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Slides Tutorial 4. Course: Application of Theories

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### T4 Slides

1. 1. How to criticize a theory Tutorial Week 4 - Application of Theories Block A 2012/2013Andreas FlacheManu Muñoz-Herrera http://manumunozh.wix.com/apptheories
2. 2. What do we know until now?Connection between the lectures
3. 3. Lave & March model: Charles A. Lave James G. March 4 Steps Observe Speculate Deduce Ask result of are implications Facts other results unknown process empirically correct?Phenomenon Process Implications Modify
4. 4. Hempel & Oppenheim model: Explanans General Law (L1) Antecedent Condition (C1) Explanandum Singular Statement (E)
5. 5. Hempel & Oppenheim model: Sentences used 2 Speculate to explain E. Explanans General Law (L1) process (model) Antecedent Condition (C1) Other resultsExplanandum Singular Statement (E) 3 Deduce Phenomenon to be explained 1 Observe
6. 6. Hempel & Oppenheim model: Explanans General Law (L1) Antecedent Condition (C1) Explanandum Singular Statement (E) This is not enough: Conditions of adequacy. 1 Explanandum follows logically from the explanans Explanans must contain general laws and conditions (any kind?) (what 2 else?) 3 Explanans must have empirical content 4 ???
7. 7. Formal Logic: How to test it? 1 Star test 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 If all capital letters are stared exactly once and there is exactly one star on the right hand side - VALID 2 Venn Diagrams 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 the conclusion is observed by drawing the premises - VALID
8. 8. ClassworkConnection of the models (from Logic)
9. 9. 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)
10. 10. 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)
11. 11. Any premise can be translatedinto 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 boosts to the population (B) are country strengtheners (S) All A is Ball bans on abortion (A) are population boosters (B) -----------------Therefore, all bans on abortion (A) are country strengtheners (S) All A is SHypothetical Syllogism: A implies B, B implies S,then A implies A.
12. 12. Explanations (syllogisms) aretestable Star test All B* is S All A* is B ? ----------------- All B is S All A is S* All A is B ----------------- Venn Diagram All A is S A B S
13. 13. Connection of two explanations:Deriving laws. 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, made a ban on abortion (B) ----------------------------------------------------------------------------------------------- In Romania, the dictator Ceausescu, strengthened his country (S) Modus Ponens: If B implies S, and I observe B, then I should observe 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)
14. 14. 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)
15. 15. Empirical ContentCondition 3: The explanans must have empirical content
16. 16. Empirical content Our theories must be testable. It must be possible to derive at least one testablestatement from the theory The most straightforward way to make a theory testable is to ﬁnd a way to measurethe variables in its premises (i.e., X and Y in “all X is Y”) and investigate whether thereis 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.
17. 17. How much empirical content? We want a lot of empirical content The empirical content of a statement is the higher the more possible states there are which would falsify the statement.Minimal Maximalempirical empirical content Empirical content scale contentstatements All bachelors are James is a statements which are not married vegetarian and which arealways true eat stakes always falseTautological Contradictory Statements should have high informational content (not maximal)
18. 18. Empirical content of implicationsWhich of the following statements have a higher empirical content? A If a person is frustrated or hurt, then she will be aggressive 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.
19. 19. Let’s recall implications from logic.Operator 4: Implication Symbol: ⊃ (horseshoe) or → Read: “if p then q” p q p⊃q 1 1 1 1 0 0 The implication of p and q is false 0 1 1 only if p is true and q is false 0 0 1 A If a person is frustrated or hurt, then she will be aggressive B If a person is frustrated and hurt, then she will be aggressive A and B are implications: statements which are false if the if-part is true and the then-part is false.
20. 20. When is a disjunction false? A If a person is frustrated or hurt, then she will be aggressiveOperator 2: Disjunction Symbol: ⋁ (vee) or || or + Read: “or” p q p⋁q 1 1 1 The disjunction of p and q is 1 0 1 false if both p and q are false 0 1 1 0 0 0 There are three possible states where the if-part is true
21. 21. When is a conjunction false? B If a person is frustrated and hurt, then she will be aggressiveOperator 3: Conjunction Symbol: ⋅ (dot) or & or ⋀ Read: “and” p q p⋅q 1 1 1 The conjunction of p and q is 1 0 0 true if both p and q are true 0 1 0 0 0 0 There is only one possible state where the if-part is true
22. 22. Empirical content of implications (2) Which of the following statements have a higher empirical content? C If a person is frustrated, then she will be aggressive or sad 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.
23. 23. When is a disjunction false? C If a person is frustrated, then she will be aggressive or sadOperator 2: Disjunction Symbol: ⋁ (vee) or || or + Read: “or” p q p⋁q 1 1 1 1 0 1 The disjunction of p and q is 0 1 1 false if both p and q are false 0 0 0 There is one possible state where the then-part is false
24. 24. When is a conjunction false? D If a person is frustrated, then she will be aggressive and sadOperator 3: Conjunction Symbol: ⋅ (dot) or & or ⋀ Read: “and” p q p⋅q 1 1 1 1 0 0 The conjunction of p and q is 0 1 0 true if both p and q are true 0 0 0 There is are three possible state where the then-part is false
25. 25. 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 More possible states when the if-part when the then-part contains a disjunction contains a conjunction than 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.
26. 26. Rational Choice Theory
27. 27. 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 discard it? Do we ﬁx it?
