Rational agents: a roadmap
Hykel Hosni
http://homepage.sns.it/hosni/
Scuola Normale Superiore, Pisa
29 November 2008
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29 November 2008
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Rationality, logic and information
Motivating idea
Rational behaviour is inferential in nature:
1 it begins with the information that some options are available
and
2 it ends with the information that some choice has been made as
the conclusion of some reasoning process
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Rationality, logic and information
Motivating idea
Rational behaviour is inferential in nature:
1 it begins with the information that some options are available
and
2 it ends with the information that some choice has been made as
the conclusion of some reasoning process
Enlightened normativism:
1
2
we do not aim at a descriptive empirically-testable model (as in
cognitive psychology, behavioural- and neuro- economics)
but we want the facts about rational behaviour to matter for our
normative models.
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Plan
1
Introduction
2
Individual rational choice: decision theory
3
Interactive rational choice: game theory
4
Collective rational choice: social choice
theory
5
Conclusions and openings
6
Essential references
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Rational agents
1
Introduction
2
Individual rational choice: decision theory
3
Interactive rational choice: game theory
4
Collective rational choice: social choice
theory
5
Conclusions and openings
6
Essential references
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Forms of agency
Hierarchy
individual agent
groups of interacting agents
collective agents (societies)
Modularity
collective agents as individuals
individuals as collective agents
Fact
The predictive power of normative models decreases as we approach
individual agency from below
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Rationality and agents
The logical approach to rational choice can be divided into:
1 individual rational choice: prescription of what rational choice
would be in well-specified decision problems
2 interactive rational choice: given general hypotheses on how
individuals act individually, predict how they would act in case of
interaction (conflict or cooperation)
3 collective rational choice: given general hypotheses on rational
individual preferences, deduce what properties a rational
collective preference should have
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General assumptions
agents are goal-directed entities which have preferences over the
possible states of the world
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General assumptions
agents are goal-directed entities which have preferences over the
possible states of the world
we do not evaluate preferences with respect to their content, but
we are only interested in their consistency (point of departure
between rationality and ethics)
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General assumptions
agents are goal-directed entities which have preferences over the
possible states of the world
we do not evaluate preferences with respect to their content, but
we are only interested in their consistency (point of departure
between rationality and ethics)
I
I
recall Carnap: In logic there are no morals . . .
de Finetti: in rational belief only consistency matters, any
consistent choice (of probabilities) counts as rational
Hykel Hosni (SNS Pisa)
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General assumptions
agents are goal-directed entities which have preferences over the
possible states of the world
we do not evaluate preferences with respect to their content, but
we are only interested in their consistency (point of departure
between rationality and ethics)
I
I
recall Carnap: In logic there are no morals . . .
de Finetti: in rational belief only consistency matters, any
consistent choice (of probabilities) counts as rational
rational behaviour in decision problems is (classically)
understood as the maximisation of an agent’s personal interest,
so rational agents are assumed to pursue their self-interest
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(Revealed) Preference
Problem: how to represent personal interest or desires?
assign to each possible outcome of a decision problem a
numerical value: mathematical theory of utility
deduce preference from an agent’s choice behaviour:
rationalizability of choice functions
The economic analysis of rational choice developed essentially after
von Neumann’s axiomatization of rational preference:
Provided that an agent’s preference satisfy a small set of constraints
(they should be complete, transitive and archimedean) there exists a
unique real-valued function u (up to a positive linear transformation)
with the property that an agent prefers outcome x 0 to x if and only if
u(x) ≤ u(x 0 ).
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Rational agents
1
Introduction
2
Individual rational choice: decision theory
3
Interactive rational choice: game theory
4
Collective rational choice: social choice
theory
5
Conclusions and openings
6
Essential references
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Decision problems
A decision situation, is a tuple hS, E, A, F, ≤i, where:
S is a non empty set of states of the world s1 , s2 , . . . (assumed
to be mutually exclusive);
E is the set of events E1 , E2 , . . . (non empty subsets of S);
F is the set of consequences f , g , h, . . . ;
A is the set of acts α1 , α2 , α3 , . . . mapping states to
consequences, that is
A = {α | α : S −→ F} ;
≤ is a preference relation that individuals have over acts
(interpreted as “it is not preferred or indifferent to”).
