Rational Choice Rational Choice SociologySociologyLecture Lecture 22: : The Explication of the Concept of Rational The Explication of the Concept of Rational Action under Certainty and under Risk in the Action under Certainty and under Risk in the Rational Choice Theory Rational Choice Theory

Rational Choice under Rational Choice under CertaintyCertainty

Differently from psychological theories of behavior RCT is formal, or logico-Differently from psychological theories of behavior RCT is formal, or logico-mathematical theory. As in many other logico-mathematical theories (e.g. mathematical theory. As in many other logico-mathematical theories (e.g. geometry), the concept of rational action is defined in axiomatic way:geometry), the concept of rational action is defined in axiomatic way:

X is rational action if (and only if) X satisfies (or corresponds, does not X is rational action if (and only if) X satisfies (or corresponds, does not violates) axioms violates) axioms

(1), (2), (3)... (n).(1), (2), (3)... (n).Like statements of logical-mathematical theories, those of RCT are apriorical, Like statements of logical-mathematical theories, those of RCT are apriorical,

i.e. not DIRECTLY related to empirical experience. If the observed i.e. not DIRECTLY related to empirical experience. If the observed behavior does not corresponds to axioms od RCT, ir means that it is behavior does not corresponds to axioms od RCT, ir means that it is irrational, not that RCT is false. Insofar as the behaviour of people irrational, not that RCT is false. Insofar as the behaviour of people sometimes (how often – open question) corresponds to RCT, RCT can sometimes (how often – open question) corresponds to RCT, RCT can work or be applied as empirical theory. When observed behaviour violates work or be applied as empirical theory. When observed behaviour violates axioms of RCT, it serves as normative theory: as a background for axioms of RCT, it serves as normative theory: as a background for identification of irrationalites in human behaviour (if you are not able to say identification of irrationalites in human behaviour (if you are not able to say what is rational to do in some situation, how you can distinguish “rational” what is rational to do in some situation, how you can distinguish “rational” from “irrational” behaviour)? from “irrational” behaviour)?

Rational Choice under Rational Choice under CertaintyCertaintyWhy accept axioms?Why accept axioms?

Self-evident statements (if you understand them, you “see” that Self-evident statements (if you understand them, you “see” that they are true); they express our preanalytical intuitions (insights) they are true); they express our preanalytical intuitions (insights) about rationalityabout rationality

Sufficient to derive (prove) theoremsSufficient to derive (prove) theorems

Preferences which satisfy (or correspond to) axioms are consistent. Preferences which satisfy (or correspond to) axioms are consistent. Rational behavior (behavior driven by consistent axioms) is Rational behavior (behavior driven by consistent axioms) is consistent behavior. So the axioms are similar to rules of formal consistent behavior. So the axioms are similar to rules of formal logic which describe conditions of consistent (not self-logic which describe conditions of consistent (not self-contradictory) thinking. If somebody violates rules of logic, this contradictory) thinking. If somebody violates rules of logic, this does not refute formal logic, but means that that violator says self-does not refute formal logic, but means that that violator says self-contradictory, absurd thingscontradictory, absurd things

Some theoreticians call RCT “logic of choice”; Vilfredo Pareto Some theoreticians call RCT “logic of choice”; Vilfredo Pareto (famous Italian economist and sociologist) called rational action (famous Italian economist and sociologist) called rational action “logical action”“logical action”

Rational Choice under Rational Choice under Certainty:Certainty:AxiomsAxioms

AAxioms of the RCT for choice under certainty describe formal properties of xioms of the RCT for choice under certainty describe formal properties of thethe preferences of an actor who can fully and truly foresee preferences of an actor who can fully and truly foresee all all outcomes outcomes of each alternative action. of each alternative action. IIn such situation the choice among actions is n such situation the choice among actions is

equivalent to the choice between outcomesequivalent to the choice between outcomes..

(1)(1) ReflexivityReflexivity: x: xii ~~xxi i

Due to this equivalence “xDue to this equivalence “xii” can be read both “action x” can be read both “action xii”” and “the outcome of and “the outcome of an action xan action xii”. ”.

