A Practicum in Behavioral Economics 5 Laboratory Experiments The Rationality of Homo economicus Versus the Reality of Homo sapiens

CHAPTER . LABORATORY EXPERIMENTS THE RATIONALITY OF HOMO VERSUS THE REALITY OF HOMO SAPIENS The laboratory experiments discussed in this chapter have been designed to test the Principle and Additional Rationality Axioms presented in Chapter . As you will see , we Homo sapiens are rather prolific in our violations of the rationality typified by Homo . TESTING THE INVARIANCE AXIOM ( VERSION ) Consider the following experiments designed by and ( 1984 ) Experiment Imagine that your hometown is preparing for the outbreak of an unusual disease that is expected to kill 600 people . Two alternative programs to combat the disease have been proposed . Assume that the BEHAVIORAL ECONOMICS

exact estimates of the consequences of the programs are as follows If Program A is adopted , 200 people will be saved . If Program is adopted , there is a probability that 600 people will be saved and a thirds probability that no people will be saved . Which of the two programs would you favor ?

Experiment Imagine that your hometown is preparing for the outbreak of an unusual disease that is expected to kill 600 people . Two alternative programs to combat the disease have been proposed . Assume that the exact estimates of the consequences of the programs are as follows If Program is adopted , 400 people will die . If Program is adopted , there is a probability that nobody will die and a probability that 600 people will die . Which of the two programs would you favor ?

Homo would quickly determine that Program A in Experiment is equivalent to Program in Experiment , and Program in Experiment is similarly equivalent to Program in Experiment . Thus , 146 ARTHUR he would recognize that the two experiments themselves are equivalent . If each experiment were conducted separately with two different groups of Homo , we would then naturally predict 50 splits between Programs A and among subjects participating in Experiment , and 50 splits between Programs and among subjects participating in Experiment . These outcomes would be consistent with the Invariance Axiom . To the contrary , when and ran the experiments , 72 ( 28 ) of the subjects in Experiment I chose Program A ( The reverse occurred in Experiment , with 22 ( 78 ) of the subjects choosing Program ( The authors surmised that this violation of the Invariance Axiom among Homo sapiens resulted from the experiments having been framed by different reference points . Experiment reference point is that people will be saved while Experiment is that people will die . This , in turn , led the Homo sapiens to make dependent choices . and identified this particular type of as a Reflection Effect . TESTING THE INVARIANCE AXIOM ( VERSION ) and ( 1979 ) provide another test of and the Reflection Effect in an experiment with two groups of roughly 70 subjects each . The first group participated in the following experiment BEHAVIORAL ECONOMICS PRACTICUM 147

Experiment Suppose you ve been given in addition to whatever you own in your life . Which lottery do you prefer ?

A 50 chance to win another ( with a 50 chance to win nothing ) Certain win of 500 . Since the two lotteries have the same expected values of 500 , a Homo with any degree of risk aversion would choose Lottery . Of and 70 Homo sapiens who participated in this experiment , 84 chose Lottery . Not bad . The second group of subjects participated in a slightly altered version of Experiment Experiment Suppose you ve been given in addition to whatever you own in your life . Which lottery do you prefer ?

A 50 chance of losing ( with a 50 chance of losing nothing ) Certain loss of 500 . Note that these two lotteries are essentially identical to the two lotteries in Experiment . Lotteries A both give 148 ARTHUR the individual a 50 chance of walking away with and a 50 chance of walking away with . Lotteries both ensure that the individual walks away wealthier with certainty . Thus , any Homo who would choose Lottery in Experiment should likewise choose Lottery in Experiment ( or to put it another way , the percentages of Homo choosing Lottery in Experiments and should be equal ) We would like to think that Homo sapiens will behave similarly . Wouldn you know it ?

Of and 70 Homo sapiens who participated in this experiment , only 31 chose Lottery . What the ?

This outcome led and to conclude that their subjects were indeed making choices . Experiment was framed in terms of winning , and the great majority of Homo sapiens responded by exhibiting risk prefer to protect certain gains . In contrast , Experiment was framed in terms of losing , and the majority of Homo sapiens responded by exhibiting decided to take a gamble that was otherwise in Experiment . The results for Experiment concur with the value function diminishing sensitivity to gains as described in Chapter , and the results for Experiment concur with the value function diminishing sensitivity to losses . TESTING THE INVARIANCE AXIOM ( VERSION ) Consider the following two experiments proposed by and ( 1979 ) BEHAVIORAL ECONOMICS PRACTICUM 149

Experiment Suppose you are offered a choice between two lotteries . Which lottery do you prefer ?

A If you roll a or a you win 160 if you roll a , or you lose 15 . If you roll a , or you win 40 if you roll a you lose 10 . Experiment Suppose you own each of the two lotteries below , and therefore you have the option of selling each of them to someone else rather than playing them yourself . How much money would you sell each one for ?

