1. Professor Stefan Collignon A Theory of Stochastic Consensus Stefan Collignon Harvard University Centre for European Studies 22. February 2006 www.stefancollignon.de

2. Professor Stefan Collignon Plan Introduction I.The Model 1.Desires and preferences 2.Consensus and agreement 3.Dissent and Conflict II.Implications 1.Overcoming conflict 2.Dissent in political systems 3.Perspectives Conclusion

3. Professor Stefan Collignon Introduction Consensus and agreement as foundations of society In philosophy –Praktische Vernunft (Kant) –Social contract (Rousseau) –Institutional facts (Searle) In economics: Pareto optimality –Preferences to which all individuals could agree –Exogenously given preferences In political sciences –Consensual vs conflictual polities (Lijpard) –Deliberative democracy (Rawls, Habermas) –Alesina’s size of nations

4. Professor Stefan Collignon Introduction My approach: consensus in political economy European integration as consensus building –Jean Monnet’s way of changing people’s ways of thinking and acting –AMUE and the power of ideas (with D. Schwarzer, 2003): trust –The European Republic (2003): institutions –Institutional facts (Searle) Public choice with endogenous preferences –Policy coordination (CES Working Paper, 2001) –Policy mix: the aggregate budget and democracy in Europe –Why do poor countries choose low human rights? (2000) –My new paper with Majid Al-Sadoon

5. Professor Stefan Collignon Introduction Preferences are mind states –Anchored in desires (utility) –Intensities –Change through deliberation Definitions: –Agreement: all individuals have same preferences –Consensus: all individuals have same preference intensities

6. Professor Stefan Collignon Introduction Stochastic consensus model –Explain the foundation and evolution of mind states Beliefs desires –Conditions for consensus and agreement –Dissent and disagreement –Speed of convergence –Impact of political structures

7. Professor Stefan Collignon I. The Model

8. Professor Stefan Collignon I. The Model 1. Desires and preferences Desires as intentional mind states (Searle) –An “inner” experience, expressible by speech acts Sincerity candidness –Directed at a potential state of the world (options) –Direction of fit: world to mind –Action required to satisfy desire

9. Professor Stefan Collignon I. The Model 1. Desires and preferences Desires are conditional on context –Physical context –Background knowledge (Lebenswelt) –“Naturalistic preferences” Intensity of desire as the probability of a desire occurring in a given context

10. Professor Stefan Collignon I. The Model 1. Desires and preferences Preferences are conditional on evaluation –New information, evidence –Moral considerations –“Rational preferences”: Accepting a desire as worthy of action Desire  preference Belief  knowledge Emotion  attitude

11. Professor Stefan Collignon I. The Model 1. Desires and preferences –The intensity of rational preferences indicates the probability of accepting a desire as worthy of action, conditional on rational arguments and evidence –“Bayesian updating” transforms desire into preference

12. Professor Stefan Collignon I. The Model 1. Desires and preferences Consequences of our probabilistic interpretation of preference intensity –Utility function Conventional: u: X  R –X=consumption set –R=real numbers Our utility function: u:M(X)  [0,1] –M(X)=intentional mind state directed at X –Interpersonal comparison of preference intensity –Ordering of options Next: how do mind states change?

13. Professor Stefan Collignon I. The Model 2. Consensus and agreement Social preferences –Bounded rationality: limited cognitive capacities –What do others think? Put yourself into their shoes: CONDIITION: i has the preference for R at t if j had it at t – 1, and i rejects that desire at t it if j rejected it at t – 1 ACCEPTANCE: A t ij be the event that at time t, i takes the view that j had at time t – 1 P(A t ij )=W ij (t) is the transition probability for going from one mind state to the next

14. Professor Stefan Collignon I. The Model 2. Consensus and agreement Social preferences –Rational individuals aggregate: Who knows what? Communication Respect and trust –We aggregate to optimise our capacity to judge –The intensity of a social preference is the weighted average of the preference intensities of everyone else at the previous period The weights represent the transition probabilities Lehrer/Wagner: assign subjective probabilities Social preferences evolve like a (homogenous) Markov process

