האוניברסיטה העברית בירושלים

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1 האוניברסיטה העברית בירושלים THE HEBREW UNIVERSITY OF JERUSALEM RULE-RATIONALITY VERSUS ACT-RATIONALITY by ROBERT J. AUMANN Discussion Paper # 497 December 2008 מרכז לחקר הרציונליות CENTER FOR THE STUDY OF RATIONALITY Feldman Building, Givat-Ram, Jerusalem, Israel PHONE: [972] FAX: [972] ratio@math.huji.ac.il URL:

2 Rule-Rationality versus Act-Rationality RobertJ.Aumann Abstract People s actions often deviate from rationality, i.e., self-interested behavior. We propose a paradigm called rule-rationality, according to which people do not maximize utility in each of their acts, but rather follow rules or modes of behavior that usually but not always maximize utility. Specifically, rather than choosing an act that maximizes utility among all possible acts in a given situation, people adopt rules that maximize average utility among all applicable rules, when the same rule is applied to many apparently similar situations. The distinction is analogous to that between Bentham s act-utilitarianism and the rule-utilitarianism of Mill, Harsanyi, and others. The genesis of such behavior is examined, and examples are given. The paradigm may provide a synthesis between rationalistic neo-classical economic theory and behavioral economics. 1. Introduction The assumption of rationality that people act in their own best interests, given their information underlies most of economic theory and indeed of economics as a whole. Economic policy revolves largely around the creation of incentives for peopletoactasthepolicymakerwouldlike;andtoactinaccordancewithone s incentives is, of course, to act rationally. Courses in Eco 101, in price theory, and in micro revolve around maximizations, first and second-order conditions, and so on. Applications of economic theory to various and sundry areas such as law, criminology, marriage, patents, health, finance, pensions, sports, what have you, work with maximizations i.e., rationality on the most basic level. Even before the advent of Behavioral Economics, the rationality assumption wascalledintoquestion,ormodified,inonewayoranother. HerbSimon[1947] CenterforRationalityandInteractiveDecisionTheory,TheHebrewUniversityofJerusalem

3 suggested the notion of satisficing: that people do not necessarily maximize, but only seek some acceptable level of utility; also, that people use heuristics rather than calculating optima[newell, Shaw, and Simon 1962]. Milton Friedman promulgated the as if dogma: that people do not consciously optimize, but only act asiftheydo. 1 Inexperimentssuchasprobabilitymatching[SiegelandGoldstein 1959] and the ultimatum game[güth et. al. 1982], subjects deviated systematically from utility maximization. Tversky and Kahneman[1974] pointed to various systematic violations of rationality. Admittedly, most of their work, and the subsequent development of Behavioral Economics, is based on polls and laboratory experiments; yet there are also actual empirical data that point to systematic deviations from rationality. Nevertheless, rationality remains the central paradigm of mainstream economics. Viewing the rationality paradigm as a thesis (in the sense of Hegel[1807]), and the apparent irrationality discussed above as its antithesis, we here suggest a synthesis, namely rule-rationality. Ordinary rationality means that when making a decision, economic agents choose an act that yields maximum utility among all acts available in that situation; to avoid confusion, we henceforth call this act-rationality. In contrast, under rule rationality people do not maximize over acts. Rather, they adopt rules, or modes of behavior, that maximize some measure of total or average or expected utility, taken over all decision situations towhichthatruleapplies;then,whenmakingadecision,theychooseanactthat accords with the rule they have adopted. Often this is the act that maximizes their utility in that situation, but not necessarily always; the maximization is over rules rather than acts. Four remarks are in order: (i) The rule need not in general, will not be consciously adopted. Its adoption couldbetheresultofevolutionaryforces,geneticormemetic. 2 Oritcouldbethe resultofalearningprocess,whichagain,mayormaynotbeconscious. (ii)often,therulewillbeexecutedbymeansofamechanism,whichexpressesthe ruleonlyindirectly. Oneexampleofsuchamechanismisthenotionof honor (as in O Neill[1999]); we will encounter others in the sequel. 1 See, e.g.,hisremarks(indented)onp.8ofhetzel(2007),whereheexplicitlydiscussesthe as if doctrine in connection with the rationality assumption. The doctrine is also discussed in Friedman(1953), in connection with assumptions such as perfect competition, or with theory building in general, not specifically with rationality. 2 RichardDawkins[1976]coinedtheword meme forthesocialanalogueofagene atrait that propagates itself in Society because it is generally successful. We will encounter many memes in the sequel. 2