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Forms of decision
decision under certainty: the agent knows the consequence of
each act
decision under risk: each act can lead to one of a set of
possible consequences whose probabilities are known to the agent
decision under uncertainty: each act can lead to one of a set
of possible consequences whose probabilities are unknown to the
agent
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Rational Decision under Uncertainty
Leonard Savage
(20 November 1917 1 November 1971)
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Rational Decision under Uncertainty
Savage proposes seven postulates, or “logic-like criteri[a] of
consistency in decision situations” which determine uniquely
a subjective probability function
an equivalence class of utility functions
by means of which the agent’s preference over uncertain outcomes
can be mathematically represented
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Representation Theorem
Theorem ([?])
The Consistency Postulates are sufficient to ensure the existence of a
probability function w defined over events and a real-valued function
u defined over the set of consequences F such that if:
(i) Ei , i = 1, . . . , n is a partition of S and α is an act with
consequence fi on Ei and
(ii) Ei0 , i = 1, . . . , m is another partition of S and α0 is an act with
consequence fi 0 on Ei0 ,
then, α ≤ α0 if and only if
n
X
i=1
u(fi )w (Ei ) ≤
m
X
u(fi 0 )w (Ei0 ).
i=1
Furthermore the utility function u is unique up to a positive linear
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RAT1
The upshot of Savage’s characterization of rational decision under
uncertainty is the following principle
Maximisation of expected utility
A rational agent is one whose preferences over uncertain outcomes
are consistent (in the way axiomatized by Savage’s postulates) and
behaves in decision problems as if s/he is maximising his/her
expected utility
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RAT1: Key concepts
single agency
revealed preference (an agent prefers f over g if whenever asked,
would choose f )
desires/desirability/intentions
utility
beliefs
probability
rationality as pursuit of individual interests
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RAT1: Limitations
1
absolute characterization of rational choice:
I
I
no relativization to other agents
purely outcome-based characterization of rational choice
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RAT1: Limitations
1
absolute characterization of rational choice:
I
I
2
no relativization to other agents
purely outcome-based characterization of rational choice
unsustainable idealization
Modern mainstream economic theory is largely based
on an unrealistic picture of human decision making.
Economic agents are portrayed as fully rational
Bayesian maximizers of subjective utility. This view of
economics is not based on empirical evidence, but
rather on the simultaneous axiomization of utility and
subjective probability [. . .](Savage 1954). One can only
admire the imposing structure built by Savage. It has a
strong intellectual appeal as a concept of ideal
rationality. However, it is wrong to assume that human
beings conform to this ideal.(Reihnardt Selten, 1999)
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Bounded Rationality
Herbert Simon
(Milwaukee 1916 - Pittsburgh 2001)
Nobel Laureate in Economic Sciences 1978
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RAT2 Bounded individual Rationality
Two intuitions on bounding rationality:
1 satisficing insetead of optimizing
2 rational reasoning amounts to the maximisation of expected
utility but the complexity of the decision is a cost which enters
the MEU equation
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Prospect theory
Idea
Agents are usually not risk-neutral: loosing and gaining are therefore
not to be treated symmetrically.