15. Professor Stefan Collignon I. The Model 2. Consensus and agreement Topology of communication: definitions –Influence Individual j influences i if W ij t >0 Individual j influences i directly if W ij >0 –Individuals communicate if they influence each other –Integration time: The time t* when every individual in society is influenced by every other Degree of separation: the length of the shortest path between two individuals

16. Professor Stefan Collignon I. The Model 2. Consensus and agreement Condition A1: If every individual influences every other, the political structure is called irreducible If if W ii >0, an individual has self-regard Condition A2: If if W ii t >0, an individual has eventual self-regard

17. Professor Stefan Collignon I. The Model 2. Consensus and agreement Convergence in preferences (Theorem I) –Assuming A1 and A2 There exists a row vector of equilibrium weights toward which each individual’s social preference converges over time In equilibrium each individual has the same row vector of weights In equilibrium the weighted average of each individual’s preference intensity is the same –Hence: consensus is the equilibrium distribution in the limit

18. Professor Stefan Collignon I. The Model 2. Consensus and agreement Consensus means each individual will accept a desire as worthy of action with the same probability as any other individual Convergence of preferences intensities to consensus is based on purely topological grounds, no matter how disparate the initial set of preferences. The consensus preference intensity does, however, depend on initial preferences as well as the weight matrix.

19. Professor Stefan Collignon I. The Model 2. Consensus and agreement Consensus in rankings –As individuals’ preference intensities converge, their order of preference rankings over options also converges –Hence we can define a (non-dictatorial) social preference relation when convergence to consensus is sufficiently advanced –In consensus, the proportion of people with the same preference intensity is 100% (unanimity of preference intensity) Voting as short cuts

20. Professor Stefan Collignon I. The Model 2. Consensus and agreement Agreement –Consensus = probability of accepting a desire as worthy of action –Agreement = actually accepting a desire as worthy of action Theorem III: if A1 and A2 –Society will eventually reach agreement –The probability of eventual agreement is equal to consensual preference intensity

21. Professor Stefan Collignon I. The Model 3. Dissent and Conflict Conflict –the conditions for convergence to consensus do not exist (violations of A1 and A2) –No agreement is possible Dissent –Definition: the average of squared deviations of the current set of preferences from the consensus preference (“variance”)

22. Professor Stefan Collignon I. The Model 3. Dissent and Conflict Speed of convergence (persistence of dissent) –Corollary I(iii) says that dissent converges to zero as fast as a geometrically decreasing function dependent on the subdominant eigenvalue and its multiplicity. The closer the subdominant eigenvalue to zero, the faster is convergence to consensus A subdominant eigenvalue close to one means high persistence of dissent A subdominant eigenvalue equal to zero means conflict

23. Professor Stefan Collignon I. The Model 3. Dissent and Conflict Violations of basic assumptions 1.Cyclicality: violation of A2 but not A1 No self-regard E.g. “going through the door” 2.Disconnectedness Violation of A1 but not A2 Deliberation as in distinct systems Consensus is impossible Agreement as joint probability of two preference intensities

24. Professor Stefan Collignon I. The Model 3. Dissent and Conflict Violations of basic assumptions 3.Dominance: Dominant group: –gives regard only to its own members and not to others –violating A1 but not necessarily A2 Disregarded group: –Distributes its regard between itself and dominant group Consequence: –Dominant group imposes its preference –Disregarded loses all self-respect

25. Professor Stefan Collignon II. Implications

26. Professor Stefan Collignon II. Implications 1. Overcoming conflict Consensus as a result of deliberation –Real influence –Not “ideal discourse settings” –Institutional structures of communication matter The role of go-betweens –Capable to re-establish conditions A1 and A2 –Examples Conflict mediators International organisations

27. Professor Stefan Collignon II. Implications 1. Overcoming conflict Loosely connected groups –Preference clusters Densely connected individuals within groups Loosely connected between groups – Short run: group members reach consensus Intra-group effects dominate “identity” –Long run: the whole system converges slowly to consensus Inter-group effects become significant

28. Professor Stefan Collignon II. Implications

29. Professor Stefan Collignon II. Implications 2. Dissent in political systems How do political structures affect subdominant eigenvalue? –Bounding the subdominant is not very illuminating Stylised facts –Intergovernmental model –International organisation –Federal republic

