Positive political Theory: an introduction General information

1. Positive political Theory: an introduction General information Credits: 9 (60 hours) Period: 8th January - 20th March Instructor: Francesco Zucchini (francesco.zucchini@unimi.it ) Office hours: Monday 17-19.30, room 308, third floor, Dpt. StudiSociali e Politici 1

2. Course: aims, structure, assessment • The course is an introduction to the study of politics from a rational choice perspective. • The course is an introduction to the study of politics from a rational choice perspective.In the first two modules we will focus on the institutional effects of decision-making processes and on the nature of political actors in the democratic political systems. In the last module we will focus on the origin of the state, on the democratization process and on the collective action problems. • All students are expected to do all the reading for each class session and may be called upon at any time to provide summary statements of it. • Evaluation of studentsis based upon the regular and active participation in the classroom activities (20%), a presentation (30%) and a final written exam (50%). 2

3. Positive political Theory: An introduction Lecture 1: Epistemological foundation of the Rational Choice approach Francesco Zucchini 3

4. What the rational choice is not “NON RATIONAL CHOICE THEORIES • Theorieswith non rational actors: • Relative deprivation theory • Imitation instinct (Tarde) • False consciouness (Engels) • Inconscient pulsions (Freud) • Habitus (Bourdieu) • Theorieswithoutactors: • System analysis • Structuralism • Functionalism (Parsons)

5. What the rational choice is • Weak Requirements of Rationality: • 1) Impossibility of contradictory beliefs or preferences • 2) Impossibility of intransitive preferences • 3) Conformity to the axioms of probability calculus

6. Weak requirements of Rationality 1) Impossibility of contradictory beliefs or preferences: if an actor holds contradictory beliefs she cannot reason if an actor hold contradictory preferences she can choose any option Important: contradiction refers to beliefs or preferences at a given moment in time.

7. Weak requirements of Rationality 2) Impossibility of intransitive preferences: if an actor prefers alternative a over b and b over c , she must prefer a over c . One can create a “money pump” from a person with intransitive preferences. Person Z has the following preference ordering: a>b>c>a ; she holds a. I can persuade her to exchange a for c provided she pays 1$; then I can persuade her to exchange c for b for 1$ more; again I can persuade her to pay 1$ to exchange b for a. She holds a as at the beginning but she is $3 poorer

8. Weak requirements of Rationality 3) Conformity to the axioms of probability calculus A1 No probability is less than zero. P(i)>=0 A2 Probability of a sure event is one A3 If i and j are two mutually exclusive events, then P (i or j)= P(i )+P(j)‏

9. A small quantity of formalization... • A choice between different alternatives • S = (s1, s2, … si)‏ • Each alternative can be put on a nominal, ordinal o cardinal scale • The choice produces a result • R = (r1, r2, … ri)‏ • An actor chooses as a function of a preference ordering relation among the results. Such ordering is • complete • transitive 9

10. Utility • A ( mostly) continuous preference ordering assigns a position to each result • We can assign a number to such ordering called utility • A result r can be characterized by these features (x,y,z) to which an utility value u = f(x,y,z) corresponds • Rational action maximizes the utility function 10

11. x A A x U U Single-peak utility functions • One dimension (the real line)‏ • Actor with ideal point A, outcome x • Linear utility function: • U = - |x – A| • Quadratic utility function: • U = - (x – A)2 + - + - 11

12. Expected utility • There could be unknown factors that could come in between a choice of action and a result • .. as a function of different states of the world M = (m1, m2, … mi)‏ • Choice under uncertainty is based associating subjective probabilities to each state of the world, choosing a lottery of results L = (r1,p1;r2,p2; … ri,pi)‏ • We have then an expected utility function • EU = u(r1)p1+u(r2)p2+ … u(ri)pi 12

13. Strong Requirements of Rationality 1) Conformity to the prescriptions of game theory 2) Probabilities approximate objective frequencies in equilibrium 3) Beliefs approximate reality in equilibrium

14. Strong Requirements of Rationality 1) Conformity to the prescriptions of game theory: digression.. • Uncertainty between choices and outcomes could also result from the (unknown) decisions taken by other rational actors • Game theory studies the strategic interdependence between actors, how one actor’s utility is also function of other actors’ decisions, how actors choose best strategies, and the resulting equilibrium outcomes 14

15. Principles of game theory • Players have preferences and utility functions • Game is represented by a sequence of moves (actors’ – or Nature – choices)‏ • How information is distributed is key • Strategy is a complete action plan, based on the anticipation of other actors’ decisions • A combination of strategies determines an outcome • This outcome determines a payoff to each player, and a level of utility (the payoff is an argument of the player’s utility function)‏ 15

16. Principles of game theory (2)‏ • Games in the extensive form are represented by a decision tree • which illustrates the possible conditional strategic options • The distribution of information: complete/incomplete (game structure), perfect/imperfect (actors’ types), common knowledge 16

17. Principles of game theory (3)‏ • Solutions is by backward induction, by identifying the subgame perfect equilibria • Nash equilibrium: the profile of the best responses, conditional on the anticipation of other actors’ best responses • A Nash equilibrium is stable: no-one unilaterally changes strategy 17

18. Strong Requirements of Rationality 2) Subjective probabilities approximate objective frequencies in equilibrium. Every “player” makes the best use of his previous probability assessments and the new information that he gets from the environment. Beliefs are updated according to Bayes’s rule.