4 (iii) The distinction between act and rule rationality is analogous to the distinction between the act-utilitarianism of Jeremy Bentham[1789] and the ruleutilitarianism of John C. Harsanyi[1980] and others. With both act-rationality and act-utilitarianism, one optimizes an act does the best one can in a specific situation; in contrast, with both rule-rationality and rule-utilitarianism, one optimizes a rule so as to do well in general, but not necessarily always. But utilitarianism (of both kinds) is very different from rationality (of both kinds). Utilitarianism is a moral imperative; it is about how moral people should act, forthebenefitofsocietyasawhole. Rationalityisegoistic;itisaboutadvancing theinterestsofthedecisionmakerhimself 3 only. (iv) Much of the material presented here is based on ideas that have been in the air for years. What we do believe to be new is the perspective putting together ideas such as evolution, the as if doctrine, rule utilitarianism, perceived deviations from rationality, and so on. 2. Evolution and Rationality 2.1. The Formal Analogy The connection between evolution and rationality has been recognized for decades [MaynardSmithandPrice1973,Dawkins1976]. Tostartwith,thereisapurely formal analogy. With rationality, a decision maker chooses an act that maximizes utility; analogously, with evolution, a population selects a trait that maximizes fitness, defined as the expected number of offspring. The decision maker corresponds to the population; his choice corresponds to evolutionary selection; and utility corresponds to fitness. In each case, an element (act or trait) is chosen from a set(feasible acts or traits) to maximize some function(utility or fitness); but whereas acts are consciously chosen by decision makers, traits are selected, totally unconsciously, by an evolutionary process that operates automatically. Astherehasbeenconfusionovertheworkingsoftheprocess,itisworthwhile to enter into some detail. Every individual in a population has a genetic endowment,whichispassedonfromgenerationtogeneration. Inonewayoranother, e.g. by mutation, occasional alterations in the gene pool of the population occur. Such alterations usually affect a single individual only. If the trait that an alteration prescribes increases the fitness of that individual, then by the definition of past. 3 Masculinepronounsindicateindeterminateaswellasmalegender,aswascustomaryinthe 3

5 fitness, that individual may expect to have more offspring than the rest of the population. These offspring also possess the altered gene, so they, too, may expecttohavemoreoffspringthantherestofthepopulation. Theproportionofthe altered gene in the population thus increases exponentially, and eventually takes overthewholepopulation. Ifthetraitstilldoesnotmaximizefitness,theninthe course of time there will be a mutation or other alteration that further improves fitness; like before, it, too, will eventually take over the population. Thus a trait that maximizes fitness emerges. Ontheotherhand, ifthealterationinquestiondecreasesfitness, itwillnot propagate in the population, and so has no significant effect. Tobesure,inpracticetheprocessisperhapsnotsocut-and-dried. The setof feasible traits is not clearly defined, expectations need not necessarily translate into realizations, the environment may change in mid-stream, sexual reproduction screws up the story, and so on. Nevertheless, the essence of the description applies. Thevitalelementtobenotedisthattheprocessisentirelymechanical. Noone consciously or even unconsciously chooses, or maximizes, anything; no volition isinvolved. Itis asif somebodywastryingtomaximizefitness;butthat snot really what s going on. In contrast, rational decision-making is all conscious, all volitional, without any as if The Substantive Relation In the above discussion, rational, utility-maximizing decision making is the primary element; evolution plays a secondary, as if role. We now reverse the roles, and assert that evolution is the fundamental driving force, that ordinary utility-maximizing rationality is a product of evolution. Rationality has evolved, alongside of physical features like eyes, stomachs, limbs, and breasts, because it maximizes fitness. A person shopping around for lower prices is maximizing fitness, because the money saved can be used to purchase food, theater tickets for a date, shelter, attractive clothing, education for the children, and so on all of which increase fitness. To be sure, there is a missing link: the relation between utility and fitness. Rationality maximizes utility; evolution maximizes fitness. Utility expresses preferences what an individual likes, what he wants to do. Does he always singlemindedly want to increase fitness the number of his offspring? An obese person craving another piece of chocolate will maximize his utility by eating it, but doing so is unlikely to enhance his fitness. 4