Two-stage decision procedure
1 Editing phase: gains and losses relative to the available options
are identified w.r.t. a neutral reference point (status quo)
2 Evaluation phase: the options are evaluated in a way that
resembles RAT1 where:
I
I
Utility is replaced by a measure that is asymmetrical between
gains and losses
Probabilities are transformed by a function that gives greater
weight to probability variations close to the ends than to those
near the centre of the distribution
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Rational agents
1
Introduction
2
Individual rational choice: decision theory
3
Interactive rational choice: game theory
4
Collective rational choice: social choice
theory
5
Conclusions and openings
6
Essential references
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Game Theory
Characterization of rational behaviour in interactive situations where
the key assumptions are:
each player is individually rational in the sense of RAT1
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Game Theory
Characterization of rational behaviour in interactive situations where
the key assumptions are:
each player is individually rational in the sense of RAT1
players’ rationality is common knowledge
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Game Theory
Characterization of rational behaviour in interactive situations where
the key assumptions are:
each player is individually rational in the sense of RAT1
players’ rationality is common knowledge
the (mathematical structure of the) game is common knowledge
Hykel Hosni (SNS Pisa)
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Game Theory
Characterization of rational behaviour in interactive situations where
the key assumptions are:
each player is individually rational in the sense of RAT1
players’ rationality is common knowledge
the (mathematical structure of the) game is common knowledge
typically there is a conflict of interest among players - they do
not share the same preferences
Hykel Hosni (SNS Pisa)
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Game Theory
Characterization of rational behaviour in interactive situations where
the key assumptions are:
each player is individually rational in the sense of RAT1
players’ rationality is common knowledge
the (mathematical structure of the) game is common knowledge
typically there is a conflict of interest among players - they do
not share the same preferences
Goal
Identifying solution concepts based on the common knowledge of
rationality
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Game Theory
Characterization of rational behaviour in interactive situations where
the key assumptions are:
each player is individually rational in the sense of RAT1
players’ rationality is common knowledge
the (mathematical structure of the) game is common knowledge
typically there is a conflict of interest among players - they do
not share the same preferences
Goal
Identifying solution concepts based on the common knowledge of
rationality
Key idea
Relativization of rationality: what counts as a rational choice depends
on the choices that we expect the other players to make
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Game Theory
John F. Nash
(Bluefield 1928 - )
Nobel Laureate in Economic Sciences 1994
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Game forms
Distinction first introduced by von Neumann 1928, possibly
anticipated by Borel 1921
1 normal form/strategic
2 extensive form
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Game forms
Distinction first introduced by von Neumann 1928, possibly
anticipated by Borel 1921
1 normal form/strategic
2 extensive form
I
I
perfect information (chess)
imperfect information (poker)
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Game forms
Distinction first introduced by von Neumann 1928, possibly
anticipated by Borel 1921
1 normal form/strategic
2 extensive form
I
I
3
perfect information (chess)
imperfect information (poker)
non-cooperative
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Game forms
Distinction first introduced by von Neumann 1928, possibly
anticipated by Borel 1921
1 normal form/strategic
2 extensive form
I
I
3
4
perfect information (chess)
imperfect information (poker)
non-cooperative
cooperative
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Strategic games
strategic independence (each player chooses simultaneously and
once and for all their plan of action)
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Strategic games
strategic independence (each player chooses simultaneously and
once and for all their plan of action)
no binding contracts available
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Strategic games
strategic independence (each player chooses simultaneously and
once and for all their plan of action)
no binding contracts available
common knowledge of game
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Strategic games
strategic independence (each player chooses simultaneously and
once and for all their plan of action)
no binding contracts available
common knowledge of game
common knowledge about each player’s rationality
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Strategic games
strategic independence (each player chooses simultaneously and
once and for all their plan of action)
no binding contracts available
common knowledge of game
common knowledge about each player’s rationality
Strategic solution concepts are only possible if players can make
rationality assumptions about their fellow players
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Formal definition
A strategic game is defined by
a finite set N (the set of players)
for each player i ∈ N a non-empty set Ai (the set of actions (or
strategies) available to player i)
for each player i ∈ N a preference relation %i on A = ×j∈N Aj
(the preference relation of player i)
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Formal definition
A strategic game is defined by
a finite set N (the set of players)
for each player i ∈ N a non-empty set Ai (the set of actions (or
strategies) available to player i)
for each player i ∈ N a preference relation %i on A = ×j∈N Aj
(the preference relation of player i)
Alternatively we can introduce a payoff function for player i
ui : A −→ R
with the property that
a %i b ⇔ ui (a) ≥ ui (b)
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Example: Joint Work
Players: {I , II }
Actions: {Cooperate, Defect}
Preference profiles:
I
I
(D, C ) %I (C , C ) %I , (D, D) %I (C , D)
(C , D) %II (C , C ) %II , (D, D) %II (D, C )
Player I
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C
D
Player II
C
D
3, 3 0, 4
4, 0 1, 1
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Example: Duopoly
Players: {I , II }
Actions: {High, Low }
Preference profiles:
I
I
(H, L) %I (L, L) %I , (H, H) %I (L, H)
(L, H) %II (L, L) %II , (H, H) %II (H, L)
Player II
H
Player I
L
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H
1000, 1000
1200, −200
L
−200, 1200
600, 600
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Dominance
The assumption of individual rationality implies the following
Dominance
A strategy s for a player i is said to be dominated by a strategy s 0 if
s never yield a better payoff no matter what the other players choose
Example
Defect dominates Cooperate in the Joint Work Game
Low dominates High in the Duopoly Game
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RAT2
Idea
Each individual is assumed to maximise their own welfare (interest,
utility, ecc.) given what they expect from the other individuals whose
choice can affect the final outcome. It is entirely reasonable to expect
that a solution concept for noncooperative game should be based on
the best response to the expectation of the other’s behaviour which
in turn includes their best response.
