Random Utility without Regularity Michel Regenwetter Department of Psychology, University of Illinois at Urbana-Champaign Winer Memorial Lectures 2018 Work w. J. Dana, C. Davis-Stober, J. Müller-Trede, M.Robinson Thanks: NSF-DRMS SES-10-62045 & SES-14-59866. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 1 / 40
Outline Context ( � ) 1 Random Utility & Random Preference 2 Context-Dependent Random Utility & Random Preference 3 Random Utility without Regularity 4 Conclusions 5 Regenwetter RUM without Regularity Winer Memorial Lectures 2018 2 / 40
Context ( � ) Outline Context ( � ) 1 Random Utility & Random Preference 2 Context-Dependent Random Utility & Random Preference 3 Random Utility without Regularity 4 Conclusions 5 Regenwetter RUM without Regularity Winer Memorial Lectures 2018 3 / 40
Context ( � ) Context ( � ) Rationality of decision making. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 4 / 40
Context ( � ) Context ( � ) Rationality of decision making. Huge amounts of heterogeneity within and across decision makers. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 4 / 40
Context ( � ) Context ( � ) Rationality of decision making. Huge amounts of heterogeneity within and across decision makers. Psychological constructs (e.g., preferences) are moving targets! Regenwetter RUM without Regularity Winer Memorial Lectures 2018 4 / 40
Context ( � ) Context ( � ) Rationality of decision making. Huge amounts of heterogeneity within and across decision makers. Psychological constructs (e.g., preferences) are moving targets! They are subject to genuine qualitative variation. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 4 / 40
Context ( � ) Context ( � ) Rationality of decision making. Huge amounts of heterogeneity within and across decision makers. Psychological constructs (e.g., preferences) are moving targets! They are subject to genuine qualitative variation. I only use classical probability theory. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 4 / 40
Random Utility & Random Preference Outline Context ( � ) 1 Random Utility & Random Preference 2 Context-Dependent Random Utility & Random Preference 3 Random Utility without Regularity 4 Conclusions 5 Regenwetter RUM without Regularity Winer Memorial Lectures 2018 5 / 40
Random Utility & Random Preference Random Utility Model Finite set A Noncoincident RVs: ∀ a , b ∈ A , a � = b , Pr ( U a = U b ) = 0 Regenwetter RUM without Regularity Winer Memorial Lectures 2018 6 / 40
Random Utility & Random Preference Random Utility Model Finite set A Noncoincident RVs: ∀ a , b ∈ A , a � = b , Pr ( U a = U b ) = 0 Random Utility Model for Best-Choice P X ( x ) = Pr ( U x = max y ∈ X U y ) , ( x ∈ X ⊆ A ) . Regenwetter RUM without Regularity Winer Memorial Lectures 2018 6 / 40
Random Utility & Random Preference Random Utility Model Finite set A Noncoincident RVs: ∀ a , b ∈ A , a � = b , Pr ( U a = U b ) = 0 Random Utility Model for Best-Choice P X ( x ) = Pr ( U x = max y ∈ X U y ) , ( x ∈ X ⊆ A ) . Random Utility Model for Best-Worst-Choice P X ( x , y ) = Pr ( U x = max v ∈ X U v , U y = min w ∈ X U w ) , ( x � = y ∈ X ⊆ A ) , Regenwetter RUM without Regularity Winer Memorial Lectures 2018 6 / 40
Random Utility & Random Preference Random Utility ↔ Random Preference Every joint realization of noncoincident RVs ( U x ) x ∈A generates a linear order ≻ on A . Linear Order: Transitive, Asymmetric, Complete. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 7 / 40
Random Utility & Random Preference Random Utility ↔ Random Preference Every joint realization of noncoincident RVs ( U x ) x ∈A generates a linear order ≻ on A . Linear Order: Transitive, Asymmetric, Complete. Every probability distribution on linear orders on A can be represented with noncoincident RVs ( U x ) x ∈A . Regenwetter RUM without Regularity Winer Memorial Lectures 2018 7 / 40
Random Utility & Random Preference Random Preference Model L : the collection of all linear orders on A Regenwetter RUM without Regularity Winer Memorial Lectures 2018 8 / 40
Random Utility & Random Preference Random Preference Model L : the collection of all linear orders on A Random Preference Model for Best-Choice � P X ( x ) = P ( ≻ ) , ( ∀ x ∈ X ⊆ A ) . ≻∈L BX ( ≻ )= x Regenwetter RUM without Regularity Winer Memorial Lectures 2018 8 / 40
