Preference Flashcards

1
Q

What is the reflexivity property of a binary relation?

A

xRx

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2
Q

What is the Irreflexivity property of a binary relation?

A

¬(xRx)

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3
Q

What is the Symetry property of a binary relation?

A

xRy ⇒ yRx

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4
Q

What is the Asymetry property of a binary relation?

A

xRy ⇒ ¬ (yRx)

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5
Q

What is the Antisymetry property of a binary relation?

A

xRyRx ⇒ x = y

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6
Q

What is the Completeness property of a binary relation?

A

xRy ∨ yRx

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7
Q

What is the Transitivity property of a binary relation?

A

xRyRz => xRz

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8
Q

What is the Negative Transitivity property of a binary relation?

A

¬(xRy) ∧ ¬(yRx) => ¬(xRz)

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9
Q

What is an equivalent relation?

A

Satisifes Symmetry and Transitivity

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10
Q

What is a Partial order Relation?

A

Satisfies Reflexivity, Antisymetry and Transitivity

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11
Q

What is a Strict order relation?

A

Satisifies Irreflexivity, Antysymetry, Transitivity

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12
Q

What is a pre order relation?

A

Satisifies reflexivity and Transitivity

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13
Q

What is a Weak order relation?

A

Satisifies Completeness and Transitivity

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14
Q

What is a rational preference?

A

It is a weak order relation => complet and transitive

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15
Q

If ≽ is rational, then…

A

1) ∼ is an equivalent relation
2) ≽ = non ≺
3) ≻ is asymetric, transitive ad negatively transitive
4) x ≻ y ≽ z => x ≻ z

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16
Q

What is a ≽-best element?

A

x is a ≽-best element if, for every y in X, x ≽y

17
Q

What is a ≽-maximum element?

A

x is a ≽-maximum element if for every y in X, y ≽ x implies x ≽ y

18
Q

If ≽ is rational then (≽-best)

A

1) x is a ≽-best element iff x is ≽-maximum element

2) If X is finite, then there exists a ≽-best element