““~” means “as good as”; “indifferent”~” means “as good as”; “indifferent”; “>” means “better”; “>” means “better”. . Reflexivity means the same as 1=1, A=A; i.e. “the value of Reflexivity means the same as 1=1, A=A; i.e. “the value of xxii= the value of x= the value of xii””

(2) (2) CompletenessCompleteness: for each x: for each xii and x and xjj from the feasible set, either x from the feasible set, either xii ≥≥xxjj, or x, or xii ≤≤xxjj, or x, or xii ~ ~ xxjj..

xxii ≥≥ x xjj means “x means “xii is as good as or better than x is as good as or better than xjj”; x”; xii ≤≤ x xjj means “x means “xii is as good is as good or worser than xor worser than xjj”.”.

(3) (3) TransitivityTransitivity: for each x: for each xii, x, xjj, x, xkk, if x, if xi i ≥≥ x xjj, and x, and xjj ≥≥ x xkk, then x, then xii ≥≥ x xkk

Rational Choice under Rational Choice under Certainty:Certainty:DefinitionDefinition

If preferences of an actor satisfy axioms (1)-(3), then for each xIf preferences of an actor satisfy axioms (1)-(3), then for each x ii from feasible from feasible choice the utility function U(x) is defined which assigns for each xchoice the utility function U(x) is defined which assigns for each x ii an utility an utility index uindex uii..

If preferences satisfy only If preferences satisfy only axioms axioms (1)-(3), then utility indexes are ordinal numbers (1)-(3), then utility indexes are ordinal numbers (or utility is(or utility is a a variable measured at ordinal level): they mean simply the place variable measured at ordinal level): they mean simply the place of an action (or its outcome) from the worst to the bestof an action (or its outcome) from the worst to the best in the order of actor’s in the order of actor’s preferencespreferences. No mathematical operations with them make sense. To have . No mathematical operations with them make sense. To have consistent preferences means simply to able to arrange all alternatives of consistent preferences means simply to able to arrange all alternatives of choice from the worst to the best. choice from the worst to the best. TTo choose rationally to choose the o choose rationally to choose the alternative with greatest or maximal utility indexalternative with greatest or maximal utility index; i.e. to maximize utility.; i.e. to maximize utility.

““Maximize the utility” means “choose the best”, or “optimize”. Utility in formal Maximize the utility” means “choose the best”, or “optimize”. Utility in formal sense does not mean “pleasure”, “money” etc. sense does not mean “pleasure”, “money” etc.

The definition simply says simply that to “choose the best” means to have The definition simply says simply that to “choose the best” means to have consistent preferencesconsistent preferences and act according to them or because of them and act according to them or because of them

Rational behavior = behavior caused or driven by consistent (ordered in Rational behavior = behavior caused or driven by consistent (ordered in thethe way way described by axioms) preferencesdescribed by axioms) preferences

Some say : rational behaviour is simply “consistent behavior” (caused or as if Some say : rational behaviour is simply “consistent behavior” (caused or as if caused by consistent preferences)caused by consistent preferences)

Application of RCT in Application of RCT in Economics:Economics:axiom of continuityaxiom of continuity

When RCT is applied in (neoclassical) Economics, the definition of When RCT is applied in (neoclassical) Economics, the definition of rational choice is supplemented by axiomrational choice is supplemented by axiom

(4) of (4) of ContinuityContinuityThere are two equivalent formulations:There are two equivalent formulations:

(4a):(4a): preferences are continuous, if for every x, y, z such that xpreferences are continuous, if for every x, y, z such that x i i >>yyii >> zzii there exists combination of x and z (say, there exists combination of x and z (say, {{xxkk,z,zkk}}) such that actor ) such that actor is indifferent between yis indifferent between y ii and and {{xxkk z zkk}}): ):

(4b): preferences are continuous, if for every x(4b): preferences are continuous, if for every x ii and y and yii, such that x, such that xii>y>yii, , there exists the quantity ofthere exists the quantity of y y y ykk such that y such that ykk>y>yii andand yykk>x>xii

i.e. preferences are continuous, if by increasing the quantity of the i.e. preferences are continuous, if by increasing the quantity of the worser alternative one can reverse the order of preferencesworser alternative one can reverse the order of preferences

Why continuity axiom is Why continuity axiom is important for Economics?important for Economics?

