Andreas Flache

Manu Muñoz-Herrera

How to criticize a theoryTutorial Week 4 - Application of Theories

Block A 2012/2013

http://manumunozh.wix.com/apptheories

What do we know until now?

Connection between the lectures

Lave & March model:

Charles A. Lave James G. March

4 Steps

Observe Speculate Deduce Ask

Facts

Phenomenon

result of unknown process

Process

other results

Implications

are implicationsempirically

correct?

Modify

Hempel & Oppenheim model:

Explanans General Law (L1)

Antecedent Condition (C1)

Explanandum Singular Statement (E)

Hempel & Oppenheim model:

Explanans General Law (L1)

Antecedent Condition (C1)

Explanandum Singular Statement (E)

Phenomenon to be explained

Observe

Sentences used to explain E.

process (model)

Speculate

Other results

Deduce

1

2

3

Hempel & Oppenheim model:

Explanans General Law (L1)

Antecedent Condition (C1)

Explanandum Singular Statement (E)

This is not enough: Conditions of adequacy.

1

2

3

Explanandum follows logically from the explanans

Explanans must contain general laws and conditions (any kind?) (what else?)

Explanans must have empirical content

4 ???

Formal Logic: How to test it?

1

2

Star test

Venn Diagrams

Find the distributed letters and underline them: Immediately after all Anywhere after no or

Star the distributed letters in the premises and the non-distributed in the conclusions

Color the areas that do not belong to the premises Mark with an x the are in which some is present in the premises

If all capital letters are stared exactly once and there is exactly one star on the right hand side - VALID

If the conclusion is observed by drawing the premises - VALID

Classwork

Connection of the models (from Logic)

The case of Social Identity

In Lecture 4 with the case social identity theory, we extracted from a text an explanation and criticized it by testing its validity

Rewrite the arguments verbally Translate your arguments into wff’s Come up with a conclusion that is valid

(include implicit assumptions if necessary)

Example from last tutorial

Ceausescu’s ban on abortion was designed to achieve one of his major aims: to rapidly strengthen Romania by boosting its population

A boost to the population (B) strengthens a country (S) *(Imp. Assump.)*A ban on abortion (A) gives a boost to the population of a country (B)Therefore, a ban on abortion (A) strengthens a country (S)

Any premise can be translated into a wff

A boost to the population (B) strengthens a country (S)A ban on abortion (A) gives a boost to the population of a country (B)Therefore, a ban on abortion (A) strengthens a country (S)

All B is SAll A is B----------------- All A is S

all boosts to the population (B) are country strengtheners (S)all bans on abortion (A) are population boosters (B)Therefore, all bans on abortion (A) are country strengtheners (S)

Hypothetical Syllogism: A implies B, B implies S, then A implies A.

Explanations (syllogisms) are testable

All B is SAll A is B----------------- All A is S

All B* is SAll A* is B----------------- All A is S*

Star test

A

B S

Venn Diagram ?

Connection of two explanations: Deriving laws.

A ban on abortion (B) strengthens a country (S)In Romania, the dictator Ceausescu, made a ban on abortion (B)----------------------------------------------------------------------------------------------- In Romania, the dictator Ceausescu, strengthened his country (S)

A boost to the population (B) strengthens a country (S) *(Imp. Assump.)*A ban on abortion (A) gives a boost to the population of a country (B)Therefore, a ban on abortion (A) strengthens a country (S)

A ban on abortion (B) strengthens a country (S)In Romania, the dictator Ceausescu, issued a law (l) that banned abortion (B)----------------------------------------------------------------------------------------------- In Romania, the dictator Ceausescu, issued a law (l) that strengthened the country (S)

Modus Ponens: If B implies S, and I observe B, then I should observe S

4 cases: Your turn

Government agents sardonically known as the Menstrual Police regularly rounded up women in their work places to administer pregnancy tests: If a woman repeatedly failed to conceive, she was forced to pay a steep “celibacy tax”.

On Christmas day of 1989 crime was at its peak in the United States... experts were predicting darker scenarios.

The evidence linking increased punishment with lower crime rates is very strong. Harsh prison terms have been shown to act as both deterrent (for the would-be criminals on the street) and prophylactic (for the would-be criminals who are already locked up).

Researchers found that in the instances where the woman was denied an abortion, she often resented her baby and failed to provide it with good home... The researchers found that these children were more likely to become criminals. (for the solution you could generalize this example from MORE LIKELY to ALL and focus it in the case of unwanted children)

Empirical Content

Condition 3: The explanans must have empirical content

Empirical content

Our theories must be testable. It must be possible to derive at least one testable statement from the theory

The most straightforward way to make a theory testable is to find a way to measure the variables in its premises (i.e., X and Y in “all X is Y”) and investigate whether there is the proposed relationship.

