Preference Relation (MSZ Ch.2 Narrative)

A weak preference relation compares alternatives by the statement that one alternative is at least as good as another. From weak preference one derives:

• strict preference, when one alternative is weakly preferred and the reverse weak preference fails;
• indifference, when each alternative is weakly preferred to the other.

For utility theory the natural abstract structure is a total preorder: preference is reflexive, transitive, and complete, but it need not be antisymmetric because distinct alternatives can be indifferent.

Lean substrate

The Lean-level vocabulary lives in the foundation.preference topic; this node is the MSZ Ch.2 domain narrative, and it cross-links into the four foundation definitions that realize it:

• weak preference and indifference: [[foundation.preference.indifferent]]
• strict preference: [[foundation.preference.strictly_preferred]]
• total preorder (no antisymmetry required): [[foundation.preference.total_preorder]]
• relation-style axioms used by vNM: [[foundation.preference.abstract_relation]]

The EconCSLib.Foundation.Preference module is the single source of truth in Lean; this node is the MSZ Ch.2 narrative wrapper and introduces no Lean definitions of its own beyond what the foundation.preference topic already provides.

References

• [MSZ, Chapter 2, Definitions 2.1-2.7] Maschler, Solan, and Zamir, Game Theory. Preference, strict preference, indifference, and total preorder vocabulary.