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Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications

Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications. Cambridge University Press, 2006 with B. Grofman, A.A.J. Marley, I. Tsetlin. Michel Regenwetter Quantitative Division Department of Psychology (& Department of Political Science)

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Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications

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  1. Behavioral Social Choice:Probabilistic Models, Statistical Inference, and Applications Cambridge University Press, 2006with B. Grofman, A.A.J. Marley, I. Tsetlin Michel Regenwetter Quantitative Division Department of Psychology (& Department of Political Science) University of Illinois at Urbana-Champaign

  2. Overview • Motivation: 2 Conceptual Distinctions in the Decision Sciences Criteria for a Unified Theory of Decision Making • Social Choice Theory: Majority Rule (Condorcet Criterion), Arrow The Obsession with Majority Cycles Need for Behavioral Social Choice Research • Behavioral Social Choice Research Multiple Representations of Preference/Utility A General Concept of Majority Rule Model Dependence of Majority Outcomes The Problem of Incorrect Majority Outcomes

  3. 2 Conceptual Distinctions in the Decision Sciences Normative Theory Descriptive Theory & Data Individual Judgment and Decision Making Behavioral Decision Research Social Choice

  4. 2 Conceptual Distinctions in the Decision Sciences Normative Theory Descriptive Theory & Data Individual Judgment and Decision Making Social Choice ??? ???

  5. 2 Conceptual Distinctions in the Decision Sciences Normative Theory Descriptive Theory & Data Individual Judgment and Decision Making ??? Social Choice

  6. Criteria for a Unified Theory of Decision Making (Inspired by Luce and Suppes, Handbook of Mathematical Psych.,1965) • Treat individual & group decision making in a unified way • Reconcile normative & descriptive work • Integrate & compare competing normative benchmarks • Reconcile theory & data • Encompass & integrate multiple choice, rating and ranking paradigms • Integrate & compare multiple representations of preference, utilities & choices • Develop dynamic models as extensions of static models • Systematically incorporate statistics as a scientific decision making apparatus

  7. Overview • Motivation: • 2 Conceptual Distinctions in the Decision Sciences • Criteria for a Unified Theory of Decision Making • Social Choice Theory: Majority Rule (Condorcet Criterion), Arrow The Obsession with Majority Cycles Need for Behavioral Social Choice Research • Behavioral Social Choice Research Multiple Representations of Preference/Utility A General Concept of Majority Rule Model Dependence of Majority Outcomes The Problem of Incorrect Majority Outcomes

  8. Majority rule: (Condorcet Criterion) • Majority Winner • Candidate who is ranked ahead of any other • candidate by more than 50% • Candidate who beats any other candidate • in pairwise competition

  9. Kenneth Arrow’s (1951)Nobel Prize winning Impossibility Theorem • List of Axioms of Rationality • Impossibility to simultaneously satisfy all Axioms • For instance: Majority permits “cycles”. • Democratic Decision Making Impossible?

  10. The Obsession with Cycles

  11. Majority Cycles ABC 1 person BCA 1 person CAB 1 person

  12. Majority Cycles ABC 1 person A beats B 2 times BCA 1 person B beats A 1 time CAB 1 person A is majority preferred to B

  13. Majority Cycles ABC 1 person B beats C 2 times BCA 1 person C beats B 1 time CAB 1 person A is majority preferred to B B is majority preferred to C

  14. Majority Cycles ABC 1 person A beats C 1 time BCA 1 person C beats A 2 times CAB 1 person A is majority preferred to B B is majority preferred to C C is majority preferred to A

  15. Majority Cycles ABC 1 person Democratic Decision Making at Risk!?! BCA 1 person CAB 1 person A is majority preferred to B B is majority preferred to C C is majority preferred to A

  16. State of the Art: Shepsle et al. 1997

  17. State of the Art: Shepsle et al. 1997

  18. State of the Art: Shepsle et al. 1997

  19. State of the Art: Shepsle et al. 1997

  20. State of the Art: Shepsle et al. 1997 GIGO?

  21. Shepsle & Bonchek (1997) “In general, then, we cannot rely on the method of majority rule to produce a coherent sense of what the group ‘wants’, especially if there are no institutional mechanisms for keeping participation restricted (thereby keeping n small) or weeding out some of the alternatives (thereby keeping m small).”

  22. $1,000,000 Question: Oops…. Little evidence that majority cycles have occurred among serious contenders of major elections. Where is the empirical evidence for the Concorcet paradox in practice? Actually, evidence circumstantial at best.