6 Nevertheless, as a rule, utility and fitness do in large measure go together. For now we leave it at that; the exact relationship is explored more carefully below (Section 6.2). 3. Some Examples 3.1. Bees and Flowers In an experiment conducted some twenty years ago, abiologistbythe name of Andreas Bertch, from Marburg, Germany, studied the behavior of bees in a field of artificial flowers. The field consisted of a rectangular array of several dozen disks, each with a diameter of several centimeters, and each colored either blue oryellow. Inthecenterofeachdiskwasatubethatcouldsupply nectar i.e., sugar water. Initially, only blue flowers were programmed to supply nectar. Whenabatchofbeesemergedfromtheircocoons,itwasletlooseonthefield, and soon learned to visit blue flowers only. After some time, Bertch changed the programming: now only yellow flowers supplied nectar. The bees, however, continuedtovisitblueflowersonly,andeventuallydiedofstarvation. 4 Thisseemshighlyirrational. Uponfindingthatthereisnonectarintheblue flowers, rational bees should have at least tried the yellow flowers. Why did they prefer death to trying something different? To understand this, one must first understand why one would expect rationalityfromabee. Theanswerissetforthintheprevioussection rationalityisan expression of evolutionary forces. In these terms, one may rephrase the question as follows: Why didn t evolution program the bee so that when blue flowers cease giving nectar, it turns to alternative sources? Theansweristhattherewasnoevolutionarypressureforthiskindofdevelopment: the situation in Bertch s laboratory never occurs in nature. In nature, the colors of nectar-supplying flowers do not change during the lifetime of a bee. Therefore,itissufficientinnatureforthebeetolearninitsyouthwhichflowers supply nectar, and stick to this throughout its life. So evolutionary pressures have produced a learning window a period of time during the bee s youth when it learns which flowers give nectar. After that, it cannot learn anything new. This 4 PrivatecommunicationfromProf. AviShmidaoftheDepartmentofEcologyandtheCenter for the Study of Rationality at the Hebrew University of Jerusalem. Shmida adds that Bertch never published his results, but that Prof. Reinhard Selten of the University of Bonn witnessed the experiments, and they were recorded on videotape by Shmida. 5

7 is sufficient for the requirements of bees in all situations that occur naturally. This is a good example of rule-rationality. The rule is, stick to what you learned in your youth. The mechanism for executing the rule is the learning window. In Bertch s laboratory, the rule does not lead to act-rationality, which wouldcallforthebeetotryyellowflowerswhentheblueonesstopgivingnectar The Ultimatum Game In1982,Güthet. al. conductedanexperimentthathascometobeknownasthe Ultimatum Game; here we discuss just one version. The rules are simple. Two players,theproposer andtheresponder,mustdividedm Iftheyagreeon the division, each receives his agreed share. If they do not agree, neither receives anything. The game was played with many pairs of players, each player participating just once. The players did not sit face to face, and could not communicate directly. Rather, they sat at computer consoles in separate rooms. The proposer startedbymakinganoffertotheresponder;theofferwasnumericalonly,withno accompanying words. The responder could respond only by typing yes or no into the computer; no other response was allowed. Once he had responded, the gamewasover. Afterthat,theplayersreceivedtheirpayoff(ifany)andleftby separatedoors. Atnostagedidtheyseeeachotherorlearneachother sidentity. The subjects were students presumably not particularly long on money. Inthissituation,onemightexpecttheproposertooffertheresponderanonnegligible amount say DM 10, taking DM 90 for himself and for the responder toaccept. Thatisbecausethereisnorationalreasonfortherespondertowalk away from a non-negligible amount of money; and taking this as given, a rational proposer should maximize his payoff. Butthatisnotwhathappened. Mostofferswereintheneighborhoodof And when they were considerably less say they were rejected: the responderactuallywalkedawayfromasmuchasdm20. Onthefaceofit,thisseemstobeaclearviolationofact-rationality. Noton the part of the proposer, who perhaps foreseeing the response is rational in not risking rejection; but on the part of the responder. Possible explanations include wounded pride, a feeling of being insulted, selfrespect, and a desire for revenge. Another explanation that might be suggested is 5 The Deutsch Mark (DM) was the currency of Germany at the time the experiment was conducted. Roughly,DM1in1982isequivalentto1Euroin

8 that the responder wishes to establish a reputation for rejecting lop-sided offers, so that in future negotiations, he will not get such offers. But that explanation does not hold water, because the game was played entirely anonymously; no one was told the players identities, so reputations could be neither established nor destroyed. There are two ways of viewing pride, insults, self-respect and revenge. One is that they themselves are legitimate sources of utility and disutility, so the responder is behaving entirely rationally when he rejects a offer; he actually gets positive utility from taking revenge, and he would get negative utility from accepting an insulting offer. That is a perfectly consistent, logical position. But conceptually and methodologically, it is not quite satisfactory; one might wishtodelvedeeper. Ratherthantakingemotionsliketheaboveasgiven,one might wish to account for them in terms of more fundamental human needs. What purpose evolutionary or otherwise does it serve to feel insulted, or to take revenge? What is the function of self-respect? That s where rule rationality comes in. We suggest that even though it isn t act-rational for the responder to reject an offer, it is rule-rational to do so. As a rule, one should reject lop-sided offers, precisely for the reputational reason discussed above: so as to be treated more even-handedly in the future. People use this rule because it is usually act-rational: specifically, in almost all or all natural, real-world negotiations, which are not anonymous. The mechanism for executing the rule is a combination of the emotions discussed above self-respect, wounded pride, a desire for revenge, and so on, which evolved, genetically or memetically, because they usually maximize fitness. In Güth s laboratory, the rule does not lead to act-rationality, which would call for the responder to accept any positive sum. Notethatthisentirediscussionisabouttheresponder;itishisbehaviorthatis rule-, but not act-rational. The behavior of the proposer, who in these experiments usuallyproposesatleastdm30totheresponder,isact-rational,sincehefearsa rejection by the responder rightfully Food Eating is an excellent example of rule-rationality. From the evolutionary point of view, itisrationalasarule; oneneedsfoodforenergyandgrowth. Butas we all know, one can overeat, and then eating becomes act-irrational. Nevertheless, people continue to eat even then. 7

