Individual Choice

1
Individual Choice

• Anomalies and Preference Functionals

2

• Judgment
• Allais paradox
• Violations of independence?
• Preference reversals
• Cognitive production and capital
• Decision theories

3
Readings

• Kagel and Roth, chapter 8 by Camerer
• Starmer, Chris, Developments in Non-Expected
  Utility Theory Developments in Non-Expected
  Utility Theory The Hunt for a Descriptive Theory
  of Choice under Risk, Journal of Economic
  Literature, XXXVIII, June 2000, 332382.
• Ballinger, T. Parker, and Wilcox, Nathaniel T.,
  Decisions, Error and Heterogeneity, Economic
  Journal, 107, July 1997, 1090-1105.
• Conlisk, John, Three Variants on the Allais
  Example, American Economic Review, 79(3), June
  1989, 392-407.
• Cox, James C., and Epstein, Seth, Preference
  Reversals Without the Independence Axiom,
  American Economic Review, 79(3), June 1989,
  408-426.
• Cubitt, Robin P. Starmer, Chris, and Sugden,
  Robert, Dynamic Choice and the Common Ratio
  Effect An Experimental Investigation, Economic
  Journal, 108, September 1998, 1362-1380.
• Harrison, Glenn W. Johnson, Eric McInnes,
  Melayne M., and Rutström, E. Elisabet,
  Individual Choice and Risk Aversion in the
  Laboratory A Reconsideration, Working Paper
  3-18, Department of Economics, College of
  Business Administration, University of Central
  Florida, 2003.
• Grether, David M., and Plott, Charles R.,
  Economic Theory of Choice and the Preference
  Reversal Phenomenon, American Economic Review,
  69(4), September 1979, 623-648.
• Hey, John D., Experimental Investigations of
  Errors in Decision Making Under Risk, European
  Economic Review, 39, 1995, 633-640.
• Holt, Charles A., Preference Reversals and the
  Independence Axiom, American Economic Review,
  76, 1986, 508-515.
• Loomes, Graham Starmer, Chris, and Sugden,
  Robert, Observing Violations of Transitivity by
  Experimental Methods, Econometrica, 59(2), March
  1991, 425-439.
• Loomes, Graham, and Sugden, Robert,
  Incorporating a Stochastic Element Into Decision
  Theories, European Economic Review, 39, 1995,
  641-648.
• Hey, John D., and Orme, Chris, Investigating
  Generalizations of Expected Utility Theory Using
  Experimental Data, Econometrica, 62(6), November
  1994, 1291-1326.
• Harless, David W., and Camerer, Colin F., The
  Predictive Utility of Generalized Expected
  Utility Theories, Econometrica, 62(6), November
  1994, 1251-1289.
• Decision Making Costs and Problem Solving
  Performance, (with Tanga M. McDaniel),
  Experimental Economics, 4, 2001, 145-161.
• Characterizing Cognitive Production Frontiers,
  (with Glenn W. Harrison and Richard Hofler),
  February 2006.

4
Judgment

• Probability judgments
• Many subjects are poorly calibrated
• They do not predict frequencies or probabilities
  well
• Overstate probabilities
• Overconfident in the stated probabilities
  (underestimate variation)
• Some, but not all, experts are well calibrated
• Most studies have not used an elicitation
  instrument that is incentive compatible like the
  scoring rule
• Critique these studies may suffer from sample
  selection bias in the tasks studied

5
Proper Scoring Rule

• An example of a popular incentive compatible
  belief elicitation mechanism
• You will be paid (2p-p2) if event happens
• You will be paid (1-p2) if event does not
  happen
• Show how truth telling (reporting the p you
  believe is the true one) maximizes payoffs

6
Bayesian Updating

• A cab was involved in a hit and run accident at
  night. Two cab companies, the Green and the Blue,
  operate in the city. You are given the following
  data
• A) 85 of the cabs in the city are Green and 15
  are Blue
• B) a witness identified the cab as Blue
• The court tested reliability of the witness under
  the same circumstances that existed on the night
  of the accident and concluded that the witness
  correctly identified each one of the two colors
  80 of the time and failed 20 of the time.
• What is the probability that the cab involved in
  the accident was Blue rather than Green?