19. Strong Requirements of Rationality Bayesian updating of beliefs

20. Bayesian updating of beliefs. Example • Suppose someone told you they had a nice conversation with someone on the train. Not knowing anything else about this conversation, the probability that they were speaking to a woman is 50%. • Now suppose they also told you that this person had long hair. It is now more likely they were speaking to a woman, since most long-haired people are women. How likely ? • Bayes' theorem can be used to calculate the probability that the person is a woman. • W = event that the conversation was held with a woman, and • L = event that the conversation was held with a long-haired person. • It can be assumed that women constitute half the population for this example. So, not knowing anything else, the probability that  W occurs is • P (W) = 0.5 • Suppose it is also known that 75% of women have long hair, which we denote as • P (L | W) = 0.75 (read: the probability of event  given event  is 0.75). • Likewise, suppose it is known that 30% of men have long hair, or • P (L | M) = 0.3 • where  M is the complementary event of W, i.e., the event that the conversation was held with a man (assuming that every human is either a man or a woman).

21. Bayesian updating of beliefs. Example • Our goal is to calculate the probability that the conversation was held with a woman, given the fact that the person had long hair, or, in our notation • P (W | L) • Using the formula for Bayes' theorem, we have: • where we have used the law of total probability. The numeric answer can be obtained by substituting the above values into this formula. This yields • i.e., the probability that the conversation was held with a woman, given that the person had long hair, is about 71%.

22. Strong Requirements of Rationality • 3) Beliefs should approximate reality • Beliefs and behavior not only have to be consistent but also have to correspond with the real world at equilibrium

23. Rational Choice: only a normative theory ? • Usual criticism to the Rational Choice theory: • In the real world people are incapable of making all the required calculations and computations. Rational choice is not “realistic” • Usual answer (M.Friedman): people behave as if they were rational: • “In so far as a theory can be said to have “assumptions” at all, and in so far as their “realism” can be judged independently of the validity of predictions, the relation between the significance of a theory and the “realism” of its “assumptions” is almost the opposite of that suggested by the view under criticism. Truly important and significant hypotheses will be found to have “assumptions” that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions (in this sense). The reason is simple. A hypothesis is important if it “explains” much by little, that is, if it abstracts the common and crucial elements from the mass of complex and detailed circumstances surrounding the phenomena to be explained and permits valid predictions on the basis of them alone. To be important, therefore, a hypothesis must be descriptively false in its assumptions;it takes account of, and accounts for, none of the many other attendant circumstances, since its very success shows them to be irrelevant for the phenomena to be explained. • As if argument claims that the rationality assumption, regardless of its accuracy, is a way to model human behaviour Rationality as model argument (look at Fiorina article)

24. Rational Choice: only a normative theory ? • Tsebelis counter argument to “rationality as model argument” : • 1)“the assumptions of a theory are, in a trivial sense, also conclusions of the theory . A scientist who is willing to make the “wildly inaccurate” assumptions Friedman wants him to make admits that “wildly inaccurate” behaviour can be generated as a conclusion of his theory”. • 2) Rationality refers to a subset of human behavior. Rational choice cannot explain every phenomenon. Rational choice is a better approach to situations in which the actors’ identity and goals are established and the rules of interaction are precise and known to the interacting agents. • Political games structure the situation as well ; the study of political actors under the assumption of rationality is a legitimate approximation of realistic situations, motives, calculations and behavior. • 5 arguments

25. Five arguments in defense of the Rational Choice Approach (Tsebelis) • Salience of issues and information • Learning • Heterogeneity of individuals • Natural Selection • Statistics

26. Five arguments in defense of the Rational Choice Approach (Tsebelis) • 3) Heterogeneity of individuals: equilibria with some sophisticated agents (read fully rational) will tend toward equilibria where all agents are sophisticated in the cases of “congestion effects” , that is where each agent is worse off the higher the number of other agents who make the same choice as he. An equilibrium with a small number of sophisticated agents is practically indistinguishable from an equilibrium where all agents are sophisticated

27. Five arguments in defense of the Rational Choice Approach (Tsebelis) • 3) Statistics: rationality is a small but systematic component of any individual , and all other influences are distributed at random. The systematic component has a magnitude x and the random element is normally distributed with variance s. Each individual of population will execute a decision in the interval [x-(2s), x+(2s)] 95 percent of the time. However in a sample of a million individuals the average individual will make a decision in the interval [x-(2s/1000), x+(2s/1000)] 95 percent of the time