9 The mechanism for executing the rule is hunger; also the other side of the same coin, namely the enjoyment of food. Usually, the direct motivation for eating is not to get energy, but hunger and food enjoyment. Both are genetic; they evolved in order to motivate organisms to eat. Evolution did not design the mechanismtocope with the sedentarynature of much of modern life, so it sometimes misfires, so to speak. Thus, in spite of the rule-rationality of eating, it is sometimes act-irrational. Overeating may be act-irrational not only for overfed people, but at the opposite end of the spectrum, also for the severely undernourished; there are documented cases of people who survived the concentration camps during the Holocaust, only tragically to die of overeating upon being liberated. Again, evolution didnotdesignthesystemtodealwiththissituation,becauseitisunusual Sex Sex is another good example of rule rationality. Engaging in sex is rational as a rule, because it increases the expected number of offspring. To execute the rule, nature evolved the mechanism of the sex drive: The reason that people(and animals) have sex is, in general, not that they consciously want children, but that they enjoy sex, it fulfills a physiological need. Butoften,themechanismmisfires;oratleast,doesnotservethepurposefor which it was designed. The sex drive leads to many activities that have no chance of producing offspring: sex with birth control, sex after the reproductive age, homosexuality, masturbation, oral sex, bestiality, pornography, and so on. At best, such activities are evolutionarily neutral neither increase nor decrease fitness. But they can also be harmful, as when a sexually transmitted disease is contracted. So sex is always rule-rational, but may be act-irrational. Human beings are not alone in engaging in act-irrational but rule-rational! sex. OrchidsofthegenusOphrys resemblefemalebees,givenonectar,andare constructed so that visiting bees cannot eat the pollen; it sticks to their brows. Male bees visit these orchids, ejaculate on them, and then visit other orchids and pollinate them with the pollen on their brows. Biologists like to say that the orchid fools thevisitingbeeintothinkingthatitisafemalebee. Itisdoubtful that that assertion is meaningful, as it implies that bees have conscious desires and make conscious decisions. But even if meaningful, it need not be true. People who masturbate over provocative erotic pictures or stories are not fooled into thinkingthat theyare havingsex; itis simplythattheirsexdrives make them 8

10 masturbate. Bees are no different. The rule-rationality of the bee thus plays an important role in the natural history of the orchid Arrow s Pacific Island Story The following story was related by Kenneth Arrow, professor emeritus at Stanford University and 1972 Economics Nobel Laureate(private communication). During World War II, a squadron of American bombers based on a Pacific island was assigned the mission of flying twenty-five bombing sorties to a Japanese-held island 800milesaway. Becauseofthegreatdistance,mostoftheweightthatthebombers could carry was needed for fuel; very little could be used for the payload: the bombs. This mission was very dangerous; in similar previous missions, only a quarteroftheairmenhadsurvived. Justasthemissionwasabouttobegin,an Operations Research officer arrived from Washington with a brilliant proposal: instead of the planned mission, half the airmen to be chosen by lot would fly just one single sortie, but this sortie would be one-way. As a result, much more weight could be devoted to bombs, and in that single one-way sortie, as many bombs could be delivered as in the twenty-five round-trip sorties. And, the survival probability of each airman would increase from 1/4 to 1/2. The airmen unanimously refused the generous offer of the OR officer from Washington. When asked the reason for their refusal in individual interviews, eachonerepliedthathe isamuchbetterpilotthanaverage,thathe willnotbe shot down. Clearly, this behavior of the airmen was act-irrational. But it was rule-rational! In the army, especially in a war, things change so rapidly and unexpectedly that it makes no sense for individual soldiers to make long-term plans. Even in a trivial matter like getting leave, if you re given a choice between this weekend and next weekend, you always take this weekend; by next weekend, your service maybecancelled,orintheoppositedirection,allleavesmaybecancelled. Sothe rule that soldiers subconsciously adopt is, look ahead just one day stay alive today tomorrow will take care of itself. That is what the airmen were doing, without being aware of it. Though act-irrational, they were being rule-rational. The story has a beautiful, surprising denouement. After three sorties, an order came from Washington cancelling the whole mission. So the airmen had after all been right the unconsciously adopted rule worked! 9

