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## Rational Choice Sociology

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**RationalChoiceSociology**Lecture2: TheExplicationoftheConceptofRationalActionunderCertaintyandunder Risk intheRationalChoiceTheory**Rational Choice under Certainty**• Differentlyfrompsychologicaltheories of behavior RCT isformal, orlogico-mathematicaltheory. Asin many otherlogico-mathematicaltheories (e.g. geometry), theconcept of rationalactionisdefinedinaxiomaticway: X isrationalactionif (andonlyif) X satisfies (orcorresponds, doesnotviolates) axioms (1), (2), (3)... (n). Likestatements of logical-mathematicaltheories, those of RCT are apriorical, i.e. not DIRECTLY related to empiricalexperience. Iftheobservedbehaviordoesnotcorresponds to axiomsod RCT, ir meansthat it isirrational, notthat RCT isfalse. Insofarasthebehaviour of peoplesometimes (howoften – openquestion) corresponds to RCT, RCT canworkor be appliedasempiricaltheory. Whenobservedbehaviourviolatesaxioms of RCT, it servesasnormativetheory: as a backgroundforidentification of irrationalitesinhumanbehaviour (ifyou are notable to saywhatisrational to doinsomesituation, howyoucandistinguish “rational” from “irrational” behaviour)?**Rational Choice under CertaintyWhy accept axioms?**• Self-evidentstatements (ifyouunderstandthem, you “see” thatthey are true); theyexpressourpreanalyticalintuitions (insights) aboutrationality • Sufficient to derive (prove) theorems Preferenceswhichsatisfy (orcorrespond to) axioms are consistent. Rationalbehavior (behaviordrivenbyconsistentaxioms) isconsistentbehavior. Sotheaxioms are similar to rules of formallogicwhichdescribeconditions of consistent (notself-contradictory) thinking. Ifsomebodyviolatesrules of logic, thisdoesnotrefuteformallogic, butmeansthatthatviolatorsaysself-contradictory,absurdthings Sometheoreticianscall RCT “logic of choice”; VilfredoPareto (famousItalianeconomistandsociologist) calledrationalaction “logicalaction”**Rational Choice under Certainty:Axioms**Axiomsofthe RCT forchoiceundercertaintydescribeformalpropertiesofthepreferencesofanactorwhocanfullyandtrulyforeseeall outcomesofeachalternativeaction. In suchsituationthechoiceamongactionsisequivalent to thechoicebetweenoutcomes. • Reflexivity: xi~xi Due to this equivalence “xi” can be read both “action xi”and “the outcome of an action xi”. “~” means “as good as”; “indifferent”; “>” means “better”. Reflexivity means the same as 1=1, A=A; i.e. “the value of xi= the value of xi” (2) Completeness: for each xi and xj from the feasible set, either xi≥xj, or xi≤xj, or xi~ xj. xi≥xj means “xi is as good as or better than xj”; xi≤xj means “xi is as good or worser than xj”. (3) Transitivity: for each xi, xj, xk, if xi ≥xj, and xj≥xk, then xi≥xk**Rational Choice under Certainty:Definition**If preferences of an actor satisfy axioms (1)-(3), then for each xifrom feasible choice the utility function U(x) is defined which assigns for each xi an utility index ui. If preferences satisfy only axioms(1)-(3), then utility indexes are ordinal numbers (or utility is a variable measured at ordinal level): they mean simply the place of an action (or its outcome) from the worst to the bestintheorderofactor’spreferences. No mathematical operations with them make sense. To have consistent preferences means simply to able to arrange all alternatives of choice from the worst to the best. To choose rationally to choose the alternative with greatest or maximal utility index; i.e. to maximizeutility. “Maximize the utility” means “choose the best”, or “optimize”. Utility in formal sense does not mean “pleasure”, “money” etc. The definition simply says simply that to “choose the best” means to have consistent preferencesandactaccording to themorbecauseofthem Rational behavior = behavior caused or driven by consistent (ordered in the way described by axioms) preferences Somesay : rationalbehaviourissimply “consistentbehavior” (causedorasifcausedbyconsistentpreferences)**Application of RCT in Economics:axiom of continuity**When RCT is applied in (neoclassical) Economics, the definition of rational choice is supplemented by axiom (4) of Continuity There are two equivalent formulations: (4a):preferences are continuous, if for every x, y, z such that xi >yi>zi there exists combination of x and z (say, {xk,zk}) such that actor is indifferent between yi and {xkzk}): (4b): preferences are continuous, if for every xi and yi, such that xi>yi, there exists the quantity of yyk such that yk>yiandyk>xi i.e. preferences are continuous, if by increasing the quantity of the worser alternative one can reverse the order of preferences**Why continuity axiom is important for Economics?