Are humans rational?
In principle, what constitutes a rational decision?
Can people actually make that decision?
What are the circumstances that affect rational decision making?
What might be the explanations for rational and irrational decisions? And the validity of those explanations?
Three kinds of theory:
- Descriptive models-models of how thought processes operate irrespective of whether the decision is good or bad.
- Prescriptive models-models that state how we ought to think in order to make the best decisions.
- Normative models-evaluate a decision in terms of the goals of the decision maker, a decision is good if it reaches these goals.
Rational thinking is normative.
--A decision is good when to enable;es the decision maker to reach their goals.
A rational decision maximises utility.
--Where utility is the extent of goal achievement.
Rationality is subjective.
--We all have different goals, what is rational to one might be (irrational/not as rational) to another.
Rational Choice Theory
->social physics: economic principle
->individuals always make prudent & logical decisions which provide them with the greatest benefit/satisfaction
->also in their highest self-interest
->people always try to maximise their advantage and minimise their losses.
->All humans base their decisions on rational calculations, act with rationality when choosing, and aim to increase either pleasure/profit.
->individuals always make prudent & logical decisions which provide them with the greatest benefit/satisfaction
->also in their highest self-interest
->people always try to maximise their advantage and minimise their losses.
->All humans base their decisions on rational calculations, act with rationality when choosing, and aim to increase either pleasure/profit.
->all complex social phenomena are driven by individual human actions
->Utility functions & probability distributions
A choice between 2/more alternatives, rational choice=option with the highest value or utility.
A choice between 2/more alternatives, rational choice=option with the highest value or utility.
Value is often numeric monetary, utility is abstract.
Choices under uncertainty:
--if the outcomes are uncertain, probability of receiving the outcome*expected value EV.
--if the outcomes are uncertain, probability of receiving the outcome*expected value EV.
- A. $100 with 50% probability, EV=$50
- B. $1000 with 2% probability, EV=$20
Expected Utility Theory:
--We can't know the future, any choice could be a gamble and we can apply Expected Value to Expected Utility, although some options have a near certain outcome while other a near zero outcome.
God exists God
does not exist
- Option A–Live holy life heaven bit less fun life
- Option B–Live secular life hell average fun
--We can assign utilities to each outcome and the probability to receive them.
- Bit less fun, Ua=-1, Average fun, Ub=0, Heaven, Ua=100, Hell Ub=-100
- P(God exists)=0.5; god does not exist=1-p(God)=0.5
- Option A–EUa= (0.5*100)+(0.5*-1)=49.5
- Option B–EUb= (0.5*-100)+(0.5*0)=-50
--Expected utility states what a rational choice is, being a normative theory.
Some arguments:
1. The long-run argument.
--EU is based on probabilities and gambles; the rational choice is based on an average of what would happen if the same decision were to made (on a number of successive occasions/a large number of people were to make the same decision).
2. The arguments from principles/the Choice Axioms.
--Weak ordering
->We must always be able to say we prefer one over the other or neither, in any set.
->x>y/x<y/x=y
->As we can express the utility of an option as an integer, the choices must be comparable.
--Transitivity
->As utility is expressed as an integer, our choices must be transitive.
->x>y, y>z, therefore x>z
--The Sure-thing principle
->Arises from the multiplications of probability, not the numerical status of utility.
Some arguments:
1. The long-run argument.
--EU is based on probabilities and gambles; the rational choice is based on an average of what would happen if the same decision were to made (on a number of successive occasions/a large number of people were to make the same decision).
2. The arguments from principles/the Choice Axioms.
--Weak ordering
->We must always be able to say we prefer one over the other or neither, in any set.
->x>y/x<y/x=y
->As we can express the utility of an option as an integer, the choices must be comparable.
--Transitivity
->As utility is expressed as an integer, our choices must be transitive.
->x>y, y>z, therefore x>z
--The Sure-thing principle
->Arises from the multiplications of probability, not the numerical status of utility.
->If there is some state of the world that leads to a particular outcome irrespective of our choices then it is cancelled out of the equation and we should not let it affect our choices.
->One should make the same decision either if he knew that an event E will obtained, if he knew the negation of event E obtained, and also if he knows nothing about event E.
->One should make the same decision either if he knew that an event E will obtained, if he knew the negation of event E obtained, and also if he knows nothing about event E.
--The utility of wealth
->St.Petersburg Paradox (Peter tosses a coin and agrees to give Paul one ducat if he gets heads on the very first throw, two ducats if he gets it on the second, four if on the third , eight if on the fourth, and so on, so that with each additional throw the number of ducats he must pay is doubled.)
->St.Petersburg Paradox (Peter tosses a coin and agrees to give Paul one ducat if he gets heads on the very first throw, two ducats if he gets it on the second, four if on the third , eight if on the fourth, and so on, so that with each additional throw the number of ducats he must pay is doubled.)
->The expected value of this gamble is infinite. However, one would sell the chance for twenty ducats that although the EV is infinite, the subjective utility is low.