Informal definition
A Nash Equilibrium is the complete prediction of how players would
choose on the assumption that no individual could benefit from
deviating unilaterally from the commonly predicted choice
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Nash Equilibrium
Definition
A Nash-equilibrium for a strategic game hN, (AI ), (%i )i, is a profile
a∗ ∈ A of actions such that for every i ∈ N:
∗
∗
(a−i
, ai∗ ) %i (a−i
, ai ),
∀ai ∈ Ai ,
∗
where a−i
is the complement of i in N.
Note the conditional aspect
Player i chooses ai∗ given the expectation that every other player j to
choose aj∗
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Examples
Player I
C
D
Player II
C
D
3, 3
0, 4
4, 0
1∗ , 1∗
Figure: Joint Work
Player I
B
S
Player II
B
S
2∗ , 1∗
0, 0
0, 0
1∗ , 2∗
Figure: BoS
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Examples
Player I
L
R
Player II
L
R
p∗, p∗
0, 0
0, 0
p∗, p∗
Figure: Driving Game
Player I
H
T
Player II
H
T
1, −1 −1, 1
−1, 1 1, −1
Figure: Matching Pennies
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Pure and mixed strategies
Pure strategies
no equilibria (Matching pennies)
multiple equilibria (Driving game)
Mixed strategies
A mixed strategy is a randomization of a players’ choice of pure
strategies - intuitively it aims at keeping the oppontent guessing
(Matching pennies, pricing games, ect)
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Example
Player I
H
T
Player II
H
T
1, −1 −1, 1
−1, 1 1, −1
Figure: Matching Pennies
The game has best-response pair if both players choose both H and
T with probability 21 .
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Existence of Equilibrium
Theorem (Nash 1951)
All finite games have at least one Nash Equilibrium when mixed
strategies are allowed
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The rationality of NE
Two interpretations
1 Steady state: NE is the point at which a potentially
unbounded repetition of plays would lead (Binmore: evolutive
character of NE)
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The rationality of NE
Two interpretations
1 Steady state: NE is the point at which a potentially
unbounded repetition of plays would lead (Binmore: evolutive
character of NE)
2 Deductive: NE is self-enforcing - if a NE exists, no other point
can be a solution of the game, for it would be rational for at last
one player to deviate from that point!
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The rationality of NE
Two interpretations
1 Steady state: NE is the point at which a potentially
unbounded repetition of plays would lead (Binmore: evolutive
character of NE)
2 Deductive: NE is self-enforcing - if a NE exists, no other point
can be a solution of the game, for it would be rational for at last
one player to deviate from that point!
Negative characterization
The best-reply criterion has a negative character which makes it
analogous to de Finetti no-Dutch book criterion for rational degrees
of belief as they both identify irrational choices and declare rational
any other choice.
