A graph-based model to discover preference structure from choice data

In this paper we demonstrate how to use graph matching to uncover heterogeneity in the structure of preferences across a population of decision-makers. We propose a novel nonparametric approach to formally capture the concept of preference structure using preference graphs, thereafter clustering decision-makers based on graph embedding methods. We explore the approach with simulated choice and empirical data from the most common classes of economic and psychological models. The approach uncovers heterogeneity in preference structure across a variety of dimensions, without requiring any prior knowledge of those structures.

[1]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[2]  R. Hertwig,et al.  The priority heuristic: making choices without trade-offs. , 2006, Psychological review.

[3]  Inês L. Azevedo,et al.  Labeling energy cost on light bulbs lowers implicit discount rates , 2014 .

[4]  H. Varian.  Non-parametric Tests of Consumer Behaviour , 1983 .

[5]  Ranjan Maitra,et al.  Merging K‐means with hierarchical clustering for identifying general‐shaped groups , 2017, Stat.

[6]  K. Small,et al.  Applied Welfare Economics with Discrete Choice Models , 1979 .

[7]  Daniel M. Oppenheimer,et al.  Heuristics made easy: an effort-reduction framework. , 2008, Psychological bulletin.

[8]  Geoffrey E. Hinton,et al.  Visualizing Data using t-SNE , 2008 .

[9]  W. Greene,et al.  计量经济分析 = Econometric analysis , 2009 .

[10]  M. Birnbaum,et al.  New Paradoxes of Risky Decision Making , 2022 .

[11]  Hong Qiao,et al.  A graph matching algorithm based on concavely regularized convex relaxation , 2014, Neurocomputing.

[12]  Vilfredo Pareto,et al.  Manuale di economia politica , 1965 .

[13]  Jordan J. Louviere,et al.  Modeling the choices of individual decision-makers by combining efficient choice experiment designs with extra preference information , 2008 .

[14]  P. Todd,et al.  Simple Heuristics That Make Us Smart , 1999 .

[15]  C. Lebiere,et al.  The Atomic Components of Thought , 1998 .

[16]  I. Erev,et al.  From Anomalies to Forecasts: Toward a Descriptive Model of Decisions Under Risk, Under Ambiguity, and From Experience , 2017, Psychological review.

[17]  J. Townsend,et al.  Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment. , 1993, Psychological review.

[18]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[19]  H. Simon,et al.  Rational Choice and the Structure , 1956 .

[20]  M. Birnbaum,et al.  Testing for intransitivity of preferences predicted by a lexicographic semi-order , 2007 .

[21]  Geoffrey E. Hinton.  Reducing the Dimensionality of Data with Neural , 2008 .

[22]  J. Bentham.  An Introduction to the Principles of Morals and Legislation , 1945, Princeton Readings in Political Thought.

[23]  Samuel J. Gershman,et al.  Computational rationality: A converging paradigm for intelligence in brains, minds, and machines , 2015, Science.

[24]  V S Ramachandran,et al.  Blind Spots , 2011, The American journal of bioethics : AJOB.

[25]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[26]  Lorenzo Livi,et al.  The graph matching problem , 2012, Pattern Analysis and Applications.

[27]  Daniel McFadden,et al.  Computing Willingness-to-Pay in Random Utility Models , 1996 .

[28]  John R. Anderson.  ACT: A simple theory of complex cognition. , 1996 .

[29]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[30]  H. M. Markowitz.  Approximating Expected Utility by a Function of Mean and Variance , 2016 .

[31]  John M. Rose,et al.  Applied Choice Analysis: Data set up for Nlogit , 2015 .

[32]  W. Torgerson.  Multidimensional scaling: I. Theory and method , 1952 .

[33]  Chandra R. Bhat,et al.  Modeling the choice continuum: an integrated model of residential location, auto ownership, bicycle ownership, and commute tour mode choice decisions , 2011 .

[34]  H. Simon,et al.  Skill in Chess , 1988 .

[35]  Robert L. Davis.  Structures of dominance relations , 1954 .

[36]  Hugo Larochelle,et al.  An Infinite Restricted Boltzmann Machine , 2015, Neural Computation.

[37]  K. Arrow,et al.  Social Choice and Individual Values , 1951 .

