Decision TheoryDecision Theory

CHOICE(Introduction)

Professor : Dr. Liang

Student : Kenwa Chu

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What is Decision Theory?What is Decision Theory?

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What is Decision Theory?What is Decision Theory? making sense of how individuals and

groups make or should make decisions EconomistsEconomists MathematiciansMathematicians PhilosophersPhilosophers social scientistssocial scientists StatisticiansStatisticians

very abstract speculations <--->practical advice ideally rational agentsideally rational agents

Decision theorists with a strong mathematical real peoplereal people

Social scientists discovering how real people actually behave

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two main branchestwo main branches normative (prescriptive) decision theory

prescribe prescribe how decisions ought to be madehow decisions ought to be made study ideally rational agents study ideally rational agents

descriptive decision theory find out find out how decisions are madehow decisions are made study human behaviorstudy human behavior

Keep both in mindstudy how expert business executives study how expert business executives

make decisions in order to find rules for make decisions in order to find rules for prescribing how ordinary folk should prescribing how ordinary folk should make their business decisionsmake their business decisions

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argumentsarguments

ideally rational agents Philosophers-little question of how humans should behave Philosophers-little question of how humans should behave

can acquire, store, and process unlimited amounts of information

never make logical or mathematical mistakes know all the logical consequences of their beliefs

The Author- valuableThe Author- valuable still serve to guide and correct our thinking Ex. Computers’ memories

some abstract decision neither normative nor descriptive ends in mindneither normative nor descriptive ends in mind

Ex. notion of rational economic man is not a descriptive model Maximizing personal profit is not necessarily the highest good

for human beings The Author- dropping the normative-descriptive distinction The Author- dropping the normative-descriptive distinction

more speculative discussion This book-abstract decision theory

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divisiondivision Individuals Decision

not be a single human beingnot be a single human being Corporations, nations, … make decisions Corporations, nations, … make decisions as as

individuals individuals to realize some organizational goalto realize some organizational goal Groups Decision

several individuals who belong to the same several individuals who belong to the same corporation…adjudicate differences about corporation…adjudicate differences about group goalsgroup goals..

game theory involve more than one individualinvolve more than one individual each individual chooses an action with the aim each individual chooses an action with the aim

of furthering his or her own goalsof furthering his or her own goals concerning how other participants will decideconcerning how other participants will decide no effort will be made to develop a policy no effort will be made to develop a policy

applying to all the participantsapplying to all the participants

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Division Division _con._con.

Case- Republican United States Presidents Elections are one way for United States citizens to Elections are one way for United States citizens to

make group decisionsmake group decisions Once elected the president also makes decisions - Once elected the president also makes decisions -

in effect an individual decision by a nationin effect an individual decision by a nation Case- post-Christmas sale

Each knows that if one has the sale and the other Each knows that if one has the sale and the other does not, the latter will get little businessdoes not, the latter will get little business

anticipating what the other will doanticipating what the other will do find a way to choose a schedule for having sales- find a way to choose a schedule for having sales- a a

group decisiongroup decision

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Match CaseMatch Case

Explosive Gas Level

Noneexplosive

Lighta Match Explosion

No Explosion

Do Not Lighta Match

No Explosion

No Explosion

Acts

States

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PROBLEMSPROBLEMS 1. Classify the following as individual or group decisions.

Which are games? Explain your classifications. a. Two people decide to marry each other.a. Two people decide to marry each other.

b. The members of a club decide that the annual dues will be $5.b. The members of a club decide that the annual dues will be $5.

c. The members of a club decide to pay their dues.c. The members of a club decide to pay their dues.

d. .The citizens of the United States decide to amend d. .The citizens of the United States decide to amend

the .Constitution.the .Constitution.

e. Two gas stations decide to start a price war.e. Two gas stations decide to start a price war.

2. If it turned out that everyone believed that 1 + 1 = 3, would that make it rational to believe that 1 + 1 = 3?

3. Although decision theory declares no goals to be irrational in and of themselves, do you think there are goals no rational being could adopt, for example, the goal of ceasing to be rational?

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The Basic FrameworkThe Basic Framework

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Match CaseMatch Case_con._con.

X Y Z

LightNo

Explosion

ExplosionNo Damage

ExplosionDamage

Do Not Light

No Explosio

n

No Explosio

n

No Explosio

n

Acts

StatesAmount of Gas Present

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determine a problem determine a problem specification specification

problem specification to be definite and complete states must be mutually exclusive and states must be mutually exclusive and

exhaustiveexhaustive one and only one of the states must obtainone and only one of the states must obtain Case- Case- MatchMatch

neglect some but not much vapor none of the abovenone of the above

Case- swine influenza vaccine paralyze a number of peopleparalyze a number of people failed to use the proper problem specificationfailed to use the proper problem specification

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Philosophical Problems about PrPhilosophical Problems about Problem Specificationsoblem Specifications

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Problem SpecifiationsProblem Specifiations the proper description of states

