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Transcript of T4 Slides
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!