11 3.6. Selten s Umbrella Until recently, 6 Reinhard Selten, professor emeritus at the University of Bonn and 1994 Economics Nobel Laureate, always carried an umbrella; even in Israel s Negevdesertinthesummer,whenitneverrains. HedidsobecauseinGermany one cannot tell when it is going to rain, so carrying an umbrella is indeed actrational; and it was too time-consuming and inconvenient to ascertain on each day in each place that he visited whether or not to carry an umbrella. This is anunusualcaseinwhich theruleof behavior, thoughnotalways leadingtoan act-rational decision, is adopted deliberately, so there is no need for a mechanism to bring about its adoption Probability Matching In 1959, Siegel and Goldstein conducted an experiment that has come to be known as Probability Matching. Since then, it has been repeated hundreds of times; here wediscussjustoneversion. Asubjectisseatedinfrontofadevicethatemits, onceintenseconds,eitheraredoragreenlightatrandom. Theprobabilityof redis1/4,thatofgreen3/4.eachtime,thesubjectmustpredictthecolorofthe light; if he succeeds, he is rewarded. Overwhelmingly, subjects predict red 1/4 of thetime,green3/4ofthetime. Thatisnotoptimal,astheprobabilityofsuccess is then only 5/8, whereas always predicting green has a success probability of 3/4. Before continuing, we observe 7 that this finding is an artifact of the experimentalset-up;intherealworld,itdoesnotobtain. Manypeoplehaveachoiceof routes in getting to work; sometimes one route is faster, sometimes another there couldbeadelaycausedbyaroadaccident,orabreakdownoftheunderground, oravisitingdignitary, orahostofotheroccurrences. If,say,RouteAisfaster 1/4ofthetime,andRouteB3/4ofthetime,thenaprobabilitymatcherwould chooseroutea1/4ofthetime, androuteb3/4ofthetime. Butthatisnot what people do. People take the same route to work every day; in this case, presumably Route B, which is precisely the optimal strategy. Why, then, do they behave as they do in the experimental setup? For one thing, peoplearenotused tosittinginfrontof devices thatemitcoloredlights at random; they have not developed rules to deal with such situations. Therefore, they use a different rule, social desirability that subjects want to be seen 6 Whenpersonalcircumstancesforcedhimtoabandonthepractice. 7 TheobservationwasprivatelycommunicatedbyProfessorJacquesDrèze. 10

12 in a favorable light which has been observed by psychologists to apply in experiments. 8 Inourcase,subjectswanttoshowtheirskillat guessingright; simply always making the same prediction would, they think, make them look obtuse, dull, obssessive. And, as noted, the situation in which they find themselves is unfamiliar; they have no experience. So they try to look good; in general, this isagoodruletoapplyininteractionswithpeople. As for people s behavior in getting to work: though this is in fact act-rational, itisunlikelytobetheproductofconsciousmaximization. Onthecontrary,itis aconsequenceofthegeneralrule, learnfromexperience,dowhatisbestforyou in general. In getting to work, looking good does not apply; one simply wants to get there asap. Thus both sides of the probability matching phenomenon its occurrence in the laboratory, and its non-occurrence in the field are attributable to rule-rationality Cooperation and the Gene for Altruism In many perhaps most human interactions, cooperation is a good idea. Generally, when people help each other, all concerned are better off. Such cooperation may be act-rational when the sides enter into an enforceable agreement, like a contract. Or, it may be act-rational in a repeated interaction, as when people repeatedly do business with each other; see, e.g., Aumann[1981, 2006]. In such casesitmaytaketheovertformofaltruism: Ihelpyoutoday,ostensiblywithout anyquidproquo,andyouhelpmetomorrow,alsoostensiblywithoutanyquidpro quo. Or,wecooperateeveryday,eventhoughoneachdayeachagentseparately would be better off acting selfishly(as in the Prisoner s Dilemma). In repeated interactions, such behavior is act-rational if each player reacts to selfish behavior on the part of the other by acting selfishly himself or perhaps even punishing the other in the future. But it could indeed does occur also in one-time encounters, even when it is quite clear that the encounter is indeed one-time. What can account for this? The answer is that acting altruistically(within limits) i.e., truly without a quid pro quo may be rule-rational. Rather than keeping accounts of who helped whom when, it may be simpler just to be generous, as a rule. Many human interactions are at least potentially repeated or long-term; in such cases, acting generouslyasarulewillworkvis-a-visotherswhoalsoaregenerousasarule,and also vis-a-vis others who do keep accounts. It is not act-rational, because in an 8 CommunicatedbyProfessorMayaBarHillel. 11

