POLS2130 – Rationality: Preferences, Completeness & Transitivity

Build preference orderings, test whether they satisfy the axioms of rationality, and see what goes wrong when they don't.

What Makes a Decision-Maker "Rational"?

In public choice and rational choice theory, rationality does not mean being smart, selfish, or emotionless. It means having preferences that are consistent enough to produce a clear ranking of alternatives.

Technical Definition of Individual Rationality

An individual is rational if she possesses a complete and transitive preference ordering over a set of outcomes (or actions).

Two properties are required:

Property 1: Completeness (Comparability)

For any two alternatives x and y, the individual can always say: x ≻ y (prefers x), or y ≻ x (prefers y), or x ~ y (indifferent).
No pair is left unranked. The individual can always compare.

Property 2: Transitivity

If x ≻ y and y ≻ z, then it must be that x ≻ z.
Likewise for indifference: if x ~ y and y ~ z, then x ~ z.
No cycles. Preferences form a coherent chain.

Both properties together guarantee that a "best" option exists and can be chosen. Without completeness, the decision-maker is paralysed. Without transitivity, the decision-maker can be exploited — she would cycle endlessly among options. This is the foundation of maximising behaviour.

Preference Builder

Suppose a voter is ranking three policy options: A (tax cuts), B (defence spending), and C (climate policy).
For each pair, choose how the voter ranks them — or leave it blank to violate completeness.