28. Rational choice: a theory for the institutions • In the rational choice approach individual action is assumed to be an optimal adaptation to an institutional environment, and the interaction among individuals is assumed to be an optimal response to each other. The prevailing institutions (the rules of the game) determine the behavior of the actors, which in turn produces political or social outcomes. • Rational choice is unconcerned with individuals or actors per se and focuses its attention on political and social institutions

29. Advantages of the Rational choice Approach • Theoretical clarity and parsimony • Ad hoc explanations are eliminated • Equilibrium analysis • Optimal behavior is discovered, it is easy to formulate hypothesis and to eliminate alternative explanations. • Deductive reasoning • In RC we deal with tautology. If a model does not work , as the model is still correct, you have to change the assumption (usually the structure of the game..).Therefore also the “wrong” models are useful for the cumulation of the knowledge. • Interchangeability of individuals

30. Positive political Theory: An introduction Lecture 2: Basic tools of analytical politics Francesco Zucchini 30

31. Spatial representation • In case of more than one dimension, we have iso-utility curves (indifference curves) • Utility diminishes as we move away from the ideal point • The shape of the iso-utility curve varies as a function of the salience of the dimensions 31

32. Continuous utility functions in 1 dimension Spatial representation Utility xi Dimension x

33. ..and in 2 Dimensions Iso-utility curves or indifference curves

34. Spatial representation • In case of more than one dimension, we have iso-utility curves (indifference curves) • Utility diminishes as we move away from the ideal point • The shape of the iso-utility curve varies as a function of the salience of the dimensions 34

35. X I Y P Z Indifference curve Player I prefers a point which is inside the indifference curve (such as P) to one outside (such as Z), and is indifferent between two points on the same curve (like X and Y)‏ 35

36. A basic equation in positive political theory • Preferences x Institutions = Outcomes • Comparative statics (i.e. propositions) that form the basis to testable hypotheses can be derived as follows: • As preferences change, outcomes change • As institutions change, outcomes change 36

37. A typical institution: a voting rule • Committee/assembly of N members • K = p Nminimum number of members to approve a committee’s decision • In Simple Majority Rule (SMR) K > (1/2)N • Of course, there are several exceptions to SMR • Filibuster in the U.S. Senate: debate must end with a motion of cloture approved by 3/5 (60 over 100) of senators • UE Council of Ministers: qualified majority (255 votes out of 345, 73.9 %) • Bicameralism 37

38. A proposition: the voting paradox • If a majority prefers some alternatives to x, these set of alternatives is called winset of x, W(x); if an alternative x has an empty winset , W(x)=Ø, then x is an equilibrium, namely is a majority position that cannot be defeated. • If no alternative has an empty winset then we have cycling majorities • SMR cannot guarantee a majority position – a Condorcet winner which can beat any other alternative in pairwise comparisons. In other terms SMR cannot guarantee that there is an alternative x whose W(x)=Ø 38

39. Condorcet Paradox ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z • Imagine 3 legislators with the following preference’s orders • Alternatives can be chosen by majority rule • Whoever control the agenda can completely control the outcome

40. ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z 1,2 choose z against x but..

41. ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z 2,3 choose y against z but again..

42. ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z 1,3 choose x against y.. z defeats x that defeats y that defeats z.

43. Whoever control the agenda can completely control the outcome ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z • Imagine a legislative voting in two steps. If Leg 1 is the agenda setter.. y x x z z

44. Whoever control the agenda can completely control the outcome ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z • If Leg 2 is the agenda setter.. x z z y y

45. Whoever control the agenda can completely control the outcome ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z • If Leg 3 is the agenda setter. y z y x x

46. Probability of Cyclical Majority

47. Median voter theorem • A committee chooses by SMR among alternatives • Single-peak Euclidean utility functions • Winset of x W(x): set of alternatives that beat x in a committee that decides by SMR • Median voter theorem (Black): If the member of a committee G have single-peaked utility functions on a single dimension, the winset of the ideal point of the median voter is empty. W(xmed)=Ø 47

48. When the alternatives can be disposed on only one dimension namely when the utility curves of each member are single peaked then there is a Condorcet winner: the median voter ranking Leg.1 Leg.2 Leg.3 1° z z x 2° x y z 3° y x y Utility 1° 2° 3° y z x

49. When the alternatives can be disposed on only one dimension namely when the utility curves of each member are single peaked then there is a Condorcet winner: the median voter ranking Leg.1 Leg.2 Leg.3 1° x z y 2° y y z 3° z x x Utility 1° 2° 3° x y z

50. When there is a Condorcet paradox (no winner) then the alternatives cannot be disposed on only one dimension namely the utility curves of each member are not single peaked ranking Leg.1 Leg.2 Leg.3 1° z y x 2° x z y 3° y x z 2 peaks Utility 1° 2° 3° x y z