A If you roll a or a you win 160 if you roll a , or you lose 15 . If you roll a , or you win 40 if you roll a you lose 10 . In this case , each subject participates in both experiments . We would expect that if Homo prefers Lottery A to Lottery in Experiment , then she would choose to sell Lottery A for more money than Lottery in Experiment . This would be consistent with the Invariance Axiom in the context of this experiment . By contrast , and found that 70 of the Homo 150 ARTHUR

sapiens who participated in the two experiments exhibited a preference reversal by choosing the relatively safe Lottery in Experiment but stating a higher selling price for risky Lottery A in Experiment A version of Experiments and designed to test for preference reversal in the context of a monetary bet was tested by et al . 1990 ) who proposed an experiment to their students similar to the following Suppose you are asked to choose between the following two lotteries . Which lottery do you prefer ?

A 75 chance of winning 10 . 10 chance of winning 100 . The students were asked two questions which lottery would you prefer to play , and which lottery is worth more to you ( in terms of the minimum amounts of money you would be willing to accept in lieu of having the chance to play either lottery ) We know how Homo would answer . He would first calculate the expected value of each lottery ( for Lottery A and 10 for Lottery ) and then answer the two questions as I prefer Lottery and Lottery is worth more to In other words , Homo economics would go Lottery all the way no . and ( 1971 ) found similar preference reversals in their earlier study with undergraduate students , as did et al . 1991 ) in later experiments . BEHAVIORAL ECONOMICS PRACTICUM 151

preference reversal there . To the contrary , et al . 1990 ) found that around 75 of their subjects chose Lottery A in answer to the first question but roughly 65 of these same subjects chose Lottery in answer to the second question . Ouch , preference reversal there . TESTING THE INVARIANCE AXIOM ( VERSION ) Consider the following three experiments , versions of which were proposed by ( 2011 ) Experiment The Islands in the Bay of Bengal off the coast of are home to several varieties of animals . The breeding grounds for one animal in particular , the Hornbill , are threatened by human settlement and consequent deforestation . Suppose a special fund supported by private donations has been set up to provide protected breeding locations for the Hornbill . Would you consider contributing something to this fund ?

If so , how much ?

Experiment , who are exposed to the sun for many 152 ARTHUR hours per day , have a higher risk of skin cancer due to climate change than general population . Frequent medical can reduce the risk . Suppose a special fund supported by private donations has been set up to provide regular medical for the farm workers . Would you consider contributing something to this fund ?

If so , how much ?

Experiment The Islands in the Bay of Bengal off the coast of are home to several varieties of animals . The breeding grounds for one animal in particular , the Hornbill , are threatened by human settlement and consequent deforestation . who are exposed to the sun for many hours per day , have a higher risk of skin cancer due to climate change than general population . Frequent medical can reduce the risk . Suppose separate special funds supported by private donations have been set up to provide protected breeding locations for the Hornbill and regular medical for the . Would you consider contributing to one or the other fund ( or both ) If so , how much ?

Suppose that subjects recruited to participate in these experiments are divided into two groups . One group BEHAVIORAL ECONOMICS PRACTICUM 153 participates in Experiments and simultaneously , the subjects are asked to contribute to a special fund for the Hornbills in Experiment and the in Experiment . The other group participates in Experiment . What would we expect from two groups of Homo here ?

If you answer that the average amounts Homo subjects pledged in Experiments and equal the same average amounts in Experiment , then you ve nailed it ! Essentially , both groups are presented with the same experiments . Thus , on average , Homo would violate the Invariance Axiom if the amounts pledged for Experiments and did not match those pledged in Experiment . that the average amount pledged by Homo sapiens in Experiment ( for Hornbills ) will exceed the average amount pledged in Experiment ( for the ) But in Experiment , the average amounts will be reversed , indicating a preference . explains that presenting subjects with two separate questions ( Experiments and ) frames their choices narrowly . Presenting the subjects with a single question ( Experiment ) instead frames their choices broadly . In this case , as with most cases , the broader the frame the more likely subjects will provide accurate in terms of pledging amounts that more accurately reflect their underlying preferences . 154 ARTHUR

TESTING THE INVARIANCE AND DOMINANCE AXIOMS ( VERSION ) Consider the following experiments proposed by and ( 1984 ) Experiment Choose between lotteries A and A 25 chance to win 240 and 75 chance to lose 760 , or 25 chance to win 250 and 75 chance to lose 750 . Experiment Now suppose you face the following pair of what are known as compound Compound Lottery Choose between , A a sure gain of 240 , or 25 chance to win and 75 to win nothing . Compound Lottery Choose between , A a sure loss of 750 , or . Taken together , these two experiments exemplify the famous Paradox designed by Maurice in 1953 . BEHAVIORAL ECONOMICS PRACTICUM 155

