professor stefan collignon

Professor Stefan Collignon

A Theory of Stochastic Consensus

Stefan CollignonHarvard University

Centre for European Studies 22. February 2006

www.stefancollignon.de

Professor Stefan Collignon

PlanIntroduction

I. The Model1. Desires and preferences

2. Consensus and agreement

3. Dissent and Conflict

II. Implications1. Overcoming conflict

2. Dissent in political systems

3. Perspectives

Conclusion

Professor Stefan Collignon

IntroductionConsensus 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

Professor Stefan Collignon

IntroductionMy 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

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

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

Professor Stefan Collignon

I. The Model

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

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

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

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

Professor Stefan Collignon

I. The Model1. Desires and preferences• Consequences of our probabilistic interpretation of

preference intensity– Utility function

• Conventional: u: XR – 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?

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: Atij be the event that at time t,

i takes the view that j had at time t – 1

•P(Atij )=Wij(t) is the transition probability

for going from one mind state to the next

Professor Stefan Collignon

I. The Model2. 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

Professor Stefan Collignon

I. The Model2. Consensus and agreement

• Topology of communication: definitions– Influence

• Individual j influences i if Wijt >0

• Individual j influences i directly if Wij >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

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 Wii >0, an individual has self-regard

• Condition A2: If if Wiit >0, an

individual has eventual self-regard

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

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.

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

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

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”)

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

Professor Stefan Collignon

I. The Model

3. Dissent and ConflictViolations 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

Professor Stefan Collignon

I. The Model

3. Dissent and ConflictViolations 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

Professor Stefan Collignon

II. Implications

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

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

Professor Stefan Collignon

II. Implications

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

Professor Stefan Collignon

II. Implications

Fig 5.1 Intergovernmental model

Professor Stefan Collignon

II. Implications

Professor Stefan Collignon

II. Implications

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

Professor Stefan Collignon

II. Implications

1. Complete ignorance• Any value goes

• FR converges fastest

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

Professor Stefan Collignon

II. Implications

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;

Professor Stefan Collignon

II. Implications

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

Professor Stefan Collignon

II. Implications

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.

Professor Stefan Collignon

II. Implications

Professor Stefan Collignon

II. Implications

Professor Stefan Collignon

II. Implications

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

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

Professor Stefan Collignon

II. Implications

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

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)

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)

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

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