Individual Choice Behavior: This is a large, sprawling literature, - - PDF document

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Individual Choice Behavior: This is a large, sprawling literature, in economics and psychology, much of which is devoted to testing the predictions of different theories of rational behavior, and to documenting deviations from those predictions. The experiments are mostly simple—often just carefully crafted questions about hypothetical choices. They have given rise to some vigorous debates, on experimental methodology, on the interpretation of the observed choice behaviors, and on their implications for economics. One of the chief methodological debates concerns the use

• f hypothetical versus real choices.

We’ll talk about some series of experiments in which phenomena initially observed in hypothetical choices were reproduced in experimental environments in which subjects made real choices Many of these experiments address questions that arise out

• f the mathematical structure of expected utility theory and

its near relations. So these experiments will also give us a chance to look at the interaction between theory and

• experiment. Often experiments start as tests of the

predictions of a theory of rational behavior, and then move

• n to become investigations of unpredicted regularities.

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What do we mean by rationality? There are lots of formulations, involving assumptions of different strength. These assumptions have shaped the experiments designed to test them. Varieties of rationality: Goal oriented, maximizing behavior, Ordinal utility maximization Expected utility maximization, (and its important special case, expected value maximization) Subjective expected utility maximization, as well as some of the component parts of those theories (such as Bayesian belief formation). We’ll also consider whether there are some robust phenomena that, while they may be consistent with rationality broadly defined, violate some of the simplifying assumptions that we sometimes take for granted.

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Let’s do a simple in class experiment. Half of you have just received a windfall gift of a classy, stylish, desirable Stanford pencil. It is yours to keep, or sell. Please examine it closely, taking note of its sleek lines and prestigious lettering. Think of yourself taking notes with such an instrument. In what follows, you will be referred to as “owners.” Half of you did not receive a pencil. You will be referred to as “non-owners.” Will each owner now please pass his/her pencil to a neighboring non-owner, so that the non-owners can also fully examine the pencil. Because I randomly chose who would become an owner, there may exist some possible gains from trade. In order to assess this, I want to elicit from each owner the minimum price at which he/she would be willing to sell the pencil. From each non-owner, I would like to elicit the maximum price she/he would be willing to pay to buy the pencil. Of course, eliciting this price is a problem that itself presents some challenges to experimental design…

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Becker, DeGroot, and Marschak (1964) designed a procedure that would give utility maximizers the incentive to reveal their reservation price. Each owner of the object will be asked to name the amount of money for which he would be willing to sell it. Each non-owner will be asked to name the amount of money for which he would be willing to buy it. Next a random price will be determined. (We will draw one

• f 30 cards, to determine a price between $0.05 and $1.50.)

Each buyer seller pair will then transact (the buyer will buy the object from the seller at the random price) if and only if the random price is higher than the seller’s demand and lower than the buyer’s offer. Note that the transaction takes place at the random price, not at the stated “willingness to pay” or “willingness to accept.” It is a dominant strategy for a utility maximizer to state his true reservation price, since if he overstates or understates it he will miss some desirable selling

• pportunities or be forced to enter into some undesirable

transactions. Are there any questions? Would everyone please write down a price.

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(Note that not only is using the BDM elicitation procedure a part of the design, so is explaining it—some theories of rationality could be taken to imply that the explanation is unnecessary☺.) And of course, if subjects aren’t utility maximizers, they may not even have unique reservation prices, so the BDM technique may have unpredictable effects. But because many modern economic theories are based on the assumption that agents are expected utility maximizers, so that it is frequently the case that the predictions of the theory can only be known if the utility functions of the subjects are elicited in an incentive compatible way, this technique has found wide application even in experiments whose primary purpose is not to estimate utility functions.

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Owner prices (WTA) Non-Owner prices (WTP)

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A version of this experiment was reported in Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler 1990, “Experimental Tests of the Endowment Effect and the Coase Theorem,” JPE, 98, 6, 1325-1348. (Why do the results say something about the ‘Coase Theorem’?) Incidentally, this experiment (with real choices, controlled incentives, etc.) arose from the observation that, in hypothetical questionnaires, that there was often a big gap between reported WTPs and WTAs—e.g. in contingent valuation studies, with questions like these: How much would you pay to eliminate some risk that presently gives you a .001 chance of sudden death

• ver the next five years?