**• If preferences are continuous, then utility indexes are cardinal numbers (=utility is variable, measurable at least at interval level). So, mathematical operations like addition or subtraction are possible • One can express or measure the utility of one outcome by the utilities of other outcomes, i.e. to find out what is their price (some say economics are about things items that have price; onlyexchangeablethingshaveprices; priceisratioofexchange ; forthings to havepricesmoneyisnotnecessary; there are relativepricesandmonetaryprices) • If preferences doesn’t satisfy axiom (4), this means that they are discontinuous or lexicographic: in the feasible set, there are “priceless” goods suchthat an actor will not trade or barter for no matter how much large amount of other goods (including money). Do you have such “priceless goods”? Are there things that you will never do no matter how much other valuable goods will be proposed in exchange? If yes, your preferences are lexicographic! See for more: Norkus Z. MaxWeber ir racionalus pasirinkimas. V.: Margi raštai, 2003, sk. 8 (pp. 255-268); sk. 15.3.1-15.3.2 (pp. 396-405) or Norkus Z. MaxWeberundRationalChoice. Marburg: MetropolisVerlag, 2001 S. 288-302; 444-456.**Application of RCT in (neoclassical) Economics: substantive**assumptions Besides theaxiom of continuity, application of RCT in (neoclassical) economics involves supplementing of 4 formal axioms bysome substantive axioms, that transform RCT from purely formal logic of choice into empirical theory • Self-interest: actors are indifferent to the consequences of their choices for the welfare of other people (externalities). Assumption of self-interest is not a part of thedefinition ofrational bevaviour in RCT. RCT doesn’t say rational behaviour=self-interested behaviourorself-interestedconsistentbehavior. Pure or “thin” (Seenext slide) RCT says just thatrational behaviour is consistent, i.e. driven by reflexive, complete, transitive and maybecontinuous preferencesbutsaysnothingabouttheircontent. An altruist, if rational, also maximizes utility. How often people choose self-interestedly, and howoften(negatively and positively) altruistically, isan empirical question. • Decreasing marginal utility (in the theory of consumer’s choice) • Decreasing marginal productivity (in the theory of producer’s choice, where the concept of production function is centralconcept) • Insatiability of consumer wants • Scarcity of resources • Specification what “utility” means. E.g., in the model of the behaviour of the producer in the competitive market: profit maximization. Central problem in (micro)economics: which allocation of scarce resources among alternative uses is optimal (maximizes the utility of an actor). In (rational) consumer choicetheory: given the budget constraints and consumer wants (preferences), which allocation of the budget maximizes consumer’s satisfaction? In (rational) producerchoice theory: under given prices for production factors and produced goods, capital and technology, what outputto produce, withwhichinputs to produce and how much to produce to maximize the profit?**“Thin” and “thick” concepts of rationality**• In the literature on the rational choice, one can find distinction between “thin” and “thick” concepts of rationality. • Thin concept of rationality is formal, or logico-mathematical; it is defined only by conditions of consistency of the preferences and probabilistic beliefs (in the case of the choice under risk); • Thick concept of rationality contains, in addition, more or less substantive assumptions about the content of the preferences • Depending on character of these assumptions there are several ways to get “thick”concept of rationality (e.g. inneoclassicaleconomics) • Generally, applying RCT to explain empirical behavior, some assumptions about the content of preferences usually are made (=“thickening” of thin rationality). • Importantly, the questions, which preferences are good, which bad doesn’t belong to RCT. It is the question of topics of ethics (is it good to maximize profit? Consumer satisfaction? To maximize votes (for politicians)? etc.)Shouldpeople care aboutothers? Orbehaveinstrictlyself-interestedway? RCT doesn’t discuss, what our ultimate ends should be; only what is to be done given some specific set of consistent preferences. • However, maybe one can choose not only according preferences, but the preferences themselves? Possibly yes, but the metapreferences should be assumed etc. See more: Norkus Z. "Apie plonąjį praktinį racionalumą ir jo pastorinimus". In: Problemos. 