7
Bayesian Updating

• P(XM) (P(MX)P(X)) / P(M)
• X is cab is blue
• M is observation is cab is blue
• P(X) P(is blue)0.15
• P(MX)P(report blue is blue) 0.80
• P(M)P(MX)P(X) P(MnX)P(nX)P(report blue)
  0.29
• P(XM)0.12/0.29 0.41
• Base rate neglect due to representativeness
  heuristic

8

• Linda is 31 years old, single, outspoken and very
  bright. She majored in philosophy. As a student,
  she was deeply concerned with issues of
  discrimination and social justice, and also
  participated in anti-nuclear demonstrations.
• Rank the following statements about Linda by
  their probability
• Linda is a teacher in elementary school
• Linda works in a bookstore and takes Yoga classes
• Linda is active in the feminist movement
• Linda is a psychiatric social worker
• Linda is a member of the League of Women Voters
• Linda is a bank teller
• Linda is an insurance salesperson
• Linda is a bank teller and is active in the
  feminist movement.

9
Conjunction Fallacy

• F Linda is active in the feminist movement
• T Linda is a bank teller
• FT Linda is a bank teller and is active in the
  feminist movement
• Also an example of representativeness heuristic

10
Wason problem

• Four cards are marked E K 4 7
• Each card has a letter on one side and a number
  on the other
• Rule If a card has a vowel on one side it has an
  even number on the other
• Which card(s) should be turned over to test the
  rule?
• Confirmation bias

11

• Judgment
• Allais paradox
• Violations of independence?
• Preference reversals
• Cognitive production and capital
• Decision theories

12
Expected Utility anomalies

• Preference axioms
• Completeness
• Transitivity
• Continuity
• Monotonicity
• Substitution/Independence
• Reduction

13
Allais paradox

• A1 (0.10), (0.66 2400) (0.33 2500)
• EV(A1) 2409
• Var(A1)2786
• B1 (1.0 2400)
• EV(B1)2400
• Var(B1)0
• Majority of people choose B1
• A2 (0.33 0) (0.34 2400) (0.33 2500)
• B2 (0.32 0) (0.68 2400)
• Majority of people choose A2

14
What is the paradox?

• Both A1 and A2 can be rewritten to show that they
  both contain the following lottery (assuming
  Reduction Axiom is fulfilled)
• A3 (1/66 0) (16/33 2400) (1/2 2500)
• A1 0.66A3 0.34B1
• A2 0.68A3 0.320
• Now compare these to B1 and B2
• A1 0.66A3 0.34B1
• B1 0.66B1 0.34B1
• Preference depends only on A3 and B1
  (Independence Axiom)
• A2 0.68A3 0.320
• B2 0.68B1 0.320
• Preference depends only on A3 and B1
  (Independence Axiom)
• Observed behavior (B1 A1 but A2 B2) is a
  violation of the independence axiom

15
Methodological issues in this literature

• Hypothetical choices
• Between vs within subject
• Within gives more statistical power
• May induce consistency
• Indifference
• Random error in expression
• Tests based on reliability
• Making the same choice twice observe proportion
  of switches
• Is violation rate significantly above such a
  switch rate?

16
HJMR

• Harrison, Glenn W. Johnson, Eric McInnes,
  Melayne M., and Rutström, E. Elisabet,
  Individual Choice and Risk Aversion in the
  Laboratory A Reconsideration, Working Paper
  3-18, Department of Economics, College of
  Business Administration, University of Central
  Florida, 2003
• Choice inconsistencies in lottery applications
• Common ratio and preference reversal lotteries
• Risk attitudes and recognition of indifference
• Can no longer reject EUT based on such choice
  inconsistencies

17
Experimental design

• Elicit risk attitudes of all subjects
• Observe choices for lotteries where, given the
  risk attitude, the subject should not be
  indifferent
• Imprecision in measures of risk attitudes
• A wider range of risk coefficients is consistent
  with indifference
• Lottery A .8U(30).2U(0) or Lottery B
  U(20)
• Lottery A 0.75(.8U(30).2U(0))
  0.25U(0)
• Lottery B 0.75U(20)0.25U(0)

18
Expected Value and Expected Utility

• Independent of risk attitude choice over A/B and
  A/B should be consistent
• Except if one allows decision errors that depend
  on relative valuations
• Assume U(x)x(1-r)/(1-r), where r0 is risk
  aversion, and r
• Certainty equivalents of the four lotteries as a
  function of r

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Indifference

• Around r0.5 all subjects are indifferent A/B and
  A/B
• As r is increasing the difference in CEs between
  A and B become very small
• r0.5, pennies

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How did we elicit risk attitudes?