If preferences are continuous, then utility indexes are cardinal numbers (=utility is If preferences are continuous, then utility indexes are cardinal numbers (=utility is variable, measurable at least at interval level). So, mathematical operations like variable, measurable at least at interval level). So, mathematical operations like addition or subtraction are possibleaddition or subtraction are possible

One can express or measure the utility of one outcome by the utilities of other 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 outcomes, i.e. to find out what is their price (some say economics are about things items that have priceitems that have price; only exchangeable things have prices; price is ratio of ; only exchangeable things have prices; price is ratio of exchange ; for things to have prices money is not necessary; there are relative exchange ; for things to have prices money is not necessary; there are relative prices and monetary prices)prices and monetary prices)

If preferences doesn’t satisfy axiom (4), this means that they are discontinIf preferences doesn’t satisfy axiom (4), this means that they are discontinuuous or ous or lexicographic: in the feasible set, there are “priceless” goods lexicographic: in the feasible set, there are “priceless” goods such such that an actor will that an actor will not trade or barter for no matter how much large amount of other goods (not trade or barter for no matter how much large amount of other goods (includingincluding money).money).

Do you have such “priceless goods”? Are there things that you will never do no matter 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?how much other valuable goods will be proposed in exchange?

If yes, your preferences are lexicographic!If yes, your preferences are lexicographic!See for more: See for more: Norkus Z. Norkus Z. Max Weber ir racionalus pasirinkimasMax Weber ir racionalus pasirinkimas. V.: Margi raštai, 2003, sk. 8 (pp. 255-. V.: Margi raštai, 2003, sk. 8 (pp. 255-

268); sk. 268); sk. 15.3.1-15.3.2 (pp. 396-405)15.3.1-15.3.2 (pp. 396-405) or or Norkus Z. Norkus Z. Max Weber und Rational ChoiceMax Weber und Rational Choice. Marburg: Metropolis Verlag, 2001 S. 288-. Marburg: Metropolis Verlag, 2001 S. 288-

302; 444-456.302; 444-456.

Application of RCT in (neoclassical) Economics: Application of RCT in (neoclassical) Economics: substantive assumptions substantive assumptions

Besides Besides the the axiom of continuity, application of RCT in (neoclassicalaxiom of continuity, application of RCT in (neoclassical)) economics economics involves involves supplementing of supplementing of 4 formal axioms 4 formal axioms by by some substantive axioms, that some substantive axioms, that transform RCT from purely formal logic of choice into empirical theorytransform RCT from purely formal logic of choice into empirical theory

(1)(1) Self-interest: actors are indifferent to the consequences of their choices for the Self-interest: actors are indifferent to the consequences of their choices for the welfare of other people (externalities).welfare of other people (externalities).Assumption of self-interest is not Assumption of self-interest is not a a part of part of the the definition definition of of rational bevaviour in RCT. rational bevaviour in RCT. RCT doesn’t say rational behaviour=self-interested behaviourRCT doesn’t say rational behaviour=self-interested behaviour or self-interested or self-interested consistent behavior. Pure or “thin” (See next slide) consistent behavior. Pure or “thin” (See next slide) RCT says RCT says just that just that rational rational behaviour is consistent, i.e. driven by reflexive, complete, transitive and behaviour is consistent, i.e. driven by reflexive, complete, transitive and maybe maybe contincontinuuous preferencesous preferences but says nothing about their content. but says nothing about their content. An altruist, if rationalAn altruist, if rational,, also maximizes utility. How often people choose self-interestealso maximizes utility. How often people choose self-interesteddlyly,, and and how often how often (negatively and positively) altruistically, is(negatively and positively) altruistically, is an an empirical question. empirical question.