13 interaction that is one-time for sure such as tipping in a far-off restaurant that will not be visited again the decision maker could perhaps do better by acting selfishly. What we are suggesting here is that altruism is a mechanism for achieving cooperation (in the absence of an explicit enforceable agreement), in much the same sense that pride, feelings of insult, self-respect and revenge are mechanisms for getting reasonable offers in the ultimatum game (Section 3.2 above). We intimated in that discussion that such traits evolved genetically or memetically because they usually, but not necessarily always, maximize fitness. Similarly here, altruism evolved, genetically or memetically, because it promotes cooperation, and so usually maximizes fitness. As between genetic and memetic(i.e., social) evolution, the latter may seem more likely to account for altruism. But in fact, the opposite is true. In surprising and beautiful recent research, Knafo et. al. [2008] identified a mollecular basis for altruism a real physiological gene, an identifiable part of the DNA! This was done in a laboratory experiment using the Dictator Game, in which one player the dictator makes a unilateral decision regarding the distribution of a fixed sum of money between himself and another player, the recipient. It was found that dictators possessing the gene in question allocated significantly more totherecipientthanotherdictators. Sowehavehereadirectbiologicalbasisfor this form of rule-rationality. As in Section 3.2, one could simply stop there: take altruism as given a legitimate source of utility just as some workers take revenge, insult, etc., as legitimate sources of utility and disutility. Indeed, workers in this area use the term other-regarding preferences to explain such behavior. But again as above, this is conceptually and methodologically not quite satisfactory; one might wish to delve deeper. Rather than taking altruistic behavior as given, one might wish to account for it in terms of more fundamental human needs. What purpose evolutionary or otherwise does it serve? What is its function? That is the question addressed in the current treatment. And that question is particularly apt in view of the existence of a mollecular basis a gene for the behavior in question. It is all well and good to speak airily about other-regarding preferences, butwhenyouhaveagenestaringyouintheface,you vegottoask yourself, from where did this come? How and why did this gene evolve? 12

14 4. Rule-Utilitarianism versus Act-Utilitarianism The distinction between rule- and act-rationality is analogous to that between rule- and act-utilitarianism. Utilitarianism is a philosophical doctrine that judges themoralityofbehaviorbytheextenttowhichitadvancestheinterestsofsociety as a whole; i.e., increases social utility, defined as an aggregate (such as the sum) of individual utilities. Thus the most moral, ethical behavior is that which maximizes social utility. The idea may be traced to the ancient Greeks; apparently the first coherent formulation is that of Bentham[1789], and the term was coined by Mill[1861]. Bentham s original concept is often called act-utilitarianism. A related concept, called rule-utilitarianism, holds that one should not always necessarily act so as to maximize social utility; rather, one should follow rules of behavior that usually but not necessarily always increase social utility. Among the prominent promoters of rule utilitarianism was Harsanyi[1980]. A forceful illustration of the idea of rule utilitarianism was provided by Fyodor Dostoyevsky[1866] in his famous novel Crime and Punishment. Raskolnikov, a penurious young student, murders a vicious, despicable old moneylender for her money. By all accounts, the murder increases social utility: For one thing, the world is much better off without the moneylender; for another, the transfer from her to Raskolnikov also increases social utility, since she does nothing at all with the money, while he starves. But obviously, the murder cannot be considered moral. Why? The reason is that Society cannot allow each individual to judge his actions on his own; inter alia, because of the moral hazard that that would entail. Society must develop rules, which apply to classes of acts. So Society has decided that murder all murder is to be considered amoral. Rule- and act-rationality, and the distinction between them, are similar in form to rule- and act-utilitarianism, and the distinction between them. Both actutilitarianism and act-rationality call for the individual to choose his acts in order to maximize some kind of utility: social in the case of utilitarianism, individual in the case of rationality. Both rule-utilitarianism and rule-rationality call for the individual to develop rules that maximize utility social or individual, as the case may be on the whole, but not necessarily in each individual case. But in substance, utilitarianism and rationality are altogether different. For one thing, utilitarianism of both kinds is normative; it tells people how they should behave, if they want to be moral. Act-rationality, too, is normative; it tells 13

