Rational Choice Theory Vocabulary

Flashcards for reviewing key vocabulary from lectures on Rational Choice Theory.

Homo Oeconomicus

An idealized, basic unit of analysis in economic theory, representing a rational agent with purposeful and optimal choice behavior.

Preference Relation (%X)

A binary relation on the set X of alternatives, representing a decision maker's (DM) preferential evaluations. x %X y means the DM either strictly prefers x to y or is indifferent between them.

Extensionality

A property of preferences where, if X = X0, then x %X y if and only if x %X0 y for all x; y 2 X; meaning the preference depends only on available alternatives, not on their description.

Reflexivity

An assumption that, for all x in X, it holds x % x, inherent to the weak nature of the preference %.

Transitivity

An assumption that, for all x; y; z in X, x % y and y % z imply x % z, requiring consistency across pairwise evaluations of alternatives.

Indifference Curves

For reflexive and transitive preferences, these are equivalence classes [x] = {y 2 X : y x} representing all alternatives the DM is indifferent between.

Strict Transitivity

A version of transitivity where, for all x; y; z 2 X, x y and y z imply x z, allowing for intransitive indifference.

Completeness

A property where, for all x; y 2 X, x % y or y % x; requiring all alternatives to be pairwise comparable.

Strict Monotonicity

For all x; y 2 X, x > y implies x y, relating the objective order structure to subjective preference (More of any good, the better).

Strong Monotonicity

For all x; y 2 X : x y implies x y, and x y implies x % y; a weaker monotonicity property.

Monotonicity

For all x; y 2 X, x y implies x % y; requiring goods' increases to never harm DMs.

Archimedean Axiom

For all x; y; z 2 X with x y z, there exist ; 2 (0; 1) such that x + (1 )z y x + (1 )z, stating there are no infinitely preferred or despised alternatives.

Convexity

For all x; y 2 X and all 2 [0; 1], x y implies x + (1 ) y % x; capturing a preference for mixing, or diversification.

Strict Convexity

For all distinct x; y 2 X and all 2 (0; 1), x y implies x + (1 ) y x; a stronger form of convexity ensuring uniqueness of optimal bundles.

Affinity

For all x; y 2 X and all 2 [0; 1], x y implies x + (1 ) y x; capturing indierence to diversification.

Preferential Rationality

A self-consistent, viable, and instrumental preferential rationality that paves the way to instrumental rationality.

Utility Function

A real-valued function u : X ! R that represents the preference relation %, such that x % y if and only if u(x) >= u(y).

Ordinal Utility

Utility represented, unique up to strictly increasing transformations.

%-Order Dense

Given a binary relation % on X, a subset Z of X is said to be %-order dense in X if, for each x; y 2 X with x y, there exists z 2 Z such that x % z % y.

Ordinality

The mental states represented by the underlying preference and measure it only ordinally.

Archimedean M-Space

A M-space (V; ; kk) where the topology is generated by a lattice M-norm kk

Order Interval

All vectors that lie in between any two of its members. It contains all the vectors that lie in between any two of its members.

Ordinal Concavity

There exists a strictly increasing function h : Im ! R such that the composite function h ' is concave.

Lexicographic Preference

DM first looks at the first coordinate: if x1 > y1, then x % y.

Consumption Bundles

The amount of each good as bundle y, while the convex combination x + (1-)y is interpreted as a mix of the two vectors.