Random Utility & Random Preference Random Preference Model L : the collection of all linear orders on A Random Preference Model for Best-Choice � P X ( x ) = P ( ≻ ) , ( ∀ x ∈ X ⊆ A ) . ≻∈L BX ( ≻ )= x Random Preference Model for Best-Worst-Choice � P X ( x , y ) = P ( ≻ ) , ( ∀ x � = y ∈ X ⊆ A ) . ≻∈L BWX ( ≻ )=( x , y ) Regenwetter RUM without Regularity Winer Memorial Lectures 2018 8 / 40
Random Utility & Random Preference Random Preference Model for Binary Choice L : the collection of all linear orders on A Random Preference Model for Best-Choice � P { x , y } ( x ) = P ( ≻ ) , ( ∀ x � = y ∈ A ) . ≻∈L x ≻ y Random Preference Model for Best-Worst-Choice � P { x , y } ( x , y ) = P ( ≻ ) , ( ∀ x � = y ∈ A ) . ≻∈L x ≻ y Regenwetter RUM without Regularity Winer Memorial Lectures 2018 9 / 40
Random Utility & Random Preference Binary Choice & Linear Ordering Polytope Regenwetter RUM without Regularity Winer Memorial Lectures 2018 10 / 40
Random Utility & Random Preference Binary Choice & Linear Ordering Polytope Triangle Inequalities (Block & Marschak, book, 1960) P { x , y } ( x ) + P { y , z } ( y ) − P { x , z } ( x ) ≤ 1 ( ∀ x , y , z ) Regenwetter RUM without Regularity Winer Memorial Lectures 2018 11 / 40
Random Utility & Random Preference Binary Choice & Linear Ordering Polytope Triangle Inequalities (Block & Marschak, book, 1960) P { x , y } ( x ) + P { y , z } ( y ) − P { x , z } ( x ) ≤ 1 ( ∀ x , y , z ) |A| : 3 4 5 6 7 8 9 > 4 . 8 × 10 8 # FDI’s: 2 10 20 910 87,472 unknown Regenwetter RUM without Regularity Winer Memorial Lectures 2018 11 / 40
Random Utility & Random Preference Binary Choice & Linear Ordering Polytope Test of Rationality (Transitivity) of Preference : Regenwetter, Dana, Davis-Stober ( Psychological Review , 2011). Regenwetter RUM without Regularity Winer Memorial Lectures 2018 12 / 40
Context-Dependent Random Utility & Random Preference Outline Context ( � ) 1 Random Utility & Random Preference 2 Context-Dependent Random Utility & Random Preference 3 Random Utility without Regularity 4 Conclusions 5 Regenwetter RUM without Regularity Winer Memorial Lectures 2018 13 / 40
Context-Dependent Random Utility & Random Preference Description-Experience Gap Binary choice among lotteries H: Win $4 with probability .8, otherwise $0. L: Win $3 for sure. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 14 / 40
Context-Dependent Random Utility & Random Preference Description-Experience Gap Binary choice among lotteries H: Win $4 with probability .8, otherwise $0. L: Win $3 for sure. Description-Experience Gap (Hertwig et al., Psych. Science , 2004) Decision makers “overweight” small probabilities in description. Decision makers “underweight” small probabilities in experience. Regenwetter RUM without Regularity Winer Memorial Lectures 2018 14 / 40
Context-Dependent Random Utility & Random Preference Description-Experience Gap Binary choice among lotteries H: Win $4 with probability .8, otherwise $0. L: Win $3 for sure. Description-Experience Gap (Hertwig et al., Psych. Science , 2004) Decision makers “overweight” small probabilities in description. Decision makers “underweight” small probabilities in experience. How about “context:” Description vs. Experience Regenwetter RUM without Regularity Winer Memorial Lectures 2018 14 / 40
Context-Dependent Random Utility & Random Preference Context-Dependent Random Preference for DE Let R { D , E } denote a finite collection of pairs of binary preference relations of the form ( ≻ D , ≻ E ) , where x ≻ D y denotes that x is preferred to y in description x ≻ E y denotes that x is preferred to y in experience according to context-dependent preference pattern ( ≻ D , ≻ E ) ∈ R { D , E } . Regenwetter RUM without Regularity Winer Memorial Lectures 2018 15 / 40
Context-Dependent Random Utility & Random Preference Context-Dependent Random Preference for DE C ONTEXT - DEPENDENT RANDOM - PREFERENCE MODEL There is a probability distribution over R { D , E } such that � P D = P ( ≻ D , ≻ E ) , xy ( ≻ D , ≻ E ) ∈R{ D , E } s . t . x ≻ Dy and P E � = P ( ≻ D , ≻ E ) . xy ( ≻ D , ≻ E ) ∈R{ D , E } s . t . x ≻ E y Regenwetter RUM without Regularity Winer Memorial Lectures 2018 16 / 40
Context-Dependent Random Utility & Random Preference Random Preference Model Regenwetter RUM without Regularity Winer Memorial Lectures 2018 17 / 40
Recommend
More recommend