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Logical tools in games
Logical models of knowledge
I
I
multi-agent epistemic logics
Aumann frames
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Logical tools in games
Logical models of knowledge
I
I
multi-agent epistemic logics
Aumann frames
Logical models of degrees belief
I
I
subjective probability
correlated equilibria
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Logical tools in games
Logical models of knowledge
I
I
multi-agent epistemic logics
Aumann frames
Logical models of degrees belief
I
I
subjective probability
correlated equilibria
Counterfactual reasoning
I
best-response strategy
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Games in logic
game semantics (IF logic, obligational semantics ecc.)
building models by games
set-theoretic games
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Against the foundations I
The Ultimatum Game: Experimental findings (replicated in many
societies across the world) have it that real people usually play fair
agreeing on a 50-50 split.
Behavioural economics suggests relaxing the fundamental postulate
that rational agents pursue (only!) their self-interest as in RAT1
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Against the foundations II
Player I
L
R
Player II
L
R
∗
∗
p ,p
0, 0
0, 0
p∗, p∗
Figure: Driving Game
Pure coordination Games: focal points effect to refine the choice
among indistinguishable NE
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RAT2 Key concepts
incentive
common knowledge of rationality
relativization of rationality
equilibrium (best response)
dominance/strategy elimination
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Keynes’ Beauty Contest
[P]rofessional investment may be likened to those
newspaper competitions in which the competitors have to
pick out the six prettiest faces from a hundred photographs,
the prize being awarded to the competitor whose choice
most nearly corresponds to the average preferences of the
competitors as a whole; so that each competitor has to
pick, not those faces which he himself finds prettiest, but
those which he thinks likeliest to catch the fancy of the
other competitors, all of whom are looking at the problem
from the same point of view.
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It is not a case of choosing those which, to the best of
one’s judgment, are really the prettiest, nor even those
which average opinion genuinely thinks the prettiest. We
have reached the third degree where we devote our
intelligences to anticipating what average opinion expects
the average opinion to be. And there are some, I believe,
who practise the fourth, fifth and higher degrees. [?, p.156]
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Rational agents
1
Introduction
2
Individual rational choice: decision theory
3
Interactive rational choice: game theory
4
Collective rational choice: social choice
theory
5
Conclusions and openings
6
Essential references
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Social Choice Theory
Two interpretations motivated by the ideal of democracy
1 preference aggregation model
I
how can individually rational preferences be aggregated so as to
represent the collective will? (The preference ordering of the
society should be a fixed function of the individual preference
orderings)
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Social Choice Theory
Two interpretations motivated by the ideal of democracy
1 preference aggregation model
I
2
how can individually rational preferences be aggregated so as to
represent the collective will? (The preference ordering of the
society should be a fixed function of the individual preference
orderings)
choice function model
I
which rationality constraints should be satisfied by any choice
function where the object of choice relates to some collective
good? (social states as alternatives)
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Social choice as aggregation
Kenneth Arrow
(New York City 1921 - )
Nobel Laureate in Economic Sciences 1972
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Social choice as aggregation
Assumptions
each indivudual is assumed to be individually rational in the
sense having a consistent (complete, transitive) preference profile
typically distinct individuals have distinct preference profiles
Problem
Definition of a social welfare function mapping individual profiles into
a collective profile interpreted as the society’s preference
Idea
The emphasis is on a conditional characterization of rational choice:
assuming that each individual preference is rational, how can we
produce a collective preference which qualifies as rational where
collective rationality is interpreted in terms of justice and democracy
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Binary social choice: simple majority
voting
Desiderata on the aggregation method for a finite number of
individuals and a binary agenda:
Monotonicity (the more individuals for an option should not
undermine its selection)
Anonimity (no option should be a priori discriminated against)
Neutrality (all individual preferences should be equally
important)
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Binary social choice: simple majority
voting
Desiderata on the aggregation method for a finite number of
individuals and a binary agenda:
Monotonicity (the more individuals for an option should not
undermine its selection)
Anonimity (no option should be a priori discriminated against)
Neutrality (all individual preferences should be equally
important)
Theorem (May 1952)
If Y is a binary agenda and the number of voters N is odd, the
alternative in Y which is preferred by the majority of voters is the
unique aggregation method satisfying monotonicity, anonymity and
neutrality.
