consumers (Ye, 2000; Ye & van Raaij, 1997, 2001a, 2001b).

The term, implicit economic cognition, is interpreted as such that implicit means that unconscious and affective components of consumer information encoding and retrieval constitute the decision process. Economic means that the decision outcome pertains to economic behavior such as marketing and financial activities. Cognition means that cognitive components such as conscious recollection, categorization, and thinking are composed in the decision process as well. If this hypothesis is applied to other activities rather than economic behavior, it may be coded as implicit cognition hypothesis.

The implicit economic cognition hypothesis is consistent with McFadden’s (1999) decision-process framework that involves decision elements such as process, attitudes, perceptions/beliefs, affect, motives, and preferences. The input is information, and the output is choice. Although behavioral researchers are trying to understand the nature of the decision elements, especially the process element, economists are focusing on the mapping from information inputs to choice, and assuming the decision process as a black box. The implicit economic cognition hypothesis is focusing on the black box. In addition, it includes unconscious information processing for choice, which is not mentioned in McFadden’s framework.

Our general argument for the implicit economic cognition hypothesis is that it provides an alternative and more complete foundation for explaining individual economic behavior, decision-making, and behavior in games, in comparison with the rational expected utility theory. It also suggests that the bounded rationality hypothesis refers to is actually the conscious proportion of human choice behavior. As a counterpart of the limited human computational capacity that is conscious, the unconscious and affective proportion of the choice behavior has been ignored and should be employed for choice behavior interpretation and prediction. This may explain why we still have the opportunity to search for mathematical laws of choice, because very few researches are looking at the whole picture of the choice process. In other words, most of them are using parts of the object, such as the conscious components, to predict the global behavior of the object with both conscious and unconscious components. The understanding of unconscious processes from a cognitive science or neuroscience perspective is a recent development that has not yet been communicated to economists. It also may mean communication and cross-fertilization between psychologists and economists need to be improved (Camerer & Weber, 1992).

A new non-expected value function for implicit decision weights and implicit utilities rooted in the implicit economic cognition hypothesis, the implicit expected utility theory, will be proposed in this paper. In the following endeavors, it will be compared with non-expected utility theories such as the weighted value function of gains and losses (Tversky & Kahneman, 1992), and the expected or subjective-expected utility functions such as logarithmic and exponential functions for wealth (Bell & Fishburn, 2000).

The multinomial decision process (MDP) model

The MDP model is proposed to depict how the information for choice stimulus is processed and to capture the conscious and unconscious processes for the decisions being made (Ye & van Raaij, 2001b; Ye, 2000).

Starting with the same input information as traditional economic models based on the Chicago man, the MDP model of the K-T man assumes that information comes to human brain for processing through three channels. One of the K-T man’s features, attention, distinguishes these channels. These channels are attention (attended), inattention (unattended), and new channels. Familiar, significant, and important information about the targets of judgment flows through the attention channel. Unfamiliar information but encountered in the past, insignificant, and trivia information of the targets of judgment flows through the inattention channel. New information about the targets of judgment goes through the new channel. The targets of judgment can be any entity under evaluation such as stocks, movies, politicians, papers, and commercial products. Here, we target at an example of financial decision-making, the stock judgment and choice. The information of the significant attributes about a stock, such as stock quote and historical diagram, is attended to and transferred to the human brain through the attention channel. The information of the insignificant attributes about the stock, such as the stock price two years’ ago, is not attended to and transferred to human brain through the inattention channel. New information about the stock, such as a new CEO of the company, is transferred to the human brain through the new channel.

Once all the information about the targets arrives, there are six individual components involved in the processing stage. Six parameters are representing the associated six components that are categorized as rational, unconscious, affective, or guessing component. These parameters are shown as follows,

$ Unconscious component, denoted by i_;

$ Rational component, denoted by e₂ and e₄;

$ Affective component, denoted by a₂;

$ Guessing component, denoted by g₁ and g₂.

After the target information is filtered and processed by the six components, the result for two types of the judgments is produced. The likelihood for both affective and rational judgments is the outcome of the process element in the decision-process framework (McFadden, 1999). It establishes the foundation of the theory of implicit expected utility for discrete choice behavior. The decision likelihood refers to the chance of one’s positive decision of either rational or affective judgment. The decision likelihood functions compute the likelihood value for rational or affective decision under various conditions. The formulas for one of the conditions, affective decision likelihood for attended stimulus, is as follows:

Df=E p(i, e₂, e₄, a₂ , g₁, g₂)=i + (1-i) e₂ a₂ + (1-i)(1- e₂) a₂ g₁

=p(i) + (1-p(i)) p(e₂)p(a₂) + (1-p(i))(1- p(e₂))p( a₂)p( g₁ ) + (1-p(i))(1-p( e₂)) p(a₂) (1-p(g₁))

Df: the decision function;

p(i): the probability of unconscious/automatic component i;

p(e₂): the probability of conscious/rational component e₂;

p (e₄): the probability of unconscious/rational component e₄;

p(a₂): the probability of affective component a₂

p(g₁): the probability of guessing component g₁

p(g₂): the probability of guessing component g₂

p(i, e₂, e₄, a₂ , g₁, g₂): the multiplications of various probabilities

Note that parameters i, e₂, e₄, a₂, g₁, g₂ are denoting both processes and probabilities.