(2)(2) Decreasing marginal utility (in the theory of consumer’s choice)Decreasing marginal utility (in the theory of consumer’s choice)(3)(3) Decreasing marginal productivity (in the theory of producer’s choice, where the Decreasing marginal productivity (in the theory of producer’s choice, where the

concept of production function is centralconcept of production function is central concept) concept)(4)(4) Insatiability of consumer wantsInsatiability of consumer wants(5)(5) Scarcity of resourcesScarcity of resources(6)(6) Specification what “utility” means. E.g., in the model of the behaviour of the producer Specification what “utility” means. E.g., in the model of the behaviour of the producer

in the competitive market: profit maximization. in the competitive market: profit maximization. Central Central problemproblem in in (micro)(micro)economics: which allocation of scarce resources among economics: which allocation of scarce resources among

alternative uses is optimal (maximizes the utility of an actor).alternative uses is optimal (maximizes the utility of an actor).In (rational) consumer In (rational) consumer choice choice theory: given the budget constraints and consumer wants theory: given the budget constraints and consumer wants

(preferences), which allocation of the budget maximizes consumer(preferences), which allocation of the budget maximizes consumer’s’s satisfaction? satisfaction?In (rational) producerIn (rational) producer choice choice theory: under given prices for production factors and produced theory: under given prices for production factors and produced

goods, capital and technology, what goods, capital and technology, what output output to produceto produce, with which inputs to produce, with which inputs to produce and how much to produce to maximize the profit?and how much to produce to maximize the profit?

““Thin” and “thick” concepts of Thin” and “thick” concepts of rationalityrationality In the literature on the rational choice, one can find distinction between “thin” and In the literature on the rational choice, one can find distinction between “thin” and

“thick” concepts of rationality.“thick” concepts of rationality. Thin concept of rationality is formal, or logico-mathematical; it is defined only by 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 conditions of consistency of the preferences and probabilistic beliefs (in the case of the choice under risk);choice under risk);

Thick concept of rationality containsThick concept of rationality contains,, in addition, more or less substantive assumptions in addition, more or less substantive assumptions about the content of the preferencesabout the content of the preferences

Depending on character of these assumptions there are several wayDepending on character of these assumptions there are several wayss to get to get “thick”concept of rationality“thick”concept of rationality (e.g. in neoclassical economics) (e.g. in neoclassical economics)

Generally, Generally, apply applyinging RCT to explain empirical behavior, some assumptions about the RCT to explain empirical behavior, some assumptions about the content of preferences content of preferences usually are usually are mademade ( (=“thickening” of thin rationality). =“thickening” of thin rationality).

Importantly, the questions, which preferences are good, which bad doesn’t belong to 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 RCT. It is the question of topics of ethics (is it good to maximize profit? Consumer satisfaction? To maximize votes (for politicians)? etc.)satisfaction? To maximize votes (for politicians)? etc.) Should people care about others? Should people care about others? Or behave in strictly self-interested way?Or behave in strictly self-interested way?RCT doesn’t discuss, what our ultimate ends should be; only what is to be done given RCT doesn’t discuss, what our ultimate ends should be; only what is to be done given some specific set of consistent preferences.some specific set of consistent preferences.

However, maybe one can choose not only according preferences, but the 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: themselves? Possibly yes, but the metapreferences should be assumed etc. See more: Norkus Z. "Apie plonąjį praktinį racionalumą ir jo pastorinimus". In: Norkus Z. "Apie plonąjį praktinį racionalumą ir jo pastorinimus". In: ProblemosProblemos. 1998. Nr. . 1998. Nr. 54. P. 39-53 (Corrected version of the paper should be used!); Norkus Z. 54. P. 39-53 (Corrected version of the paper should be used!); Norkus Z. Max Weber ir Max Weber ir racionalus pasirinkimasracionalus pasirinkimas. V.: Margi raštai, 2003, pp. 185-191; 196-201, 228-230. V.: Margi raštai, 2003, pp. 185-191; 196-201, 228-230

Maybe there are some “last preferences” common for all people? Which ones? Maybe there are some “last preferences” common for all people? Which ones? On theseOn these difficult topics difficult topics

See See Norkus Z. “Pirmenybių endogenizacijos problema racionalaus pasirinkimo teorijoje” Norkus Z. “Pirmenybių endogenizacijos problema racionalaus pasirinkimo teorijoje” Seminarai 2001. Atviros visuomenės kolegija.Seminarai 2001. Atviros visuomenės kolegija. V.: Strofa, 2002 pp.29-37 V.: Strofa, 2002 pp.29-37

Becker G. S. Becker G. S. Accounting for TastesAccounting for Tastes. Cambridge, Mass.: Harvard UP, 1996. Ch.1 . Cambridge, Mass.: Harvard UP, 1996. Ch.1 ““Preferences Preferences and values“, Ch. 2 and values“, Ch. 2 "De Gustibus Non Est Disputandum"De Gustibus Non Est Disputandum", p. 1 -49.", p. 1 -49.