75 chance to lose and 25 chance to lose nothing . Begin by noting that Lottery in Experiment dominates Lottery A . This is because the expected winnings from Lottery are greater than those from Lottery A , and the expected losses from Lottery are less than those from Lottery A . Obviously , Homo will choose Lottery , thus not violating the Dominance Axiom . Next comes the hard part . In Experiment , adding the sure win of 240 ( Lottery A in Compound Lottery ) to Lottery in Compound Lottery yields a 25 chance of winning 240 and a 75 chance to lose 760 . Note that this is exactly Lottery A in Experiment ! Similarly , adding the sure loss of 750 ( Lottery A in Compound Lottery ) to Lottery in Compound Lottery yields a 25 chance to win 250 and a 75 chance to lose 750 . But this is precisely Lottery in Experiment ! Thus , since Homo will choose Lottery in Experiment , in Experiment he will choose Lottery in Compound Lottery and Lottery A in Compound Lottery What about Homo sapiens ?

Thankfully , none of and subjects in Experiment chose Lottery A , implying that Homo sapiens also abided by the Dominance Axiom . However , in Experiment , the great . Note that by choosing Lottery A in Compound Lottery , Homo demonstrates that he does not suffer from loss aversion . 156 ARTHUR

majority of subjects chose Lottery A in Compound Lottery and Lottery in Compound Lottery . This is the opposite of Homo choices and demonstrates a preference reversal for these Homo sapiens ( relative to their choices of Lottery in Experiment ) In other words , once again a majority of Homo sapiens have violated the Invariance Axiom . 2011 ) reminds us that Experiment is an example of narrow broad Narrow framing occurs when subjects consider the two compound lotteries separately from each other ( narrowly ) rather than taking the time necessary to consider the two compound lotteries jointly ( broadly ) Subjects who broadly frame the two compound lotteries are capable of abiding by the Invariance Axiom , all else equal , they will be more likely to choose Lottery in Compound Lottery and Lottery A in Compound Lottery because they take the time to compare the two compound lotteries . As ( 2011 ) points out , in real life broad framing induces Homo sapiens to choose high for insurance policies , eschew choosing extended warranties for the products they purchase , and not regularly check their retirement balances . Broad framing encourages adherence to risk policies that lead Homo sapiens to make choices with favorable odds in the long . Also known as narrow broad bracketing . See Read et al . for a seminal discussion on the topic of choice bracketing among Homo sapiens . BEHAVIORAL ECONOMICS PRACTICUM 157

TESTING THE INVARIANCE AND DOMINANCE AXIOMS ( VERSION ) Consider the following two experiments proposed by and ( 1986 ) Experiment The following lottery is described by the percentage of marbles of different colors in each box and the amount of money you win or lose depending upon the color of a randomly drawn marble . Which lottery do you prefer ?

Lottery A Purple 90 chance to win Red chance to win Green chance to win Blue chance to lose Grey chance to lose Lottery Purple 90 chance to win Red chance to win Green chance to win Blue chance to lose Grey chance to lose Experiment 158 ARTHUR The following lottery is described by the percentage of marbles of different colors in each box and the amount of money you win or lose depending upon the color of a randomly drawn marble . Which lottery do you prefer ?

Lottery A Purple 90 chance to win Red chance to win Green chance to win Grey chance to lose Lottery Purple 90 chance to win Red chance to win Green chance to lose Grey chance to lose Begin by noting that , just as in Version above , Lottery in Experiment dominates Lottery A . This is because the expected winnings from Lottery are greater than those from Lottery A , and the expected losses from Lottery are less than those from Lottery Homo chooses Lottery and thus again does not violate the Dominance Axiom . Next , note that Experiment is effectively identical to Experiment . Specifically , Lotteries A in both experiments offer the same percentages of winning , and , respectively , and the same percentage of losing . Lotteries similarly offer the same percentages of winning and , BEHAVIORAL ECONOMICS PRACTICUM 159

respectively , and the same percentages of losing and , respectively . Since Homo chooses Lottery in Experiment via the Dominance Axiom , in Experiment she will also choose Lottery , thus abiding by the Invariance Axiom . What about Homo sapiens ?