ALL-Star Games BettingALL-Star Games Betting Second order decision (secondorder pr

oblem specification) a decision about decision problem specificationsa decision about decision problem specifications choosing between decision tableschoosing between decision tables whenever we apply decision theory we must make swhenever we apply decision theory we must make s

ome choicesome choices right decisions and

rational decisions

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the proper description of the proper description of states states _ALL-Star Games Betting_ALL-Star Games Betting

American LeagueWins

National LeagueWins

BetAmerican +$5 -$2

BetNational -$2 +$3

• how probable you thought the American League to win

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the dominance principlethe dominance principle_ALL-Star Games Betting_ALL-Star Games Betting

I Win My Bet I Lose it

BetAmerican +$5 -$2

BetNational +$3 -$2

• to rule out dominated acts

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dominance principledominance principlemisapplication misapplication _Disarmament Case_Disarmament Case

War No War

Arm Dead Status Quo

Disarm RedImprove Society

•but that continuing to arm makes war very unlikely•have not considered act we choose affects the probabilities of the states

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Secondorder decisionSecondorder decision _Car Buying Case _Car Buying Case

Case- Car Buying askingasking price : $4,000 price : $4,000 alternative bidsalternative bids

$3,000 ? $3,500 ? $4,000 ?

wider range of bidswider range of bids bids with smaller incrementsbids with smaller increments

Secondorder decision a decision about decision problem specificationsa decision about decision problem specifications choosing between decision tableschoosing between decision tables Be Trapped in infinite regress - Be Trapped in infinite regress - benefitbenefit

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immediate decision immediate decision

not always rational

gut reactions

Case-angry bear is chasing youangry bear is chasing you

Car drivingCar driving

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right decisions andright decisions andrational decisions rational decisions _leasing an oil field case_leasing an oil field case

decision base Baker-hires a decision analystBaker-hires a decision analyst

not bid on the lease Smith-on the flip of a coinSmith-on the flip of a coin

pays dearly for the lease finds one of the largest oil reserves

was Baker's use of decision theory irrational? Unfortunately, most of our decisions must be based on Unfortunately, most of our decisions must be based on

what we think mightwhat we think might happen. happen. Yet we still should tryYet we still should try to make choices based on the to make choices based on the

information we do haveinformation we do have a rational decision can be entirely praiseworthy even a rational decision can be entirely praiseworthy even

though it did not turn out to be the right decision though it did not turn out to be the right decision

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PROBLEMSPROBLEMS 1.Set up a decision table for the following decision

situation. Jack, who is now twenty, must decide whether to marry his true love Jill immediately or not see her again until he is twenty-one. If he marries her now then he will lose the million dollars his uncle has left him in trust. If he waits to see her until he is twenty-one, he will receive the money and can marry Jill at that time if she still loves him. (Part of your problem is selecting an appropriate set of acts, states, and outcomes.)

2.Pascal reasoned that it was better to lead the life of a religious Christian than to be a pagan, because if God exists, religious Christians go to Heaven and everyone else goes to Hell, whereas if God does not exist, the life of the religious Christian is at least as good as that of the pagan. Set up a decision table for this argument and explain why the dominance principle supports Pascal's reasoning.

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Certainty, Ignorance, and Certainty, Ignorance, and RiskRisk

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decision under certainty decision under certainty Be certain that our acts will result in given

outcomes all you need to do is determine which

outcome you like best you know which act (or acts) is certain to produce ityou know which act (or acts) is certain to produce it Case-select a glass of tomato juice Case-unloaded dice Case-date a potential mate

everything concerning is certain , which will be your choose? Case-from New York to Los Angeles

linear programming

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decision under riskdecision under risk a given decision problem is possible to

assign probabilities to all the outcomes arising from each act Case-Case-

Choices between bets on fair coins roulette wheels dice

usual Case-Case-

classify investment decisions bets on horse races marketing decisions choices of crops to plant

even when we cannot assign an exact probability

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decision under ignorancedecision under ignorance(decision under uncertainty)(decision under uncertainty)

when it makes no sense to assign probabilities to the outcomes emanating from one or more of the acts

Ignorance may be partial or totalmay be possible to assign probabilities may be possible to assign probabilities

to some of the outcomes emanating to some of the outcomes emanating from some of the acts, but to none from some of the acts, but to none emanating from the other acts emanating from the other acts

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philosophically controversialphilosophically controversial Classification

estimate upper and lower bounds on estimate upper and lower bounds on probabilitiesprobabilities

decision under risk the range of probabilities is very widethe range of probabilities is very wide

decision under ignorance the only certainties are mathematical

and logical there are few true decisions under certaintythere are few true decisions under certainty

we are never totally ignorant of the probabilities of the outcomes resultant from an act there are no true decisions under ignorancethere are no true decisions under ignorance