->Bernoulli suggested that EV≠EU, instead the utility of wealth is proportional to its logarithm. Each additional unit of wealth worth less than the previous one. The utility of additional currency units decreases as the number of currency units increase.
->Bernoulli suggested that EV≠EU, instead the utility of wealth is proportional to its logarithm. Each additional unit of wealth worth less than the previous one. The utility of additional currency units decreases as the number of currency units increase.
->Thus the extra utility of the high winnings is no longer high enough to compensate for the very low probabilities.
->If I have $1000000 I care less about an additional $500 than if I only have $1000.
->If I have $1000000 I care less about an additional $500 than if I only have $1000.
Three violations of normative theory:
1. The Allais Paradox
>>Maurice Allais (1953) showed that people do not maximise expected utility and violate Savage's choice axiom, the sure-thing principle.
Situation 1
Situation 1
A $10 000 p=1
B $50 000 p=0.1
$10 000 p=0.89
$0 p=0.01
Situation 2
C $10 000 p=0.11
$0 p=0.89
D $50 000 p=0.1
$0 p=0.9
--Most people prefer 1A ($10 000 for sure) and 2D (10% chance 50 000).
--We should subtract common outcomes and outcomes with zero utility from the equation because these should not affect out choice.
--As result, Situation 1 becomes A<B.
--Situation 2 becomes C<D.
Although the utilities are the same the removal of common outcomes ($0) results in a now rational preference for the option that maximises expected reality.
2. Risk seeking vs. risk averse behaviour
>>Would you prefer a certain gain of $3000/an 80% chance of gaining $4000, otherwise nothing?
--Most people prefer a sure gain, although the EV of the risky option is higher.
>>Would you prefer an 80% chance to lose $4000, otherwise nothing/ a certain lose of $3000?
--Preferences are reversed, most people prefer the risky option.
>>Would you prefer a certain gain of $5/ a 0.001 chance of gaining $5000?
>>Would you prefer a certain loss of $5/ a 0.001 chance of losing $5000?
--When probabilities are smaller people become risk seeking for gains and rick averse (prefer the sure thing) for losses.
3. People do not integrate prospects with existing assets.
>>Imagine that you have been given $1000. Would you choose a 50% chance go gaining $1000/a certain gain of $500?
>>Imagine that you have been given $2000. Would you choose a 50% chance of losing $1000/a certain loss of $500?
--Utility theory suggest that we should integrate decision outcomes with our current assets (it should be A=2000*0.5/1000*0.5 or B=$1500).
--However, most people prefer a certain low gain and uncertain high loss.
--They made decisions according to the situation without associating current assets.
**Rationality in evolutionGigerenzer (2000)-Heuristics were evolved in the Environment of Evolutionary Ancestry (Pleistocene period). So utility is redefined as genetic fitness. Heuristics evolved on an ad hoc basis to satisfy particular problems.
$10 000 p=0.89
$0 p=0.01
Situation 2
C $10 000 p=0.11
$0 p=0.89
D $50 000 p=0.1
$0 p=0.9
--Most people prefer 1A ($10 000 for sure) and 2D (10% chance 50 000).
--We should subtract common outcomes and outcomes with zero utility from the equation because these should not affect out choice.
--As result, Situation 1 becomes A<B.
- u(10 000)<0.89 u(10 000)+0.1 u(50 000)
- 1-0.89=> 0.11 u(10 000)<0.1 u(50 000)
--Situation 2 becomes C<D.
- 0.11 u(10 000)<0.1 u(50 000)
Although the utilities are the same the removal of common outcomes ($0) results in a now rational preference for the option that maximises expected reality.
2. Risk seeking vs. risk averse behaviour
>>Would you prefer a certain gain of $3000/an 80% chance of gaining $4000, otherwise nothing?
--Most people prefer a sure gain, although the EV of the risky option is higher.
>>Would you prefer an 80% chance to lose $4000, otherwise nothing/ a certain lose of $3000?
--Preferences are reversed, most people prefer the risky option.
>>Would you prefer a certain gain of $5/ a 0.001 chance of gaining $5000?
>>Would you prefer a certain loss of $5/ a 0.001 chance of losing $5000?
--When probabilities are smaller people become risk seeking for gains and rick averse (prefer the sure thing) for losses.
3. People do not integrate prospects with existing assets.
>>Imagine that you have been given $1000. Would you choose a 50% chance go gaining $1000/a certain gain of $500?
>>Imagine that you have been given $2000. Would you choose a 50% chance of losing $1000/a certain loss of $500?
--Utility theory suggest that we should integrate decision outcomes with our current assets (it should be A=2000*0.5/1000*0.5 or B=$1500).
--However, most people prefer a certain low gain and uncertain high loss.
--They made decisions according to the situation without associating current assets.
**Rationality in evolutionGigerenzer (2000)-Heuristics were evolved in the Environment of Evolutionary Ancestry (Pleistocene period). So utility is redefined as genetic fitness. Heuristics evolved on an ad hoc basis to satisfy particular problems.
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