1998. Nr. 54. P. 39-53 (Correctedversion of thepapershould be used!); Norkus Z. MaxWeber ir racionalus pasirinkimas. V.: Margi raštai, 2003, pp. 185-191; 196-201, 228-230 • Maybe there are some “last preferences” common for all people? Which ones? Onthese difficult topics See Norkus Z. “Pirmenybių endogenizacijos problema racionalaus pasirinkimo teorijoje” Seminarai 2001. Atviros visuomenės kolegija. V.: Strofa, 2002 pp.29-37 Becker G. S. AccountingforTastes. Cambridge, Mass.: Harvard UP, 1996. Ch.1 “Preferencesandvalues“, Ch. 2 "De Gustibus Non EstDisputandum", p. 1 -49.**Rational choice under risk: the concept of prospect**• Choice under certainty (perfect foreknowledge or prediction) happens, but perhaps rather rarely. Therefore, many theorists doesn’t consider it very important or interesting, and focus on the choice under risk. Some of them assertthat choice under certainty may be considered as a limiting case of the choice under risk. So (theymaintain), theory of the RCT under risk is more general, and if wehavesatisfactoryexplication of themore complex concept of the rational choice under risk, thenthisexplanationwill imply as its part also what it means to chooserationallyunder certainty • Choosing under risk, an actor is not able foresee truly and fully the consequences of alternative actions. There is no equivalence between the choice among the actions and the choice among the outcomes. Depending on thecircumstances (notknownforanactorinadvance), an action can lead to different outcomes. However, choosingunder risk, an actor is able to estimate relative probabilities of outcomesforeach action. So she chooses among prospects that are associated with action. Her preferences have as their objects the prospects. Prospect is the set of probable outcomes of an action (something like lottery)**Choice under risk: the concept of prospect (an example)**• Jonas is businessman and hasanurgentneed to come from Vilnius to Svetlovsk (somewhere in Russia). There are two possibilities to travel: by train and by plane. If he takes train he will arrive to Svetlovskafter 7 hours (nomatterwhichweather) . If he takes the plane he will be Svetlovsk after 2 hours if good weather over Svetlovsk, but it will take 16 hours if because of bad weather the plane will not be able to land in due time in Svetlovsk. The probability of good weather over Svetlovsk believed by John is p=0,8; that of bad 1-p=0,2. Considerations of the the price of the ticket and travel comfort do not matter. There are two ways to model choice situation. The first is decision table or matrix. It consists of 4 submatrixes: 1) Outcome matrix, including two prospects train {r11, r12}, plane (r21, r22)**Choice under risk: expected utility matrix – derived from**utility matrix by weighting utility with probability**Chance node**r11 ; p11=0,8; u11=-7; eu11=-5,6 Modeling rational choice under risk: decision tree method (generally, more commendable) train eu (train)=-7 r12; p12=0,2; u12=-7; eu12=-1,4 r21; p21=0,8; u21=-2; eu21=-1,6 Chance node Actor (decision node) eu(plane)=-4,8 plane r22; p22=0,2; u22=-16; eu22=-3,2**The concept of the rational choice under risk**• To behave rationally under risk is to maximize expected utility; to choose the action with the prospect that has the maximal possible expected utility. • This is so-called Bayesian rule (not to conflate with Bayesian theorem whichisthe rule of the rational learning from experience; see Norkus Z. „Tikėjimas: racionalaus pasirinkimo teorijos perspektyva“, kn. Tikėjimo prieigos. Sud. N. Putinaitė. V.:Aidai, pp. 92-140 or Elster J. ExplainingSocialBehavior. MoreNutsandBoltsfortheSocialSciences. Cambridge: Cambridge UP, 2007, Ch. 7, pp. 124-144, Ch.11, pp. 202-206. • However, strictly speaking, what was maximized by Jonas in this example, was not theexpected utility (eu) , but expected value (ev); expected utility=expected value if actors attitudes to risk are neutral. Normally this is not the case. Besides, we got the u-values making simplifying assumption that Jonas cares only about the travelling time. Again this is not the case. Also, p values were simply assumed. Can one measure the u values and p values of an actor, instead of assuming or postulating them in more or less arbitrary way? This the subject of next lecture