30. Professor Stefan Collignon II. Implications Fig 5.1 Intergovernmental model

31. Professor Stefan Collignon II. Implications

32. Professor Stefan Collignon II. Implications

33. Professor Stefan Collignon II. Implications Simulating speed of convergence –Question: how likely is it that a given model will converge faster (or slower) than a given rate? We assume certain qualitative relations in the coefficients of the system We simulate random coefficients respecting the qualitative restriction –Test for stochastic dominance relations –Problem: we do not know the “correct” distribution of random coefficients

34. Professor Stefan Collignon II. Implications 1. Complete ignorance Any value goes FR converges fastest

35. Professor Stefan Collignon II. Implications 2. Pig-headedness and Open- mindedness. –Definition Pig-heads are people who are highly convinced by their own views an unyielding to others Open-minded people give higher regard to others –Results Pig-heads maintain dissent Open-minded people converge faster in all models

36. Professor Stefan Collignon II. Implications

37. Professor Stefan Collignon II. Implications 3. Liberal and Authoritarian Governments. Definition –A liberal government (including the Federal Republic) has relatively high regard for its people –An authoritarian government gives less regard to its people than it does to anyone else. Results –Wider dispersion rate of convergence –for a given political structure, the authoritarian arrangement converges faster than the liberal arrangement –IG against IO models does not yield a clear picture;

38. Professor Stefan Collignon II. Implications

39. Professor Stefan Collignon II. Implications 4. Popular and Unpopular Governments. Definition –popular governments: citizens give more regard to their government than they give to anyone else. –unpopular governments: citizens give less regard to their governments than they give to anyone else. Results –The popular governments arrangement has a faster rate of convergence than the unpopular governments arrangement in all models

40. Professor Stefan Collignon II. Implications

41. Professor Stefan Collignon II. Implications 5. The Liberal/Popular Combinations. –Results popular authoritarian arrangements are the fastest-converging, Starting from unpopular liberal regime –in IG model: the move towards the authoritarian unpopular arrangement increases the rate of convergence by more than a move towards the popular liberal governments arrangement. –IO and FR models : The exact opposite occurs - the move towards popular liberal arrangements increases the speed of convergence by more than the move towards authoritarian unpopular arrangements.

42. Professor Stefan Collignon II. Implications

43. Professor Stefan Collignon II. Implications

44. Professor Stefan Collignon II. Implications

45. Professor Stefan Collignon II. Implications 6. Nationalism and Subsidiarity. Definition –IG and IO cases: Nationalism: governments give less regard to international institutions than to domestic entities. Internationalism: the opposite –FR case: Subsidiarity: the Federal government gives high regard to the lower-level state governments centralizing federalism: the opposite

46. Professor Stefan Collignon II. Implications 6. Nationalism and Subsidiarity. Results –IG and IO cases: internationalist arrangements converge faster –FR case: centralization converges faster than the subsidiarity

47. Professor Stefan Collignon II. Implications

48. Professor Stefan Collignon II. Implications 3. Perspectives Existing literature on consensus –Deterministic unanimity Preferences are not a random variable Pareto-optimality Constitutional unanimity  Buchanan and Tullock, 1962

49. Professor Stefan Collignon II. Implications 3. Perspectives Existing literature on consensus –Consensus as reflective equilibrium Autonomous, rational individuals make judgements on the reasonableness of certain actions –Requires normative standards consensus when we can agree If reasonable we must agree (rational coherence) –Rational coherence –Fundamental norm: non-pluralist –Great virtue (Rawls) –Critique of unrealism  Theories of deliberative democracy (Habermas, Rawls)

50. Professor Stefan Collignon II. Implications 3. Perspectives Existing literature on consensus –Consensus as opinion-pooling Aggregating individual opinions about utility function Weighted by subjective probabilities  DeGroot (1974), Lehrer and Wagner (1981)

51. Professor Stefan Collignon II. Implications 3. Perspectives –Consensus as stochastic process Our model reformulates utilities as mind states Likelihood of mind states depends on environment, evidence and cognitive capacities Bounded rationality Dissent and consensus structured by institutional topology of communication

52. Professor Stefan Collignon Conclusion There is a rich research agenda waiting for us This paper as the opening shot deliberative process leading to stochastic consensus on stochastic consensus