Thankfully , none of and subjects in Experiment chose Lottery A , implying again that Homo sapiens also abide by the Dominance Axiom . However , in Experiment , a slight majority of subjects chose Lottery A . This is another demonstration of preference reversal for these Homo sapiens , which , as we now know well , is a violation of the Invariance Axiom . TESTING THE SUBSTITUTION AXIOM Consider the following experiments proposed by and ( 1979 ) Experiment Choose between lotteries A and A 45 chance to win 90 chance to win Experiment 160 ARTHUR

Choose between lotteries A and A chance to win chance to win Homo notices two things about Experiments and . First , in each experiment , the two lotteries have identical expected payoffs . In Experiment , the expected payoff is for both Lotteries A ( and ( and in Experiment , the expected payoff is for both Lotteries A ( and ( Thus , we would expect a sample of Homo to split roughly 50 in choosing between Lotteries A and in Experiment and 50 in choosing between Lotteries A and in Experiment . Second , being the omniscient creature that he is , Homo also recognizes that the probabilities in Experiment for Lotteries A and are actually multiplied by a common factor of to obtain the corresponding probabilities in Experiment for Lotteries A and . Thus , Homo understands fully the substitution that has occurred here between the two experiments . Its a different story for Homo sapiens . Based upon a sample of 66 students , and found a split of 14 between Lotteries A and in Experiment , and 73 between Lotteries A and in Experiment . In other words , the sample of Homo sapiens seems to have understood neither that the expected payoffs for each lottery are equal in each respective BEHAVIORAL ECONOMICS PRACTICUM 161

lottery , nor that the percentages in Experiment are merely substitutes for the percentages in Experiment . This latter miscue is what leads Homo sapiens to violate the Substitution Axiom . TESTING THE PRINCIPLE Consider the following experiments proposed by and ( 1992 ) Experiment Imagine you havejust taken a difficult examination . It is the end of the fall semester , you feel tired and rundown , and you are not sure that you passed the exam . If you failed you will have to take the exam again in a couple of the semester break . You now have an opportunity to buy a very attractive vacation package to the Bahamas at an exceptionally low price . The special offer expires tomorrow , while the exam grade will not be available until the day after tomorrow . Would you A Buy the vacation package . Not buy the vacation package . Pay a 150 fee to retain the right to buy the vacation package at the same low price the day after you learn whether you passed the exam . 162 ARTHUR

Experiment Imagine you havejust taken a difficult examination . It is the end of the fall semester , you feel tired and rundown , and you out that you passed the exam . You now have an opportunity to buy a very attractive vacation package to the Bahamas at an exceptionally low price . The special offer expires tomorrow . Would you A Buy the vacation package . Not buy the vacation package . Pay a 150 fee to retain the right to buy the vacation package at the same low price the day after tomorrow . Experiment Imagine you havejust taken a difficult examination . It is the end of the fall semester , you feel tired and rundown , and you out that you failed the exam . You now have an opportunity to buy a very attractive vacation package to the Bahamas at an exceptionally low price . The special offer expires tomorrow . Would you A Buy the vacation package . Not buy the vacation package . Pay a 150 fee to retain the right BEHAVIORAL ECONOMICS PRACTICUM 163

to buy the vacation package at the same low price the day after tomorrow . These experiments do not provide a clear context within which to test Homo Homo sapiens ( which is nice for a change , given that Homo sapiens have thus far paled in comparison to Homo in terms of not violating our cherished rationality axioms ) Rather , because Experiments and are sure things in the sense that the outcome of the exam is known before the decision is made about whether to purchase the vacation package , and Experiment is an unsure thing given that the result of the exam is unknown prior to making the decision , we would expect that if the percentages of those participants choosing A , and in Experiment are roughly equal to their corresponding percentages in Experiment , then these same percentages should in turn roughly equal those in Experiment . In other words , the percentage of participants in Experiment choosing A should roughly equal the percentage of participants in Experiment choosing A , which should roughly equal the percentage of participants in Experiment choosing A , and so on for choices and across the experiments . In other words , we would expect that the uncertainty embodied in Experiment should not cause its results to noticeably deviate from the results in Experiments and . Using different samples of roughly 70 students per 164 ARTHUR

experiment , and report the results ( in percentages ) A 32 54 57 16 12 following 61 30 31 Note that the percentages across choices A are roughly the same for Experiments and . But the percentages deviate quite considerably from those for Experiment . Thus , and claim that their groups of Homo sapiens violate the Principle . STUDY QUESTIONS . Can you design a laboratory experiment to test the axiom that was not considered in this Independence Axiom ?

In Testing the Invariance and Dominance Axioms ( Version ) it is clear that broad framing leads to better outcomes than narrow framing . Can you think of a situation in real life where narrow framing could lead to a better outcome than broad framing ?

Which biases discussed in Chapter are most likely to be avoided through broad framing ?

Explain . BEHAVIORAL ECONOMICS PRACTICUM 165 . Can you think of three deficiencies associated with the laboratory experiments ( discussed in this chapter ) that were conducted with the researchers own students ?

State in words why a violation of the Transitivity Axiom introduced in Chapter also implies what We are calling a preference reversal in this chapter ( see Testing the Invariance Axiom ( Version ) Can you design a simpler experiment to test for the Principle than the one presented in this chapter ?

Media Table ( Chapter ) Arthur is licensed under a BY Attribution license 166 ARTHUR