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Some Details of Formulation Some Details of Formulation _ CASE-eat at Greasy Pete's_ CASE-eat at Greasy Pete's

the food will make you sick relevant outcomesrelevant outcomes

get sick and you do not get sick StatesStates

food is spoiled is not certain to result in your getting sickis not certain to result in your getting sick

exactly one outcome for each act-state pairexactly one outcome for each act-state pair How can we use decision tables to represent this si

mple problem? introduce outcomes that themselves involve elements of uncintroduce outcomes that themselves involve elements of unc

ertaintyertainty replace the outcomes － a chance of getting sick more refined division of the environment into states

the food is spoiled but you can handle itthe food is spoiled but you can handle it the food is spoiled and you cannot handle itthe food is spoiled and you cannot handle it the food is not spoiled the food is not spoiled

each act-state pair determines a unique outcome

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Some Details of Formulation Some Details of Formulation _ CASE-eat at Greasy Pete's_ CASE-eat at Greasy Pete's

decision under risk probabilities will be assigned to states rather than probabilities will be assigned to states rather than

outcomesoutcomes assign probabilities to that compound state and thassign probabilities to that compound state and th

e other statese other states CASE

SupposeSuppose food being spoiled is 70% unable to handle spoiled food is 50%

probabilityprobability getting rotten food at Greasy Pete's and being unable to h

andle it is 35 % get bad food but will be able to handle it is 35 % food will be fine is 30 %

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Some Details of Formulation Some Details of Formulation _co_con.n.

unconditional probability CASE-CASE-lung cancerlung cancer

state is independent of an act conditional probability of the state given the act is the same as the uconditional probability of the state given the act is the same as the u

nconditional probability of that statenconditional probability of that state contracting lung cancer is not independent of smoking earning good grades is not independent of studying surviving a marathon is not independent of training for it

Reformulate you have the protective factor and do (do not) get terminal lung can

cer from nonsmoking causes you do not have the protective factor and you do (do not) get termin

al lung cancer from nonsmoking causes Case-Joan's problem

AbortionAbortion give it up for adoptiongive it up for adoption

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PROBLEMSPROBLEMS 1. Classify the following as decisions under

certainty, risk, or ignorance. Justify your classifications. a. Jones chooses his bet in a roulette game.a. Jones chooses his bet in a roulette game. b. Smith decides between seeking and not seeking a b. Smith decides between seeking and not seeking a

spouse.spouse. c. A veterinarian decides whether to put a healthy stray dog c. A veterinarian decides whether to put a healthy stray dog

to sleep or to adopt it as his own pet.to sleep or to adopt it as his own pet. d. A student trying to satisfy degree requirements chooses d. A student trying to satisfy degree requirements chooses

among the courses currently available.among the courses currently available. e. A lawyer decides whether to accept an out-of-court e. A lawyer decides whether to accept an out-of-court

settlement or to take her client's case to trial.settlement or to take her client's case to trial. 2. Set up a decision table for the last version

of the Greasy Pete problem. Why is the outcome description you do not get sick in more than one square? What is the total probability that you will get an outcome so described?

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Decision TreesDecision Trees

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Decision Tree Decision Tree _Disarmament Case_Disarmament Case

DecitionNode

ChanceNode

ChanceNode

Red

Improve Society

Dead

Status Quo

War

Peace

War

Peace

Disarm

Do Not

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DescriptionDescription _Seashore Case_Seashore Case

Suppose you must first choose between going to the seashore or staying at home. If you go to the seashore, you will wait to determine whether it is raining. If it rains, you will decide whether to fish or stay inside. If you fish and the fishing is good, you will be happy; if the fishing is not good, you will be disappointed. If you stay in, you will feel so-so. On the other hand, if there is no rain, you will sunbathe and be happy. Finally if you stay home, you will feel so-so.

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practical advantage of trees practical advantage of trees _Seashore Case_Seashore Case

DecitionNode

ChanceNode

so so

Go to

seashore

stay at home

DecitionNode

DecitionNode

ChanceNode

Stay in

No rain

rain

fish

sun bathe

Fishing

good

Fishing not good

so so

happy

happy

disappointed

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Strategy Strategy _Seashore Case_Seashore Case

S1 : I will go to the shore; if it rains, I will fish; if it does not rain, I will sunbathe. is a strategy appropriate for the problem analyzed is a strategy appropriate for the problem analyzed

by the preceding tree. by the preceding tree.

S2 : I will go to the shore; if it rains, I will stay in; if it does not, I will sunbathe.

S3 : I will stay at home (under all circumstances).

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Seashore CaseSeashore Case

Rain & Good

Fishing

Rain & Bad Fishing

No Rain

S1 Happy Disappointed Happy

S2 So So So So Happy

S3 So So So So So So

Strategy

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PROBLEMSPROBLEMS 1. Formulate the following decision problem using a

decision tree. Danny, who has been injured by Manny in an automobile accident, has applied to Manny's insurance company for compensation. The company has responded with an offer of $10,000, Danny is considering hiring a lawyer to demand $50,000. If Danny hires a lawyer to demand $50,000, Manny's insurance company will respond by either offering $10,000 again or offering $25,000. If they offer $25,000, Danny plans to take it. If they offer $10,000, Danny will decide whether or not to sue. If he decides not to sue, he will get $10,000. If he decides to sue, he will win or lose. If he wins, he can expect $50,000. If he loses, he will get nothing. (To simplify this problem, ignore Danny's legal fees, and the emotional, temporal, and other costs of not settling for $10,000.)

2. Mimicking the method used at the end of this section, reformulate Danny's decision problem using a decision table.