How much would you have to be paid to accept an additional .001 chance of sudden death over the next five years? Putting prices on unfamiliar things turns out to be a difficult task, and the results are sensitive to how you’re

• asked. (Dan Ariely has some nice results on this…☺

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Let’s take a step back and consider some general formulations of what constitutes rational behavior. Two closely related formulations of “simple” rationality: 1. Goal oriented, maximizing behavior in which choices can be represented by preferences. Each individual i’s choices on sets of alternatives can be represented by a preference relation Ri (>) (with strict component Pi and indifference relation Ii) such that an individual i’s choice from a set A can always be represented by [ Ci(A) = {x in A| x Ri y for all y in A}]

• 2. Ordinal utility maximization: individual i’s choices can

be represented by a real valued utility function ui [ Ci(A) = {x in A| ui(x) > ui(y) for all y in A}]

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Not every binary relation on a set A can be represented by a utility function [u(x) > u(y) iff xRy]. Two necessary conditions for a preference R to be representable by a utility function u are that it be:

• 1. complete: for each x,y in A either xRy or yRx

(since either u(x) > u(y) or u(y) > u(x)).

• 2. transitive: xRyRz implies xRz

(since u(x) >u(y) > u(z) implies u(x) > u(z)). These are sometimes also viewed as prescriptive rationality conditions: Completeness can be viewed either as a formality (if we’re willing to define xIy whenever neither xPy or yPx), or, more interestingly, as a kind of integrated personality condition (you shouldn’t fall apart when presented with choices between x and y) Transitivity can be viewed as an elementary rationality condition insofar as it avoids being the victim of a “money pump” among choices in a cycle xPyPzPx. Theorem: If A is finite or countable, then completeness and transitivity are sufficient as well as necessary conditions for a preference to be representable by a utility function.

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Some experiments concerned with the rational preference model. An intransitivity demo: you like your tea with two spoons

• f sugar; you are presented with 101 cups of tea ordered

from zero to two spoons of sugar in increments too small to taste the difference. So, you are indifferent between any two adjacent cups. Transitivity implies you should be indifferent between any two cups, but you are not… If we were testing utility theory to see if it were precisely true, we could stop here (although simple modifications to take account of “just noticeable differences” would quickly suggest themselves). But it’s less clear how we should think about this kind of evidence if we are considering utility theory to be some kind of approximation. (Maybe we could improve the approximation by incorporating just noticeable differences – e.g. by modeling choices via preferences and utilities such that xPy iff u(x) > u(y) + jnd, where jnd is a number to be determined empirically. But maybe this would just make the theory cumbersome, and not matter much for most of the choices we’re interested in…

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Intransitivity can arise in other ways also, more related to cognition than to perception (K. May, Econometrica, 1954) [note the date]: “The subjects were 62 college students. The alternatives were three hypothetical marriage partners, x, y, and z. In intelligence they ranked xyz, in looks yzx, in wealth zxy… subjects were confronted at different times with pairs labelled with randomly chosen letters. On each occasion x was described as very intelligent, plain looking, and well

• ff; y as intelligent, very good looking, and poor; z as fairly

intelligent, good looking, and rich…. During the experiment proper, the subjects were never confronted with all three alternatives at once.” [repeated choice showed consistency] results: xyz: 21; xyzx: 17; yzx: 12; yxz: 7; zyx: 4; xzy: 1; zxy: 0; xzyx: 0. Note that the intransitive cycle xyzx chosen by 17 subjects is a Condorcet “majority rule” cycle—each alternative beats the next in two out of three dimensions. So far, we’ve seen some evidence that choices may not always be resolvable into transitive preferences over

• alternatives. But we can also ask whether choices can be

represented by preferences at all.

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Choosing cancer treatments (McNeil, Pauker, and Tversky (1988) Survival Frame Mortality Frame (% alive) (% dead) Radiation Surgery Radiation Surgery After treatment 100 90 10 After 1 year 77 68 23 32 After 5 years 22 34 78 66 Percentage Choosing each: American MD’s 16 84 50 50 and students

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Presentation effects present a different kind of challenge to theories of choice based on preferences, since they suggest that choices between two alternatives may depend on how the decision is presented or “framed” (and not merely on the properties of the alternatives). That is, they suggest that there may not necessarily be any underlying preferences that are tapped when we ask a question or demand a choice. Instead, sensitivity of choices to how they are “framed” can be interpreted as suggesting that different “frames” elicit different psychological choice processes, and these may result in different choices. Kahneman and Tversky developed a big class of such

• demonstrations. The examples below were collected in

Thaler, Richard “The Psychology of Choice and the Assumptions of Economics,” in A.E. Roth, editor, Laboratory Experimentation in Economics: Six Points of View,” Cambridge University Press, 1987.

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Problem 4. Which of the following options do you prefer?