There are twelve decision likelihood functions for different conditions in the MDP model (See Appendix A for the table of formulas). These formulas are estimated at an equilibrium point where the maximization of the multinomial likelihood function is reached (Batchelder & Riefer, 1990; Ye & van Raaij, 2001; Ye, 2000). Combinations of these formulas may create new decision weights and new utility functions for the implicit expected utility theory, which will be proposed in the following section.

A new foundation for choice behavior: implicit expected utility theory

On the basis of the MDP model (Ye & Van Raaij, 2001) and the implicit economic cognition hypothesis, a new non-expected utility theory will be proposed. It is the implicit expected utility theory. It combines prospect theory and the multinomial decision process model. Extracted from the MDP model, a new construct, implicit decision weights, will be extending the decision weights function for probability, p(p_i), of the prospect theory. The implicit decision weights will represent mental processes such as conscious, unconscious, and affective processing, etc. Also, the utility function, u(x_i), of the weighted value function in prospect theory will be extended with a new implicit utility function that involves mental processes coming from the MDP model. Therefore, the implicit expected utility theory can be described as follows:

V(q)=IEu(q)=E_i Df $ iu(x_i)

IEu(q): implicit expected utility value

q: a probability distribution=(p₁, p₂, ,p_n)

Df: decision likelihood function

iu(x_i): implicit utility function

The theoretical advantage of the implicit expected utility theory is that it is also based on the implicit economic cognition hypothesis. The implicit economic cognition hypothesis is a more complete description for human choice behavior over the rationality hypothesis (McFadden, 1999). It advances the idea of bounded rationality, identifying the ignored or unconscious proportion of the behavior ('iceberg’) being unconscious processes, in addition to the limited conscious computational capacity for human choice behavior. Implicit expected utility theory will also advance the current non-expected utility theories such as the weighted value function from prospect theory, because it may involve in the value function with unconscious and affective decision-making processes in addition to rational and conscious choice process. The expected and subjective expected utility functions are based on only rationality hypothesis without involving psychological processes, not mentioning the unconscious decision process. Meanwhile, the weighted value function doesn’t include parameters representing human judgment processes in the model. The details of the comparisons will be studied following this paper. As more may be understood, the new theory will provide a new foundation for economic and social choice behavior.

FIGURE 1

THE MDP MODEL

THEORETICAL ISSUES TO BE INVESTIGATED

In our following endeavors, we like to explore, but not limited to, the following questions:

$ What are the formulas for the implicit decision weights and implicit utility function?

$ Establish the new value function for the implicit expected utility theory?

$ What is the advantage of the implicit expected utility theory, over classic expected and subjective expected utility theories?

$ Using the implicit expected utility theory as axioms to interpret the law of diminishing marginal utility with partial derivatives.

$ What is the relationship between the decision likelihood functions with unconscious components and the weighted value function of the prospect theory?

$ Can the foundation of the interactive decision theory, game theory, use decision likelihood functions, or the new non-expected utility function and implicit decision weights?

$ How to estimate the implicit decision weights and the implicit expected utility function with frequencies from finance (?) experiments?

$ How to estimate the implicit decision weights with individual satisfactory (utility) ratings?

$ How to derive formulas for the mental process parameters (probabilities) from the individual ratings?

Insights on experimental bubbles and crashes phenomenon

Alan Greenspan, chairman of the Federal Reserve Board in Washington, used the term irrational exuberance to describe the behavior of stock market investors on December 5, 1996. This term reflects that the markets may have been bid up to unusually high and unsustainable levels under the influence of market psychology (Shiller, 2000). Therefore, the stock markets exhibit price bubbles.

In research on experimental asset markets, price bubble is operationally defined as the trade in high volumes at prices that are considerably at variance from intrinsic values. The story behind the price bubbles are originally assumed to be that the existence of lack of common knowledge of rationality and consequent speculation. Recent research has proven that it is not the case because strong evidence has shown that the ability to speculate is not essential to create the bubble-crash price dynamics. As admitted by the authors, the reasons behind the bubble phenomenon are far beyond of their current investigation (Lei, Noussair, and Plott, 2001). However, they are suspecting that the conscious pursuit of capital gains does not occur in their experiments. In other words, the actual irrationality may be the cause. In our view, the actual irrationality may be interpreted as unconscious process.

Implicit expected utility theory may explain the bubble-crash phenomenon by offering the understanding on unconscious and affective information processing (Van Raaij, 1989; Ye & Van Raaij, 2001b; Payne, 2001) of choice behavior.

APPENDIX A

THE TABLE OF EQUATIONS OF THE MDP MODEL

APPENDIX B

ESTIMATING THE PARAMETERS OF THE MDP MODEL WITH CELL FREQUENCIES

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