Rational choice under risk: the concept of Rational choice under risk: the concept of prospectprospect

Choice under certainty (perfect foreknowledge or prediction) Choice under certainty (perfect foreknowledge or prediction) happens, but perhaps rather rarely. Therefore, many theorists happens, but perhaps rather rarely. Therefore, many theorists doesn’t consider it very important or interesting, and focus on the doesn’t consider it very important or interesting, and focus on the choice under risk. Some of them choice under risk. Some of them assert assert that choice under certainty that choice under certainty may be considered as a limiting case of the choice under risk. Somay be considered as a limiting case of the choice under risk. So (they maintain)(they maintain), theory of the RCT , theory of the RCT under risk under risk is more general, and is more general, and if if we have satisfactory explication of the we have satisfactory explication of the more complex concept of more complex concept of the rational choice under risk, the rational choice under risk, then this explanation then this explanation will implwill implyy as as its part also its part also what it means to choose rationally what it means to choose rationally under certaintyunder certainty

Choosing under risk, an actor is not able foresee truly and fully the Choosing under risk, an actor is not able foresee truly and fully the consequences of alternative actions. There is no equivalence consequences of alternative actions. There is no equivalence between the choice among the actions and the choice among the between the choice among the actions and the choice among the outcomes. Depending on outcomes. Depending on the the circumstances circumstances (not known for an (not known for an actor in advance), actor in advance), an action can lead to different outcomes. an action can lead to different outcomes. However, However, choosing under risk, anchoosing under risk, an actor is able to estimate relative actor is able to estimate relative probabilities of probabilities of outcomes for outcomes for each action. So she chooses among each action. So she chooses among prospects that are associated with action. Her preferences have prospects that are associated with action. Her preferences have as their objects the prospects. Prospect is as their objects the prospects. Prospect is thethe set of probable set of probable outcomes of an action (something like lottery)outcomes of an action (something like lottery)

Choice under risk: the concept of prospect Choice under risk: the concept of prospect (an example)(an example)

Jonas is businessman and Jonas is businessman and has an urgent has an urgent need to come from Vilnius to Svetlovsk need to come from Vilnius to Svetlovsk (somewhere in Russia). There are two possibilities to travel: by train and by plane. If he (somewhere in Russia). There are two possibilities to travel: by train and by plane. If he takes train he will arrive to Svetlovsktakes train he will arrive to Svetlovsk after 7 hours (no matter which weather) after 7 hours (no matter which weather) . If he . If he takes the plane he will be Svetlovsk after 2 hours if good weather over Svetlovsk, but it 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 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 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 p=0,8; that of bad 1-p=0,2. Considerations of the the price of the ticket and travel comfort do not matter.comfort do not matter.

There are two ways to model choice situation. The first is decision table or There are two ways to model choice situation. The first is decision table or matrix. It consists of 4 submatrixes: matrix. It consists of 4 submatrixes:

1) Outcome matrix, including two prospects train 1) Outcome matrix, including two prospects train {r{r1111, r, r1212}, plane (r}, plane (r2121, r, r2222))

Good Good weatherweather

Bad Bad weatherweather

To take trainTo take train rr1111== 7 hours7 hours rr1212== 7 hours7 hours

To take planeTo take plane rr2121= 2 hours= 2 hours rr2222= 16 hours= 16 hours

Choice under risk: probability and utility Choice under risk: probability and utility matrixesmatrixes

Good weatherGood weather Bad weatherBad weather

TrainTrain pp1111=0,8=0,8 pp1212=0,2=0,2

PlanePlane pp2121=0,8=0,8 pp2222=0,2=0,2

Good weatherGood weather Bad weatherBad weather

TrainTrain uu1111=-7=-7 uu1212=-7=-7

PlanePlane uu2121=-2=-2 uu2222=-16=-16

Choice under risk: expected utility matrix – derived Choice under risk: expected utility matrix – derived from utility matrix by weighting utility with from utility matrix by weighting utility with probabilityprobability

