EITM 2007 Institutions Week John Aldrich Duke University Arthur Lupia University of Michigan.

EITM 2007Institutions Week

John AldrichDuke University

Arthur LupiaUniversity of Michigan

An Introduction to EITM 2007

EITM Fundamentals

What is EITM? Literature reviews? New training? NO Research design? YES

Why is it important? real problems. Better science yields social value.

What we hope to accomplish. Clarify the value and challenges of methodologically integrated

research. Help you conduct more effective research.

EITM Fundamentals

Our emphasis is asymmetric.

Theoretical Models We focus on formal models

Cooperative Game Theory Non-Cooperative Game Theory Agent-Based Modeling

Empirical Implications of… Large N-statistical studies Experiments More detailed analysis of substantive properties

This Week’s Outline

Monday: Principles of Institutional Modeling

Tuesday: Theory and Empirics Interact Evening Session: Introduction to Modeling (optional)

Wednesday: Coalition Governance Guest Speaker: Sona Golder

Thursday: Delegation and Political Parties Guest speaker: Michael Thies

Friday: Information & Experiments

Why EITM Matters

Science contributes to society by simplifying complex phenomena. Its value increases with the value of the

simplification.

Interesting topics are insufficient. You must be able to lead people from where they

are to a better conclusion.

Your research design problem Where are they?

Who is your target audience? What factual premises/truth claims will they

accept.

Where do they want to be? Which alternate conclusion will benefit them? What burden of proof and standard of evidence

do they impose?

Scientific Research Designs (KKV 7-8) 1. The goal is inference. 2. The procedures are public. 3. The conclusions are uncertain. 4. The content is the method.

It is a social phenomenon…

The Basic Research Design Problem N problems = . For any problem, N theories = . For any theory, N models = . For any problem, the number of empirical

specifications = .

What will you choose?

All political scientists make assumptions about: Players, Actions, Strategies, Information, Beliefs,

Outcomes, Payoffs, and Method of inference (e.g., “I know it when I see it,” path

dependence, Nash Equilibrium, logit plus LLN).

Some state their assumptions more precisely than others.

Conclusions depend on assumptions.

The Basic Research Design Problem N problems = . For any problem, N theories = . For any theory, N models = . For any problem, the number of empirical

specifications = .

Your time at EITM should help you make more effective choices.

Paper Presentation Format

M. Motivation NH. Null Hypotheses P. Premises

KEY. What choices did they make? Would you make the same ones?

C. Conclusions

Social Choice Theory

And the Formal Study of Political Institutions

Structure

1. Review several results. Specify the argument. Clarify theoretical implications.

2. Why EITM matters What do the results imply about concepts such as

collective will? Do others apply the results in a manner that is

consistent with the mathematics?

Key Premise and Questions

Collective choice is a necessary and useful part of social life. What characteristics do you want a collective choice to

have?

If there exist no decision rules that have all the characteristics you desire, which combinations of characteristics can you have?

Are contemporary claims about collective choice consistent with existing logic?

Social Choice Theory

Examines the relationship between individual will and collective decisions.

Focuses on preference aggregation and its implications for political/institutional engineering.

The foundations (cooperative game theory) are positive, the uses (how preferences should be aggregated) tend to be normative. Concepts: Equity. Utilitarian. Majority rule. Anonymity.

Monotonicity.

Social Choice Theory (peak activity late 1940’s-mid 1980’s) How do collective choices correspond to individual desires?

Elements of Cooperative Game Theory Alternatives: {x, y, z}S Individuals: iN. Preferences: x Pi y: strong (>). x Ri y weak ()

A preference profile is a preference matrix.

C(R,S) => Social/Collective Choice A CCR converts a set S and profile R into a subset of S called a

choice set.

Condorcet’s Paradox (18th C)

M. Is majority rule optimal?

NH. MMD aggregates preferences clearly.

P. At least 3 voters and 3 alternatives. Complete information. Originally, sincere voting.

C. MMD is not sufficient to produce a stable relationship between individual preferences and collective outcomes.

Example

Voter 1 2 3

Best A B C

B C A

Worst C A B

MR Agendas: (ABC)C, (ACB)B, (BCA)A.

The agenda determines the outcome. There is no 1:1 relationship between individual will and collective choice.

Arrow’s Theorem

M. How do individual desires affect collective choices?

NH (inexact). A CCR can always resolve interest conflicts.

P. At least 2 voters and 3 alternatives. People are their preferences. There is no adaptation.

C. No such CCR exists.

Arrow’s General Possibility TheoremCollective Rationality

Complete. x, y S, either x R y, y R x or both. Reflexive. x, y S, x R x. Transitive x, y, z S, x R y and y R z x R z.

C. A collectively rational CCR cannot satisfy the following four conditions simultaneously. If you want all but one of these desirable properties to hold for

every conceivable preference profile, then you must sacrifice the remaining property.

Arrow’s General Possibility Theorem Unrestricted Domain: The CCR allows us to consider any set of

preferences.

Pareto: If everyone prefers X to Y, then Y is not chosen when X is available.

Independence of Irrelevant Alternatives. x,yS, and all R, R’, x Ri y x R’i y C(S,R)=C(S,R’)

D  There is no dictator. There is no i N, s.t. x, y S, x Pi y x P y.

Violations

Completeness: simple majority rule with many alternatives. Transitivity: see Condorcet paradox. Pareto: Random choice. IID: Borda Rule.

ri(x, R, S) = |{yS| x Pi y}| # of alts to which i prefers x.

r(x, R, S) = {iN| ri(x, R, S)} Borda votes for x. CBorda(R, S) = {xS| r(x, R, S) r(y, R, S) y S.} Win set. 

Example. 1: xyzw. 2: xyzw. 3: zwxy.

What happens after y is removed?