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Rational agents: a roadmap
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Arrovian (non-binary) social choice
Conditions on aggregation functions:
Unrestricted domain (U)
I
no ordering is excluded a priori
Pareto principle (P)
I
if x ≺i y ∀i ∈ N then x ≺ y
Independence of irrelevant alternatives
I
Given any two profiles of individual preferences, if they agree on
every pair of alternatives (x, y ) ∈ X , then the social preference
for the between x and y shoud be the same for the two profiles
Dictatorship
I
∃i ∈ N such that if x ≺i y then x ≺ y
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Impossibility theorem
Arrow 1951
For a finite number of individuals and at least three distinct social
alternatives, if a social welfare function satisfies U, P and I, then it
must be dicatorial.
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Rational agents: a roadmap
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Impossibility theorem
Arrow 1951
For a finite number of individuals and at least three distinct social
alternatives, if a social welfare function satisfies U, P and I, then it
must be dicatorial.
Getting around the impossibility: Two lines of research
1 restricting the domain of preference profiles
2 replacing transitivity with acyclicity
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Social choice functions
Amartya Sen
(Santiniketan 1933 - )
Nobel Laureate in Economic Sciences 1998
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Motivation
A rational preference ordering (transitivity and completeness) need
not be assumed to formulate the problem of rational (i.e. consistent)
social choice.
Example
Suppose that K = {x, y , z} is a set of social states and x y ,
y z, z ≈ x. Then for a piecewise or global choice the set, the of
best elements R(K ) is always non-empty:
R({x, y }) = {x}
R({y , z}) = {z}
R({z, x}) = {z, x}
R({x, y , z}) = {x}
yet the ordering is obviously non-transitive
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Rational agents: a roadmap
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Social choice functions
The fundamental ingredients of the choice-function model are:
X any subset of a universal domain U
A choice function R such that ∅ =
6 R(X ) ⊆ X .
R(X ) (the choice set) contains those elements of X that an
agent has reason to prefer over every other element of X .
A choice function R is said to be razionalizable by a
(pre-)ordering relation ≺ if the choice set R(X ) selects the
maximal elements of X according to ≺:
R(X ) = max(X ) = {x ∈ X | 6 ∃y ∈ X , y ≺ x}
Lemma (Existence of a choice set)
If is reflexive and complete then R(X , ) is defined over a finite X
if and only if is acyclical.
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RAT3: Consistent choice functions
We can ask which properties could be desirable for a choice function
R without committing to any specific underlying ordering
Contraction - Property α
if X1 ⊆ X2 , then X1 ∩ R(X2 ) ⊆ R(X1 )
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RAT3: Consistent choice functions
We can ask which properties could be desirable for a choice function
R without committing to any specific underlying ordering
Contraction - Property α
if X1 ⊆ X2 , then X1 ∩ R(X2 ) ⊆ R(X1 )
Expansion - Property γ
R(X1 ) ∩ R(X2 ) ⊆ R(X1 ∪ X2 )
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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RAT3: Consistent choice functions
We can ask which properties could be desirable for a choice function
R without committing to any specific underlying ordering
Contraction - Property α
if X1 ⊆ X2 , then X1 ∩ R(X2 ) ⊆ R(X1 )
Expansion - Property γ
R(X1 ) ∩ R(X2 ) ⊆ R(X1 ∪ X2 )
Sen 1971,1979
A choice function R is rationalizable by a pre-ordering if and only if R
satisfies property α and γ
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Rational agents: a roadmap
29 November 2008
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Other properties
Arrow’s Axiom
if X1 ⊆ X2 , and R(X2 ) ∩ K1 6= ∅ then R(X2 ) ∩ X1 = R(X1 ).
Nash’s axiom
if R(X2 ) ⊆ X1 ⊆ X2 then R(X1 ) = R(X2 ).