28. 28. 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!
29. 29. 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
30. 30. 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
31. 31. So, are we assuming non-empiricalimplications? RCT assumes other things about preferencesCompleteness: for any two lotteries, either A≼B, A=B, or A≽BTransitivity: if A≽B and B≽C, then A≽CContinuity: if A≼B≼C, then there is a probability p between 0 and 1, such thatthe 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
32. 32. GAmE ThEOry i n t r o
33. 33. stability learning expectations Selﬁsh strategies players dominance Nash signaling Distrustpayoffs simultaneous Rational common knowledgetypes Equilibrium information preferences subgame matrix tree sequential repetition games backward induction
34. 34. Strategic HISTORY Borel (1938)Interaction Theory Applications aux jeux des Hazard von Neumann - Morgenstern (1944) Theory of Games and Economic Behavior John Nash (1950) Equilibrium points in n-person games
35. 35. StraTegiC StraTegiC StraTegiC eXtenSivEStraTegiC eXtenSivE StraTegiC StraTegiCeXtenSivE StraTegiC eXtenSivE StraTegiC GamesStraTegiC eXtenSivE StraTegiC eXtenSivEStraTegiC eXtenSivE StraTegiC eXtenSivEStraTegiC eXtenSivE StraTegiC eXtenSivEStraTegiC eXtenSivE StraTegiC eXtenSivE
36. 36. Battle of Sexes Battle of Sexes They want different things, but can’t live without the other... B S B 3,2 1,1 S 0,0 2,3 oneSIMULTANEOUS STRATEGIC this is a game shot
37. 37. ThiS is a seQueNTial GAME B (3 , 2) B S (1 , 1) Players B (0 , 0) Timing S Available Actions S (2 , 3) Payoffs Rules & Consequences
38. 38. Solution Concepts Dominance IDSDS Nash Eq. pure mixed ? Backward Backward Induction Induction
39. 39. Strictly Dominant Strategy No matter what others do, you will ALWAYS use this strategy Strictly Dominated Strategy No matter what others do, you will NEVER use this strategyDOMiNANcE (solvable games)
40. 40. P Q R RA 2,7 2,0 2,2 B 3,2B 7,0 1,1 3,2 P RC 4,1 0,4 1,3 B 7,0 3,2 IDSDS P Q R P RA 2,7 2,0 2,2 A 2,7 2,2B 7,0 1,1 3,2 B 7,0 3,2
41. 41. HOW possible? Common Knowledge Is thisI 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, I KNOW I KNOW that you know, that I know, that you know, that I know, that youknow, 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 youknow, 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
42. 42. Nash Equilibrium NO unilateralincentives to change my action... BEST RESPONSE
43. 43. B S B 3,2 1,1 S 0,0 2,3 If you choose BB B 3,2 S 1,1 I will choose B B B 3,2 S 1,1S 0,0 2,3 If you choose S S 0,0 2,3 I will choose S B S B 3,2 1,1 S 0,0 2,3
44. 44. N B S E B 3,2 1,1 S 0,0 2,3
45. 45. PrObleMs M U L T I P L I CI T YSoLutiOn reﬁnements
46. 46. SubgameBackward Induction Perfect Equilibrium Start at the END B (3 , 2) and move to the BEGINNING B S (1 , 1) B (0 , 0) S S (2 , 3)
47. 47. Prospect TheoryA famous experiment Amos Tversky Daniel Kahnemann 1937-1996 1934 Nobel Prize 2002
48. 48. Condition 1: Imagine that the US is preparing for the outbreak of an unusual Asian disease, whichis expected to kill 600 people. Two alternative programs to combat the disease havebeen proposed. Assume that the exact scientiﬁc estimates of the consequences of theprogram are as follows: A If program A is adopted, 200 people will be saved If program B is adopted, there is a one-third probability B 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?
49. 49. Condition 1: Answer A If program A is adopted, 200 people will be saved If program B is adopted, there is a one-third probability B 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?
50. 50. Condition 2: Imagine that the US is preparing for the outbreak of an unusual Asian disease, whichis expected to kill 600 people. Two alternative programs to combat the disease havebeen proposed. Assume that the exact scientiﬁc estimates of the consequences of theprogram are as follows: C If program C is adopted, 400 people will die If program D is adopted, there is a one-third probability D that nobody will die and a two-third probability that 600 people will die Which of the two programs would you favor?
51. 51. Condition 2: Answer C If program C is adopted, 400 people will die If program D is adopted, there is a one-third probability D that nobody will die and a two-third probability that 600 people will die 78% of the subjects chose D (N=155) WHY?
52. 52. Explanations The decision problems are identical. Still, the different framing (save lives vs. loosethem) of the effects leads to different decisions Kahnemann and Tversky concluded that there is more risk seeking in the secondversion of the problem than there is risk aversion in the ﬁrst. The framing effect Kahnemann and Tversky demonstrated contradicts the idea thathumans 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 What do we do when, after testing a theory, we ﬁnd it is wrong? Do we discard it? Do we ﬁx it?
53. 53. Currently, is there something better? A theory (good model), according to Lave and March, should be fertile, simple andsurprising. As long as we don’t have a better theory, we will have to elaborate the theory ofrational choice Different decision rules (bounded rationality) Social preferences (fairness) Include further assumptions about the perceptions of risk So, we ﬁx it!