15 people how they should behave to advance their self-interest. But rule-rationality is a positive concept: it describes how people do behave. Indeed, when rule- and act-rationality conflict, a decision-theorist would almost always advise a decisionmaker to act in accordance with act-rationality, not rule-rationality. For example, in the ultimatum game (Section 3.2), a decision-theorist would certainly advise therespondertoacceptanofferofdm20 orevendm1! Another distinction between rule-utilitarianism and rule-rationality is that the former involves a deliberate choice on the part of the decision maker; a ruleutilitarian Raskolnikov would deliberately reject the idea of murdering the moneylender,becauseitviolatesrule-utilitarianism i.e.,isamoral. 9 Incontrast,arulerational choice is almost never deliberate, in the sense of being made because it is rule-rational. 10 Forexample, in the ultimatumgame, aresponderwhowalks awayfromdm20willtellyouthatheisdoingso toteachtheoffereralesson, or something similar; he won t tell you that he s aware that the experimental setup precludes reputational effects, but nevertheless wants to follow a rule that enhances his reputation. 5. A Formal Framework For clarity, a formal framework is useful. We now provide formal definitions of rationality, of both kinds; mutatis mutandis, they apply also to utilitarianism, of both kinds. The elements of the formalism are (1) a chooser, (2)asetO(thechooser soptions), (3)afunctionufromOtotherealnumbers(thechooser sutilityfunction),and (4)anelementcofO(thechooser schoice). The choice is rational if it maximizes the chooser s utility over all his options; i.e., (5)u(c)=max{u(o):o O}. The difference between act- and rule-rationality is not in the formalism, but in its interpretation. Act-rationality concerns a specific decision scenario; the 9 Wedonotnecessarilyequatemoralitywithrule-utilitarianism;butarule-utilitarianRaskolnikov would, and we are discussing him. We ourselves take no position on this matter. 10 Well,almostnever. ApossibleexceptionisSelten sumbrella(section3.6above). 14

16 chooser is a decision maker, and the options are possible acts what the decision maker might do in that specific scenario. For example, on a specific Sunday morning in Bonn, Professor Selten must decide whether or not to take an umbrella on his walk. There are only two options: taking or not taking the umbrella. The utility is determined by the convenienceofhavingtheumbrellaifitrains,theinconvenienceofhavingitifit does not rain, and Selten s estimate of whether it will rain, and how much, on that specific morning in Bonn. Rule-rationality, on the other hand, concerns a whole class of decision scenarios. The options now are not acts what to do but rules for determining what to do in each specific scenario in the class. Formally, any function from specific decision scenarios to acts in such scenarios is a possible rule, though some such rules mightbeimpractical. Theutilityofaruleisdeterminedbyitsutilityin each decision scenario in which it is applied, and also bythe complexityof the rule itself, the informational requirements involved, and the resulting costs. Forexample,inthecaseofSelten sumbrella,therulemustspecifynotonly whetherornottotaketheumbrellaonaspecificsundaymorninginbonn,but whentotakeit,andwhennot,onanyday,anywhereintheworld. Onesuchrule could be, always take an umbrella; another, never take it; still another, always take it, except in Israel in the summer; yet another, decide act-rationally in each case. Notethatwhenreferringtothechoiceofarule,theterm decisionmaker which implies a deliberate decision process is inappropriate. That s why in describing our formalism, we used the more general term chooser, which allows for rules that are not deliberately chosen as in most of the above examples. In brief, act- and rule-rationality are determined by parallel processes: actrationality chooses an act from a set of acts; rule-rationality, a rule from a set ofrules. Thepointofthispaperisthattheterm rule-rational appliesalsoto acts: an act may well be rule-rational but not act-rational. That happens when the act, though itself not maximizing utility over all relevant acts, is prescribed by a rational rule one that maximizes utility over all relevant rules. Indeed that isthecaseintheaboveexamples. The same formalism applies to act- and rule-utilitarianism, except that one must replace the chooser s personal utility function by social utility. 15

17 6. Discussion 6.1. Formalism and Reality Awordofcaution: theformalismdescribedinsection5shouldnotbetakentoo literally, at least with rule-rationality. Applying the idea of rationality to rules rather than acts should be seen as a perspective a way of looking at things rather than as a fully laid-out theory. Thus in the case of rule-rationality, items (2)and (3) the set O of options (i.e., rules) and the utility function u are often not very well specified. To define O,oneshouldfirstspecifythesetof decisionscenarios towhichthechosenrule ismeanttoapply;andevenafterthissethasbeenspecified,itisnotalwaysclear whatmakesarulefeasible,whenweconsideritamemberofthesetooverwhich wewishtomaximize. AndevenafterthesetOhasbeenspecified,it snotclear howtodefinetheutilityfunctionu.isthisanaverageoftheutilitiesoftheacts thatareengenderedbytherule? Orisitthemedian,ortheninetiethpercentile, orsomeotheraggregate? Howdoesonefiguretheutilityofarule? Finally,whenwesaythatthechosenrulecmaximizesu,theninviewofthe fuzziness described in the previous paragraph, it does not really make sense to think of an absolute maximum. Rather, we should think of the rule as doing very well in the aggregate, and/or in general, but not necessarily achieving the absolute maximum Utility and Fitness We return now to the above discussion(section 2.2) of the relation between rationality and evolution, where we suggested that rationality has evolved because it maximizes fitness. The missing link there was that rationality maximizes utility, whereas evolution maximizes fitness. By the usual definition, utility expresses preferences what a person likes, what he wants to do; he does not always singlemindedly want to increase fitness the number of his offspring. Thus an obese person craving another piece of chocolate maximizes his utility by eating it,butsurelynothisfitness. When utility is defined in this way by preferences the behavior characterized in the foregoing as rule-rational is, strictly speaking, in fact act-rational: itmaximizesutilitynotonlyasarule,butalways. Indeed,onemightarguethat all behavior is then act-rational; that act-rationality is a tautology. Indeed, preferencesareusuallydefinedintermsofwhatonewoulddoiffacedwithachoice 16

