Preference Flashcards
What is the reflexivity property of a binary relation?
xRx
What is the Irreflexivity property of a binary relation?
¬(xRx)
What is the Symetry property of a binary relation?
xRy ⇒ yRx
What is the Asymetry property of a binary relation?
xRy ⇒ ¬ (yRx)
What is the Antisymetry property of a binary relation?
xRyRx ⇒ x = y
What is the Completeness property of a binary relation?
xRy ∨ yRx
What is the Transitivity property of a binary relation?
xRyRz => xRz
What is the Negative Transitivity property of a binary relation?
¬(xRy) ∧ ¬(yRx) => ¬(xRz)
What is an equivalent relation?
Satisifes Symmetry and Transitivity
What is a Partial order Relation?
Satisfies Reflexivity, Antisymetry and Transitivity
What is a Strict order relation?
Satisifies Irreflexivity, Antysymetry, Transitivity
What is a pre order relation?
Satisifies reflexivity and Transitivity
What is a Weak order relation?
Satisifies Completeness and Transitivity
What is a rational preference?
It is a weak order relation => complet and transitive
If ≽ is rational, then…
1) ∼ is an equivalent relation
2) ≽ = non ≺
3) ≻ is asymetric, transitive ad negatively transitive
4) x ≻ y ≽ z => x ≻ z