This would mean that you directly test the assumptions of the theory. BUT...

Social scientific theories often include concepts which are very difficult to measure. For two reasons:

The concept is not defined properly. The concept is latent in the sense that it cannot be observed directly.

How much empirical content?

The empirical content of a statement is the higher the more possible states there are which would falsify the statement.

We want a lot of empirical content

Minimalempirical content

Maximalempirical contentEmpirical content scale

statementswhich are

always true

statementswhich are

always false

Tautological Contradictory

All bachelors are not married

James is a vegetarian and

eat stakes

Statements should have high informational content (not maximal)

Empirical content of implications

Which of the following statements have a higher empirical content?

If a person is frustrated or hurt, then she will be aggressiveA

B If a person is frustrated and hurt, then she will be aggressive

The empirical content of a statement is the higher the more possible states there are which would falsify the statement.

We need to study under which conditions the statements are false.

Let’s recall implications from logic.Operator 4: Implication

Symbol: ⊃ (horseshoe) or → Read: “if p then q”

p q p⊃q1 1 11 0 00 1 10 0 1

The implication of p and q is false only if p is true and q is false

A and B are implications: statements which are false if the if-part is true and the then-part is false.

If a person is frustrated or hurt, then she will be aggressiveA

If a person is frustrated and hurt, then she will be aggressiveB

When is a disjunction false?

If a person is frustrated or hurt, then she will be aggressiveA

Operator 2: Disjunction Symbol: ⋁ (vee) or || or + Read: “or”

p q p⋁q1 1 11 0 10 1 10 0 0

The disjunction of p and q is false if both p and q are false

There are three possible states where the if-part is true

When is a conjunction false?

There is only one possible state where the if-part is true

If a person is frustrated and hurt, then she will be aggressiveB

Operator 3: Conjunction Symbol: ⋅ (dot) or & or ⋀ Read: “and”

p q p ⋅ q1 1 11 0 00 1 00 0 0

The conjunction of p and q is true if both p and q are true

Empirical content of implications (2)

Which of the following statements have a higher empirical content?

If a person is frustrated, then she will be aggressive or sadC

D If a person is frustrated, then she will be aggressive and sad

C and D are implications: statements which are false if the if-part is true and the then-part is false.

When is a disjunction false?

If a person is frustrated, then she will be aggressive or sadC

Operator 2: Disjunction Symbol: ⋁ (vee) or || or + Read: “or”

p q p⋁q1 1 11 0 10 1 10 0 0

The disjunction of p and q is false if both p and q are false

There is one possible state where the then-part is false

When is a conjunction false?

There is are three possible state where the then-part is false

If a person is frustrated, then she will be aggressive and sadD

Operator 3: Conjunction Symbol: ⋅ (dot) or & or ⋀ Read: “and”

p q p ⋅ q1 1 11 0 00 1 00 0 0

The conjunction of p and q is true if both p and q are true

In sum: The empirical content of a statement is the higher the more possible states there are which would falsify the statement.

Implications are false if the if-part is true and the then-part is false

More possible states when the if-part

contains a disjunction than a conjunction

More possible states when the then-part

contains a conjunction than a disjunction

The empirical content of a statement is the higher when the if-part contains a disjunction and the then-part contains a conjunction.

Rational Choice Theory

Do we discard it?

The theory of rational action:This is a good example of a wrong theory

What do we do when, after testing a theory, we find it is wrong?

Do we fix it?

The theory of rational action:This is a good example of a wrong theory

A core assumption in RCT is that individuals maximize utility

What is maximize? What is utility?

Unless something is said about it, the concepts are not properly defined

There are other implicit assumptions!

People have preferences

RCT assumes agents have preferences

Can we test this? Does this implication has empirical content?

Think: If you had enough money would you donate 1000 euros help a poor hospital in Asia?

Yes No

Preferences are hard to test

Think: What if I gave you the 1000 euros and ask you to donate them right away. Would you

answer the same?

Yes No

People lie! Even if they don’t want to... Even to themselves

So, are we assuming non-empirical implications?

RCT assumes other things about preferences

Completeness: for any two lotteries, either A≼B, A=B, or A≽B

Transitivity: if A≽B and B≽C, then A≽C

Continuity: if A≼B≼C, then there is a probability p between 0 and 1, such that the lottery pA + (1-p)C is equally preferred to B.