  23. Where is the evidence for cycles? • Majority Winner • Candidate who is ranked ahead of any other candidate by more than 50% • Candidate who beats any other candidate in pairwise competition • Plurality: Choose one • SNTV & Limited Vote: Choose k many • Approval Voting: Choose any subset • STV (Hare), AV (IRV): Rank top k many • Cumulative Voting: Give m pts to k many • Survey Data: Thermometer, Likert Scales Data are incomplete!!

  24. Need for “Behavioral Social Choice Research”: • Real world ballot or survey data hardly ever take the form of (deterministic) linear orders. • Social choice concepts are defined in terms of theoretical primitives that are not directly observed in social choice behavior. • We need to bridge this gap in order to study social choice theoretical concepts empirically.

  25. Overview • Motivation: • 2 Conceptual Distinctions in the Decision Sciences • Criteria for a Unified Theory of Decision Making • Social Choice Theory: • Majority Rule (Condorcet Criterion), Arrow • The Obsession with Majority Cycles • Need for Behavioral Social Choice Research • Behavioral Social Choice Research Multiple Representations of Preference/Utility A General Concept of Majority Rule Model Dependence of Majority Outcomes The Problem of Incorrect Majority Outcomes

  26. Binary Preference Relations A binary relation R on a set of objects C is a collection of ordered pairs of elements of C

  27. A General Concept of Majority Rule Linear Orders “complete rankings” Weak Orders “rankings with possible ties” Semiorders “rankings with (fixed) threshold” Interval Orders “rankings with (variable) threshold” Partial Orders asymmetric, transitive Asymmetric Binary Relations

  28. B Real Representation of Linear Orders a | b | c | d 42 | 5 | 2 | 1

  29. B Real Representation of Weak Orders a b | c | d 7 7 | 3 | 1

  30. B Real Representation of Semiorders a b c | d 3 1.9 1.8 | 1.8

  31. Variable/Uncertain Preferences: Probability Distribution on Binary Relations Variable/Uncertain Utilities: Jointly Distributed Family of Utility Random Variables (Random Utilities) (parametric or nonparametric)

  32. Random Utility Representations Linear Orders Weak Orders (Block and Marschak, 1960, chapter)

  33. Random Utility Representations Semiorders Interval Orders (Heyer & Niederee, 1992, MSS) (Niederee & Heyer, 1997, Luce vol.) (Regenwetter, 1997, JMP) (Regenwetter & Marley, 2002, JMP)

  34. A General Definitionof Majority Rule

  35. A General Definitionof Majority Rule For Utility Functions or Random Utility Models choose a Random Utility Representation and obtain a consistent Definition

  36. Examples:

  37. $1,000,000 Question: Oops…. Little evidence that majority cycles have occurred among serious contenders of major elections. Where is the empirical evidence for the Concorcet paradox in practice? Actually, evidence circumstantial at best.

  38. Let’s analyze National Survey Data! 1968, 1980, 1992, 1996 ANES Feeling Thermometer Ratings translated into Weak Orders or Semiorders

  39. .03 H W N 1968 NES Weak Order Probabilities .04 0 H W N H W N H N W .02 W H N .32 H N W W H N .03 .08 .02 N H W W N H .06 N H W W N H .27 N W H .05 .01 No impartial culture! .07

  40. .03 H W N 1968 NES Weak Order Probabilities .04 0 H W N H W N H N W .02 W H N .32 H N W W H N .03 .08 .02 N H W W N H .06 N H W W N H .27 N W H .05 .01 No impartial culture! .07

  41. a b c a versus b a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  42. a b c a versus c a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  43. a b c b versus c a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  44. a b c Sen’s NB(a) a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  45. a b c Net NB(a) a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  46. a b c Generalized Net NB(a) a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  47. Sen’s NM(a) a b c a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  48. a b c Net NM(a) a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  49. a b c Generalized Net NM(a) a b c a b c a c b a c b a c b c a b a c b b a c c b b a c a b b c a c a c a b b c a c b a

  50. .03 (-.04) H W N ANES 1968 .04 (.03) 0 (-.05) H W N H W N H N W W H N .02 (.-25) .32 (.26) .03 (-.05) H N W W H N .08 (.05) .02 (0) N H W W N H .06 (-.26) .27 (.25) N H W W N H N W H .01 (-.03) .05 (.05) .07 (.04)

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