18 (see, e.g., Savage [1954], pp. 17 and/or 27-30). Thus by definition, the actual choicemustbe thepreferredone; soifutilityisdefinedbypreference, andactrationality maximizes utility, then the actual choice must be act-rational. From that viewpoint, then, much of the literature on bounded rationality, behavioral economics,andsoon aswellasthecurrentwork areoffthemark. 11 To make sense of this literature, one must define utility more substantively in terms of basic desiderata like time, money, family welfare, life, health, food, and so on which are indeed closely related to fitness. With such a definition, an act that maximizes utility is then indeed act-rational, and a rule that usually maximizes it, rule-rational The Literature In the introduction we noted several bibliographic sources for the idea of bounded rationality or indeed irrationality. But the basic idea of rule-rationality that much irrational behavior can, after all, be accounted for by the rational paradigm is not really implicit in this literature. Closest, perhaps, is Milton Friedman s as if doctrine [Hetzel, 2007]. But that, too, comprises just one aspect that behavior may be act-rational without any conscious attempt at maximization; but not the evolutionary genesis of rule-rationality, possible systematic failures of act-rationality, the concept of a rule and its maximality among all rules, and the matter of mechanisms. Asfarasweknow,thefirstpublisheduseoftheterm rulerationality isin Aumann[1997], 12 whichhasalsoaone-pageaccountoftheconcept(section2.3). 7. References Aumann, Robert J. (1981) Survey of Repeated Games, in Böhm, V. (ed.), Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern, Mannheim: Bibliographisches Institut, Wissenschaftsverlag, Ratherthanpointingtospecificchoicesthatsppearirrational,someofthebehavioralliterature points to allegedly inconsistent choice patterns. These, too, can often be understood in terms of rule rationality e.g., allegedly inconsistent choices may be covered by different rules. 12 Awrite-upofthe1986NancyL.SchwartzMemorialLectureatNorthwesternUniversity;a preliminary version is Aumann[1992]. 17

19 (1992) Perspectives on Bounded Rationality, in Moses, Y.(ed.), Theoretical Aspects of Reasoning about Knowledge, Proceedings of the Fourth Conference, San Mateo: Morgan Kaufmann, (1997) Rationality and Bounded Rationality, Games and Economic Behavior 21, (2006), WarandPeace, ingrandin, K.(ed.), Les Prix Nobel 2005, Stockholm: The Nobel Foundation, Also, Proceedings of the National Academy of Sciences(USA) 103, Bentham, Jeremy(1789), An Introduction to the Principles of Morals and Legislation, London: T. Payne. Dawkins, Richard(1976), The Selfish Gene, Oxford: Oxford University Press. Dostoyevsky, Fyodor(1866), Prestuplenie i nakazanie(crime and Punishment), The Russian Messenger (in twelve monthly installments). Friedman, Milton (1953), The Methodology of Positive Economics, in Essays in Positive Economics, Chicago: University of Chicago Press. Güth, Werner, Rolf Schmittberger, and Bernd Schwarze(1982), An Experimental Analysis of Ultimatum Bargaining, Journal of Economic Behavior and Organization 3, Harsanyi, John C.(1980), Rule Utilitarianism, Rights, Obligations, and the Theory of Rational Behavior, Theory and Decision 12, Hegel, Georg W. F.(1807), Phänomenologie des Geistes (Phenomenology of the Spirit), Bamberg and Würzberg: Joseph Anton Gebhardt. Hetzel, Robert L.(2007), The Contributions of Milton Friedman to Economics, Federal Reserve Bank of Richmond Economic Quarterly 93, Knafo, Ariel, Salomon Israel, Ariel Darvasi, Rachel Bachner-Melman, Florina Uzefovsky, Lior Cohen, Esti Feldman, Elad Lerer, Efrat Laiba, Yael Raz, Lubov Nemanov, Inga Gritsenko, Christian Dina, Galila Agam, Brian Dean, Gary Bornstein, and Richard P. Ebstein (2008), Individual Differences in Allocation of Funds in the Dictator Game associated with Length of the Arginine Vasopressin 1a Receptor RS3 Promoter Region and Correlation between RS3 Length and Hippocampal mrna, Genes, Brain, Behavior 7, Maynard Smith, John, and G. R. Price(1973), The Logic of Animal Conflict, Nature 246, Mill, John S. (1861), Utilitarianism, Fraser s Magazine 64, , ,

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