Interdependence: if A=B, then pA + (1-p)X= pB + (1-p)X

With this, preferences (latent variables) are not observable, but choices are: people choose what they prefer

GAmE ThEOry intro

intro

Selfish

Distrust

RationalEquilibrium

Nash

matrixtree

payoffs

strategies

games

players

sequential

common knowledge

learning

repetition

expectations

information

stability

preferences

dominance

backward induction

types

signaling

simultaneous

subgame

Rational

Strategic Interaction Theory

HISTORYBorel (1938)

Applications aux jeux des Hazard

von Neumann - Morgenstern (1944)

Theory of Games and Economic

Behavior

John Nash (1950)Equilibrium points in

n-person games

GamesStraTegiC StraTegiC

StraTegiC StraTegiC

StraTegiC StraTegiC

StraTegiC StraTegiC

StraTegiC StraTegiC StraTegiC

StraTegiC eXtenSivE StraTegiC StraTegiC

StraTegiC StraTegiC

GameseXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

eXtenSivE

B S

B 3 , 2 1 , 1S 0 , 0 2 , 3

Battle of SexesBattle of SexesThey want different things, but can’t live without the other...

oneone

this is a game

shotshot

SIMULTANEOUSSTRATEGIC

B

S

B

S

B

S

(3 , 2)

(1 , 1)

(0 , 0)

(2 , 3)

ThiS is a seQueNTialGAME

Players

Timing

Available Actions

PayoffsRules & Consequences

Solution ConceptsDominanceDominance

Nash Eq.Nash Eq.

IDSDSIDSDS

puremixed

BackwardInduction

BackwardInduction

?

DOMiNANcE (solvable games)

Strictly Dominant Strategy

Strictly Dominated Strategy

No matter what others do, you will ALWAYS

use this strategy

No matter what others do, you will NEVER

use this strategy

P Q R

A 2 , 7 2 , 0 2 , 2

B 7 , 0 1 , 1 3 , 2

C 4 , 1 0 , 4 1 , 3

P Q R

A 2 , 7 2 , 0 2 , 2

B 7 , 0 1 , 1 3 , 2

P R

A 2 , 7 2 , 2

B 7 , 0 3 , 2

P R

B 7 , 0 3 , 2

R

B 3 , 2

IDSDSIDSDS

HOWIs thispossible?

I know that you know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know,

that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you

know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know,

that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you

know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that you know, that I know, that

you know, that I know, that you know, that we are both...

RaTiONaL

I KNOWI KNOW

Common Knowledge

RaTiONaL

Nash Equilibrium

NO unilateral incentives to change

my action...BEST

RESPONSE

B SB 3 , 2 1 , 1S 0 , 0 2 , 3

B SB 3 , 2 1 , 1S 0 , 0 2 , 3

B SB 3 , 2 1 , 1S 0 , 0 2 , 3

B SB 3 , 2 1 , 1S 0 , 0 2 , 3

If you choose BI will choose BIf you choose SI will choose S

B S

B 3 , 2 1 , 1

S 0 , 0 2 , 3

N E

PrObleMs

M U L T I P L I C I T Y

SoLutiOnrefinementsrefinements

Backward InductionStart at the END and move to the

BEGINNING B

S

S

B

S

(1 , 1)

(0 , 0)

(2 , 3)

(3 , 2)B

SubgamePerfect

Equilibrium

Prospect Theory

Amos Tversky1937-1996

Daniel Kahnemann1934

Nobel Prize 2002

A famous experiment

Condition 1:

Imagine that the US is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the program are as follows:

If program A is adopted, 200 people will be savedA

BIf program B is adopted, there is a one-third probability that 600 people will be saved and a two-third probability that no people will be saved

Which of the two programs would you favor?

Condition 1: Answer

If program A is adopted, 200 people will be savedA

BIf program B is adopted, there is a one-third probability that 600 people will be saved and a two-third probability that no people will be saved

72% of the subjects chose A (N=152)

WHY?

Condition 2:

Imagine that the US is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the program are as follows:

If program C is adopted, 400 people will dieC

DIf program D is adopted, there is a one-third probability that nobody will die and a two-third probability that 600 people will die

Which of the two programs would you favor?

Condition 2: Answer

78% of the subjects chose D (N=155)

If program C is adopted, 400 people will dieC

DIf program D is adopted, there is a one-third probability that nobody will die and a two-third probability that 600 people will die

WHY?

Explanations

The decision problems are identical. Still, the different framing (save lives vs. loose them) of the effects leads to different decisions

Kahnemann and Tversky concluded that there is more risk seeking in the second version of the problem than there is risk aversion in the first.

The framing effect Kahnemann and Tversky demonstrated contradicts the idea that humans form decisions based on utility maximization.

Their results contradict the assumption of completeness - the theory of rational choice is wrong

According to the fourth condition of adequacy, explanations which assume utility maximization are not adequate

Do we discard it? Do we fix it?

What do we do when, after testing a theory, we find it is wrong?

Currently, is there something better?

A theory (good model), according to Lave and March, should be fertile, simple and surprising.

As long as we don’t have a better theory, we will have to elaborate the theory of rational choice

Different decision rules (bounded rationality) Social preferences (fairness) Include further assumptions about the perceptions of risk

So, we fix it!