• A. A sure win of $30

[78%] B. An 80% chance to win $45 [22%] Problem 5. Consider the following two-stage game. In the first stage, there is a 75% chance to end the game without winning anything and a 25% chance to move into the second stage. If you reach the second stage you have a choice between C. A sure win of $30 [74%]

• D. An 80% chance to win $45

[26%] Your choice must be made before the game starts, that is, before the outcome of the first-stage game is known. Please indicate the option you prefer. Problem 6. Which of the following options do you prefer? E. A 25% chance to win $30 [42%] F. A 20% chance to win $45 [58%] [Source: Tversky and Kahneman, 1981] We might have expected subjects to treat problems 5 and 6 as equivalent, but they come much closer to treating problem 5 as equivalent to problem 4. (So this might be a presentation effect [a “pseudo-certainty effect in problem 5], or perhaps a compound lottery effect.)

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Problem 7. Imagine that you face the following pair of concurrent decisions. First examine both decisions; then indicate the options you prefer: Decision (i). Choose between

• A. A sure gain of $240

[84%] B. 25% chance to gain $1,000 and 75% chance to lose nothing` [16%] Decision (ii). Choose between C. A sure loss of $750 [13%]

• D. 75% chance to lose $1,000

and 25% chance to lose nothing [87%] [Source: Tversky and Kahneman, 1981] Problem 8. Choose between

• E. 25% chance to win $240

and 75% chance to lose $760 [0%] F. 25% chance to win $250 and 75%chance to lose $750 [100%] [Source: Tversky and Kahneman, 1981] But E = A&D and F = B&C

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mental accounting Problem 9. Imagine that you are about to purchase a jacket for ($125)[$15] and a calculator for ($15)[$125]. The calculator salesman informs you that the calculator you wish to buy is on sale for ($10)[$120] at the other branch of the store, a 20-minute drive away. Would you make the trip to the other store? [Source: Tversky and Kahneman, 1981] Problem 10. Imagine that you have decided to see a play, admission to which is $10 per ticket. As you enter the theater you discover that you have lost a $10 bill. Would you still pay $10 for the ticket to the play? Yes: 88% No: 12% Problem 11. Imagine that you have decided to see a play and paid the admission price of $10 per ticket. As you enter the theater you discover that you have lost your ticket. The seat was not marked and the ticket cannot be recovered. Would you pay $10 for another ticket? Yes: 46% No: 54% [Source: Tversky & Kahneman, 1981]

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sunk costs Problem 12. You have tickets to a basketball game in a city 60 miles from your home. On the day of the game there is a major snow storm, and the roads are very bad. Holding constant the value you place on going to the game, are you more likely to go to the game (1) if you paid $20 each for the tickets or (2) if you got the tickets for free? [Source: Thaler, 1980] This has been replicated fairly cleanly in an experiment (Arkes and Blumer, ’85) in which season ticket holders to a campus theater group were randomly divided into two groups, one of which was given a refund on part of the price of the tickets. This group attended the first half of the season less regularly than the control group, which received no refund.

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The relationship between time of payment and consumption is further explored in Gourville, J.T. and Soman, D. (1998). "Payment Depreciation: The Behavioral Effects of Temporally Separating Payments from Consumption." Journal of Consumer Research, 25 (September), 160-174. Gourville and Soman look at participation rates of health club members as a function of when their twice- yearly dues come due. The fact that participation is highest in the month following billing supports the general contention that consumption of services is in part a function

• f when they were paid for.

(This is also a phenomenon first explored through hypothetical questions.)

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There is a large literature on intertemporal choices. Which would you prefer: $10 today,

• r

$15 in 2 weeks? $10 in 50 weeks

• r

$15 in 52 weeks? Laibson and Rabin are two of the names associated with the burgeoning literature on modeling time preferences as hyperbolic rather than exponential, i.e. as U = U0 + βΣδtut (summing over discounted future utilities received at times t = 1 to infinity) instead of the more conventional (stationary over time) exponential formulation U = U0 + Σδtut A good deal of thoughtful work has gone into drawing out the differences to be expected between rational and irrational hyperbolic discounters, a distinction based on whether they correctly anticipate their future preferences…

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Preferences over other complex domains (not just gains and losses); e.g. preferences for fairness. Problem 13. You are lying on the beach on a hot day. All you have to drink is ice water. For the past hour you have been thinking about how much you would enjoy a nice cold bottle of your favorite brand of beer. A companion gets up to make a phone call and offers to bring back a beer from the only nearby place where beer is sold (a fancy resort hotel)[a small, rundown grocery store]. He says that the beer may be expensive and so asks how much you are willing to pay for it. He says that he will buy the beer if it costs as much as or less than the price you state, but if it costs more than the price you state he will not buy it. You trust your friend and there is no possibility of bargaining with (the bartender)[the store owner]. [Source:Thaler, ‘85] Problem 14. If the service is satisfactory, how much of a tip do you think most people leave after ordering a meal costing $10 in a restaurant that they visit frequently? Mean response: $1.28 Problem 15. If the service is satisfactory, how much of a tip do you think most people leave after ordering a meal costing $10 in a restaurant that they do no expect to visit again? Mean response: $1.27