Borda Violates IID

B 1 2 3 Total

x 3 3 1 7

y 2 2 0 4

z 1 1 3 5

w 0 0 2 2

C(R,S)=x

B 1 2 3 Total

x 2 2 0 4

z 1 1 2 4

w 0 0 1 1

C(R,S/y)={x,z}

What Does Arrow’s Theorem Mean for Politics?

Institutions matter.

Reactions to Arrow

A search for permissible properties of CCRs. Arrow actually examined social welfare functions,

but CCRs are functionally equivalent.

Inquiries into the robustness of the result.

McKelvey 1979

M. Arrow: R that yields an intransitive social ordering for any CCR. With what likelihood?

NH. Majority rule generally forces outcome towards “median” alternatives.

P. N voters, N >1 dim policy space, MMD. Solved by means of cooperative game theory

C. If conditions are right, MMD yields an indeterminate outcome.

The Extent of Intransitivity

Theorem: If m 2, n 3 and ~ total median, then x, y X, a sequence of alternatives, {0,…, N} with 0=x and N =y, such that i+1 > i, for 0iN-1.

“When transitivity breaks down, it completely breaks down, engulfing the whole space in a single cycle set.” Possible regardless of voter preferences.

Key assumptions

The chairman must know a lot about voter preferences to cause the result.

Voters make fine distinctions without becoming indifferent.

Voters vote sincerely & do not collude.

Empirical Implications of Social Choice Theory

Claims about Arrow

Law “It is well established, via mathematical proofs, that every method of

social or collective choice – every arrangement whereby individual choices are pooled to arrive at a collective decision – violates at least one principle required for reasonable and fair democratic decision making.” Segal and Spaeth (1993: 62)

Political Science “Unfortunately, as Arrow has demonstrated, no method of decision

(short of a dictator) can guarantee the aggregation of citizen preferences transitively under all preference configurations, even if each citizens preferences are transitive.” (Jones 1994: 85)

Michael Kinsley misinterprets Arrow

“Election Day” NY Times. 11/5/06

Interpretations

Arrow – Nothing will work?

McKelvey – Chaos? Anything can happen?

Both interpretations are overstated.

Lupia and McCubbins (2005)

M. Social Choice Theory results are used in politics & law. But is their application consistent with the mathematics?

NH. Collective intent & majority will are vacuous.

P. The validity of current claims depend on what Arrow proved. SCT does not allow resource or cognitive limits.

C. Important aspects of social choice theory are “lost in translation.”

Empirical Implications of

Arrow’s Theorem

Arrow’s Claim

C: Given sufficient individuals and alternatives, there is no CCR for which conditions CUPID can hold simultaneously.

But one of these conditions is universal domain. This fact allowed the proof to be relatively short.

What Arrow Proved

Arrow proved that for every CCR there exists a preference profile for which conditions CPID cannot hold simultaneously.

He did not prove the same result for all preference profiles.

Therefore, for any CCR, Arrow’s Theorem allows CPID to be satisfied for up to P-1 preference profiles, with P possibly large.

Implications

Arrow did not prove that transitive collective preferences are impossible.

Arrow did not prove that achieving transitive collective preferences requires a dictator.

If you insist on universal domain, all but one of the others can be satisfied simultaneously.

Main Implication: If you want to understand collective choice when individuals have different preferences, institutions matter.

Empirical Implications of

The Instability Results

A Debate About the Meaning of ChoiceRiker: [P]olitics is the dismal

science because we have learned from it that there are no fundamental equilibria to predict. In the absence of such equilibria, we cannot know much about the future at all.

Disequilibrium “is the characteristic feature of politics.”

Shepsle; Shepsle and Weingast

“institutional structure … has an important independent impact on the existence of equilibrium”

Q: “Why so much stability?”

A: “Institutional arrangements do it.”

Riker’s Response

Institutions are no more than rules and rules are themselves the product of social decisions. Consequently, the rules are also not in equilibrium.”

The claim “Institutional arrangements do it” begs, rather than answers, the question “Why so much stability?”

Our Response

Seek N/S conditions for stability.

The roots of stability are found in: the requirements for collective action systematic and universal limits on human energy, cognition, and

communicative ability.

Stability is likely for many important collective choices.

What is Stability? A collective choice w is stable if and only if, holding S, R, and the

CCR constant, w has an empty win set. Example 1: Stability

1 2 3y y zz z yx x x

Example 2: Instability 1 2 3

y z xz x yx y z

The Problem

Two assumptions “stack the deck” in favor of finding instability in SCT’s.

There is no scarcity. Scarcity makes holding another vote or implementing a new

policy costly.

There is no complexity. Complexity makes people uncertain about the consequences of

change.

Add Scarcity and Complexity

Decision making is costly, like using a machine. What is the cost to individual i of using a collective choice rule? Maintaining the status quo, q, does not require use of the CCR.

Implementation is costly. What is the cost to individual i of implementing alternative x instead of the

status quo q.

Information asymmetries can make persuasion difficult and change prohibitive. Consider: The way things are versus how they might be.

Conclusion

Why do we observe so much stability? Collective action is not trivial. Complexity and scarcity are ubiquitous.

Implications

Instability results identify a bounded set of universal claims that are not logically valid. These results do not rule out all conditional claims about the

relationship between preference and choice.

SCT does not clarify institutional dynamics in the presence of potentially adaptive actors with resource and information limits. A different formal modeling approach – non-cooperative game

theory -- is needed.

Formal Models of Institutions

Allow precision Assumptions. Conclusions. Their relation.

Main topics How (exogenous) institutional variations affect choice or policy outcomes. Choice of institutions.

Provide a potentially powerful platform for empirical work. Theory need not precede empirics, but when it does it can help you be more

effective in using data to evaluate causal hypotheses.