[38]  R. Ratcliff,et al.  Multialternative decision field theory: a dynamic connectionist model of decision making. , 2001, Psychological review.

[39]  Richard C. W. Kao,et al.  On a connection between factor analysis and multidimensional unfolding , 1960 .

[40]  Michel Regenwetter,et al.  Testing Transitivity of Preferences on Two-Alternative Forced Choice Data , 2010, Front. Psychology.

[41]  D. McFadden.  The Revealed Preferences of a Government Bureaucracy: Theory , 1975 .

[42]  Carey E. Priebe,et al.  Fast Approximate Quadratic Programming for Graph Matching , 2015, PloS one.

[43]  Eric J. Johnson,et al.  The adaptive decision maker , 1993 .

[44]  Jeremy J. Michalek,et al.  Will subsidies drive electric vehicle adoption? Measuring consumer preferences in the U.S. and China , 2015 .

[45]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[46]  Guillermo Sapiro,et al.  Graph Matching: Relax at Your Own Risk , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[47]  J. Neumann,et al.  Theory of Games and Economic Behavior. , 1945 .

[48]  D. McFadden.  The Revealed Preferences of a Government Bureaucracy: Empirical Evidence , 1976 .

[49]  H. Maturana,et al.  The Tree of Knowledge: The Biological Roots of Human Understanding , 2007 .

[50]  Y. Aflalo,et al.  On convex relaxation of graph isomorphism , 2015, Proceedings of the National Academy of Sciences.

[51]  Ajay Rana,et al.  K-means with Three different Distance Metrics , 2013 .

[52]  Hongxun Yao,et al.  Auto-encoder based dimensionality reduction , 2016, Neurocomputing.

[53]  Catherine L. Kling,et al.  Nonlinear Income Effects in Random Utility Models , 1999, Review of Economics and Statistics.

[54]  David A. Hensher,et al.  A latent class model for discrete choice analysis: contrasts with mixed logit , 2003 .

[55]  H. D. Block,et al.  Random Orderings and Stochastic Theories of Responses (1960) , 1959 .

[56]  M. Birnbaum,et al.  Organizational Behavior and Human Decision Processes Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence Generic Rank-dependent Utility Generic Analysis of Violations of Branch Independence and Distribution Independence Birnbaum and Mcintosh Model: N , 2022 .

[57]  H. Simon,et al.  Rational choice and the structure of the environment. , 1956, Psychological review.

[58]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[59]  Nick Chater,et al.  Salience driven value integration explains decision biases and preference reversal , 2012, Proceedings of the National Academy of Sciences.

[60]  Ali Ridho Barakbah,et al.  Hierarchical K-means: an algorithm for centroids initialization for K-means , 2007 .

[61]  Robert Tibshirani,et al.  Estimating the number of clusters in a data set via the gap statistic , 2000 .

[62]  A. Tversky.  Intransitivity of preferences. , 1969 .

[63]  P. Slovic,et al.  Reversals of preference between bids and choices in gambling decisions. , 1971 .

[64]  J. Payne,et al.  An overall probability of winning heuristic for complex risky decisions: Choice and eye fixation evidence , 2014 .

[65]  Baruch Fischhoff,et al.  Cognitive Processes in Stated Preference Methods , 2005 .

[66]  Полухина Полина Александровна.  Oxford English Dictionary online: подготовка к третьему изданию словаря на примере Updates 2016 , 2018 .

[67]  László Babai,et al.  Canonical labeling of graphs , 1983, STOC.

[68]  Geoffrey E. Hinton.  Training Products of Experts by Minimizing Contrastive Divergence , 2002, Neural Computation.

[69]  Kevin P. Murphy,et al.  Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.

[70]  H. Williams.  On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit , 1977 .

[71]  K. Train,et al.  Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level , 1998, Review of Economics and Statistics.

[72]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[73]  Peter C. Fishburn,et al.  A Study of Lexicographic Expected Utility , 1971 .

[74]  Alessandro Sperduti,et al.  A Preference Optimization Based Unifying Framework for Supervised Learning Problems , 2010, Preference Learning.

[75]  Denis Bouyssou,et al.  Binary Relations and Preference Modeling , 2010, Decision-making Process.

[76]  Kathleen M. Carley,et al.  Some Simple Algorithms for Structural Comparison , 2005, Comput. Math. Organ. Theory.