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One attempt to summarize a number of observed or hypothesized regularities was Kahneman and Tversky’s Prospect Theory (1979, Econometrica). (See also the updated version,

Tversky, Amos, and Daniel Kahneman. "Advances in Prospect Theory: Cumulative Representation of Uncertainty." Journal of Risk and Uncertainty 5 (1992): 297-323)

Prospect Theory posits both a nonlinear “value function” that scales different monetary payoffs, and a nonlinear “weighting function” that scales different probabilities.

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Prospect Theory

p Π v $ x

Evaluate Lotteries at ∑ Π(px) v (x) instead of ∑ px u (x)

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• Distinctive Fourfold Pattern Summarized by CPT:

(1) risk-seeking over low-probability gains (2) risk-aversion over low-probability losses (3) risk-aversion over high-probability gains (4) risk-seeking over high-probability losses

• Reflection of risk attitude:

low and high probability loss and gain

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As prospect theory has become better known, it has also started to attract the kind of critical attention from experimenters that utility theory has attracted. Let’s look quickly at two of these. Harbaugh, Krause, and Vesterlund (2002), “Prospect Theory in Choice and Pricing Tasks,” working paper HK&V report that the predictions of prospect theory are sensitive to the way the questions are asked.

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Gambles examined in HK&V’s study:

Table 1: The Six Prospects Prospect Number Prob. Payoff Expected Value FFP Prediction 1 .1 +$20 $2 Seeking 2 .4 +$20 $8 Neutral 3 .8 +$20 $16 Averse 4 .1

• $20
• $2

Averse 5 .4

• $20
• $8

Neutral 6 .8

• $20
• $16

Seeking

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Experimental Procedure:

• Probability presented both by spinner and as probability
• Elicitation:

(1) Choice-based procedure (Harbaugh et al., 2000).

• chose between gamble and its expected value

(2) Price-based procedure

• Report maximum willingness to pay
• to play a gamble over gains
• to avoid playing a gamble over losses.
• BDM procedure to determine whether subjects

get risky prospect or pay the randomly determined price to play the gamble (gain), or avoid the gamble (loss)

• Participants: 96 college students
• 64 use the choice method first and price method second

(choice-subjects)

• 32 use the price method first and choice method second

(price-subjects)

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How much would you pay to avoid playing this game? 50% -$20 50% -$0 SAMPLE

No Spin,

• $10

50% -$0 50% -$20

SAMPLE

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• Risk Attitudes of Price-subjects in the Price Task

Round 1 Decisions (N=32)

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Risk Attitudes of Choice-subjects in the Choice Task (N=64)

So HK&V find they can reverse prospect theory’s fourfold pattern of risk attitudes for high and low probabilities and gains and losses.

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Similarly, Ralph Hertwig, Greg Barron, Elke U. Weber, and Ido Erev, in a recent working paper called Decisions From Experience and the Effect

• f Rare Events, look at choices over gambles in

three conditions, which they call

• Description: “The Description condition is the

condition used by Kahneman and Tversky. The subjects were presented with a description of the problems (as described above) and were asked to state which gamble they prefer in each problem.”

• Feedback: “In the Feedback condition, the

participants did not see the description of the relevant

• gambles. Rather, the participants were presented with

two unmarked keys and were told that in each trial of the experiment they can select one of the two keys. Each selection led to a draw from the keys payoff distributions (a play of the relevant gambles).”

• Sampling: “In the Sampling condition the

participants were told that their goal is to select once between two gambles. They were not presented with a description of the gambles, but were allowed to sample as many time as they wish the relevant payoff

• distributions. Thus, like the Feedback condition they

had to make decisions from experience, but like the Description condition they had to make a single choice.”

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HBW&E also find that CPT’s overweighting

• f small probabilities and underwaiting of

large probabilities occurs only in the description condition.

Problem 1: Choose between: Problem 2: Choose between: Option Outcome and likelihood Descript ion Feedback Sampling

H

4 with probability 0.8; 0 otherwise 35% 65% 88%

L

3 for sure Option Outcome and likelihood

H

4 with probability 0.2; 0

• therwise

68% 51% 44%

L

3 with probability 0.25; 0 otherwise

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So, there are systematic departures from simple models of rational choice. But it is hard to find general descriptive

• models. The same tools used to show that e.g. utility

theory isn’t a general description seem to work well on prospect theory too.