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Rational agents: a roadmap
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Rational agents
1
Introduction
2
Individual rational choice: decision theory
3
Interactive rational choice: game theory
4
Collective rational choice: social choice
theory
5
Conclusions and openings
6
Essential references
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Rational agents: a roadmap
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Conclusions
centrality of intentional attitudes (preferences, desires,
intentions, beliefs, knowledge)
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Conclusions
centrality of intentional attitudes (preferences, desires,
intentions, beliefs, knowledge)
reference to consistency principles amounts to forbidding certain
patterns (of choice, preference, belief, reasoning)
I
I
I
consistent subjective probabilities
elimination of dominated strategies
contraction/expansion properties of choice functions
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Rational agents: a roadmap
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Openings
role of rationality in the evolution of social behaviour
(predictability, communication, cooperation, understanding)
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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Openings
role of rationality in the evolution of social behaviour
(predictability, communication, cooperation, understanding)
refinement of consistency to give positive characterizations
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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Openings
role of rationality in the evolution of social behaviour
(predictability, communication, cooperation, understanding)
refinement of consistency to give positive characterizations
I
rational degrees of belief beyond consistency
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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Openings
role of rationality in the evolution of social behaviour
(predictability, communication, cooperation, understanding)
refinement of consistency to give positive characterizations
I
I
rational degrees of belief beyond consistency
selection among outcome-indistinguishable Nash Equilibria
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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Openings
role of rationality in the evolution of social behaviour
(predictability, communication, cooperation, understanding)
refinement of consistency to give positive characterizations
I
I
I
rational degrees of belief beyond consistency
selection among outcome-indistinguishable Nash Equilibria
rationalization by multiple rationales (i.e. maximise monetary
utility provided that ethical value does not fall beyond treshold)
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
59 / 62
Openings
role of rationality in the evolution of social behaviour
(predictability, communication, cooperation, understanding)
refinement of consistency to give positive characterizations
I
I
I
rational degrees of belief beyond consistency
selection among outcome-indistinguishable Nash Equilibria
rationalization by multiple rationales (i.e. maximise monetary
utility provided that ethical value does not fall beyond treshold)
context-dependent constraints on rational choice
process-based vs. outcome-based characterization of rationality
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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The rationality of a belief may derive from the process by
which that belief is arrived and maintained, but not every
(conceivably) effective way of arriving at true belief would
mark a belief as rational. [. . . ] [R]ationality is not simply
any kind of instrumentality. It requires a certain type of
instrument, namely reasons and reasoning. Suppose, then,
that a particular procedure is a reliable way to arrive at a
true belief. If an action or belief yielded by that procedure
is to be rational, not only must the procedure involve a
network of reasons and reasoning, but this also must be (in
part) why the procedure is reliable. The reasons and
reasoning contribute to the procedure’s reliability. (Nozick
1993)
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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Rational agents
1
Introduction
2
Individual rational choice: decision theory
3
Interactive rational choice: game theory
4
Collective rational choice: social choice
theory
5
Conclusions and openings
6
Essential references
Hykel Hosni (SNS Pisa)
Rational agents: a roadmap
29 November 2008
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1
Individual decision theory
I
I
2
Game theory
I
I
3
Binmore, Ken, Game Theory: A Very Short Introduction.
Oxford University Press (2008)
Osborne, M. J. and Rubinstein, A., A Course in Game Theory,
MIT Press, Cambridge (1994)
Social choice theory
I
I
I
4
Savage, Leonard, The Foundations of Statistics. New York:
Wiley 1954.
(See also nearly all references below!)
Arrow, Kenneth J., Social Choice and Individual Values. Wiley,
New York. 2nd ed. (1963)
Sen, Amartya, Collective Choice and Social Welfare,
Holden-Day, (1970)
Gaertner, Wulf, A Primer in Social Choice Theory, Oxford
University Press, (2006)
General reference (for all topics):
I
Aumann, R. J., and S.Hart, eds. Handbook of Game Theory
with Economic Applications. North-Holland, (1992 - 2002.)
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Rational agents: a roadmap
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