Good Good weatherweather

Bad Bad weatherweather

Take trainTake train eueu1111= -7= -7×0,8= ×0,8=

-5,6-5,6

eueu1212= -7= -7×0,2=×0,2=

-1,4-1,4

eu (train)eu (train) = =

eueu1111 + eu + eu1111==

-7-7

Take planeTake plane eueu2121= -2= -2×0,8=×0,8=

-1,6-1,6

eueu2222=-16 =-16 ×0,2=×0,2=

-3,2-3,2

eu (plane)=eu (plane)=

eueu2121+ eu+ eu22 22 ==

-4,8-4,8

Choice under risk: combined decision Choice under risk: combined decision matrixmatrix

Good weatherGood weather Bad weatherBad weather

Take trainTake train rr1111== 7 hours7 hours

pp1111=0,8=0,8

uu1111=-7=-7

eueu1111= = -5,6-5,6

rr1212== 7 hours7 hours

pp1212=0,2=0,2

uu1212=-7=-7

eueu1212= = -1,4-1,4

eu (train)eu (train) = =

eueu1111 + eu + eu1111==

-7-7

Take planeTake plane rr2121== 2 hours2 hours

pp2121=0,8=0,8

uu2121=-2=-2

eueu2121==-1,6-1,6

rr2222== 16 hours16 hours

pp2222=0,2=0,2

uu2222=-16=-16

eueu2222==-3,2-3,2

eu (plane)=eu (plane)=

eueu2121+ eu+ eu22 22 ==

-4,8-4,8

Modeling rational choice under risk: decision tree Modeling rational choice under risk: decision tree methodmethod (generally, more commendable) (generally, more commendable)

Chance nodeChance node rr11 11 ;; p p1111=0,8; u=0,8; u1111=-7; eu=-7; eu1111=-5,6=-5,6

Actor (decision node)

Chance node

r12; p12=0,2; u12=-7; eu12=-1,4

r21; p21=0,8; u21=-2; eu21=-1,6

r22; p22=0,2; u22=-16; eu22=-3,2

eu (train)=-7

eu(plane)=-4,8

train

plane

The concept of the The concept of the rational choice under riskrational choice under risk

To behave rationally under risk is to maximize expected utility; to choose the To behave rationally under risk is to maximize expected utility; to choose the action with the prospect that has the maximal possible expected utility.action with the prospect that has the maximal possible expected utility.

This is so-called Bayesian rule (not to conflate with Bayesian theorem This is so-called Bayesian rule (not to conflate with Bayesian theorem which is which is the rule of the rational learning from experience; see the rule of the rational learning from experience; see Norkus Z. „Tikėjimas: Norkus Z. „Tikėjimas: racionalaus pasirinkimo teorijos perspektyva“, kn. racionalaus pasirinkimo teorijos perspektyva“, kn. Tikėjimo prieigosTikėjimo prieigos. Sud. N. . Sud. N. Putinaitė. V.Putinaitė. V.::Aidai, pp. 92-140Aidai, pp. 92-140 or or Elster J. Elster J. Explaining Social Behavior. More Explaining Social Behavior. More Nuts and Bolts for the Social SciencesNuts and Bolts for the Social Sciences. Cambridge: Cambridge UP, 2007, Ch. 7, . Cambridge: Cambridge UP, 2007, Ch. 7, pp. 124-144, Ch.11, pp. 202-206pp. 124-144, Ch.11, pp. 202-206..

However, strictly speaking, what was maximized by Jonas in this example, was However, strictly speaking, what was maximized by Jonas in this example, was not not the the expected utility (eu) , but expected value (ev); expected utility=expected expected utility (eu) , but expected value (ev); expected utility=expected value if actors attitudes to risk are neutral. Normally this is not the case. 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 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 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, 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?instead of assuming or postulating them in more or less arbitrary way?

This the subject of next lectureThis the subject of next lecture