• Holt and Laury (2002)
• Multiple Price List

23
So if we want to test EUT

• With these subjects we need a different set of
  lotteries
• That generate larger CE differences
• We find these lotteries in Grether and Plott
  (1979) Preference Reversal paper
• We do not compare subjects choice between binary
  choice and pricing
• We simply predict their choices for each lottery,
  given their risk attitude, and compare to their
  actual to their predicted choice

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26

• Judgment
• Allais paradox
• Preference reversals
• Cognitive production and capital
• Decision theories

27
Preference Reversal

• Choice over lotteries vs. pricing of lotteries
• P-bet .99 win 4, .01 lose 1 EV3.95
  VAR0.0895
• -bet .33 win 16, .67 lose 2 EV3.94
  VAR50.518
• P-bet chosen over -bet 50 of the time
• -bets are priced higher than P-bets when selling
  the bets

28
Intransitivity interpretation

• Asymmetric reversal
• P bets preferred to bets 50 of the time
• bets selling prices are higher than selling
  prices for P bets
• Set WTAi to a value between those stated for
  and P bets
• bet WTAi (based on pricing task)
• WTAi P bet (based on pricing task)
• But P bet bet

29
Independence interpretation

• Since elicitation done using compound lotteries
• Pricing gambles using BDM
• Random lottery procedures
• These reversals can be explained by violation of
  independence rendering these elicited preferences
  invalid

30
Independence violation

• Independence axiom
• If X Y
• Then pX (1-p)Z pY (1p)Z
• In RLS p is the probability that this task is
  selected
• In BDM p is the probability that the randomly
  drawn value is the stated WTA

31
Initial findings

• Lichtenstein and Slovic (1971, 1973)
• Hypothetical
• Procedural invariance
• Intransitive preferences
• Grether and Plott (1979)
• Incentives
• BDM procedure
• Verified reversal pattern

32
Preference Reversal

• Holt (1986) and Karni and Safra (1987)
• PR can be explained by violations of the
  independence axiom because Random Lottery
  Selection was used
• Even in absence of RLS, Becker-deGroot-Marshak
  use for pricing task assumes independence
• Violation of transitivity is a more serious
  violation than that of independence
• Segal (1988)
• PR can be explained by violations of the
  reduction principle

33
Reduction violations

• Compound form lottery
• 0.750 .253000
• .750 .25(.84000 .20)
• Reduced form lottery
• .750 .253000
• .800 .204000
• Isolate and ignore the common part
• Independence has been less of a problem when
  reduction is violated in this way
• Thus, if reduction is violated in BDM perhaps the
  mechanism works well because independence is not
  violated

34
Notes on Starmer and Sugden 1991

• They show that the reduction axiom is violated
• Thus Holts proof that Random Lottery Procedures
  are not demand revealing does not apply
• Thus the criticism of using BDM in PR experiments
  does not apply
• Starmer and Sugdens results show that reduction
  axiom is violated and thus EUT
• Valid preferences could still be based on
  combination of substitution, monotonicity and
  transitivity axioms
• Observations consistent with PR in non-BDM and
  non-RLS environments show that it is not only
  reduction axiom that is violated perhaps
  substitution?

35
Counter arguments to the blaming of BDM

• BDM is proven to fail only if independence is
  violated but reduction is obeyed
• BDM may work well if reduction is violated
• Same reversals are also observed when using other
  elicitation methods
• Safra, Segal, and Spivak (1990a, 1990b)
• Two testable implications of BDM failure have
  been rejected
• Same proportion of reversals observed for
  subjects who do not fan out as for those who do
  (McDonald, Huth, and Taube (1991))
• Selling Price and Certainty Equivalent do not
  always lie on same side of EV (Keller, Segal, and
  Wang (1993))

36
Conclusion

• So it seems reduction is violated by isolation
• Thus perhaps BDM (and Random Lottery Procedure)
  is demand revealing after all
• No final answer here yet

37
The literature and where it was published

• Lichtenstein and Slovic (1971)
• Journal of Experimental Psychology
• Lichtenstein and Slovic (1973) Las Vegas
  experiments
• Journal of Experimental Psychology
• Grether and Plott (1979) AER
• Schneider and Zweifel (1982) AER
• Reilly (1982) AER
• Berg, Daley, Dickhaut and OBrien (1985)Research
  in Experimental Economics vol 3
• Loomes and Sugden (1983) regret theory and
  preference reversals
• Economic Journal
• Holt (1986)
• AER
• Karni and Safra (1987)
• hEconometrica

38
Recent evidence

• Wedell and Bockenholt (1992)
• Reversals disappear when choosing over portfolios
  of gambles played repeatedly (?)
• Irwin et al. (1993)
• Journal of Risk and Uncertainty
• Opposite pattern of reversals observed in gambles
  over real losses
• McDonald, Huth, and Taube (1991) JEBO
• Casey (1991) Organizational Behavior and Human
  Decision Processes
• Casey (1994) Management Science
• Cox and Epstein (1989) AER
• Avoided BDM, value and P bets, then compare
  ranking of valuations with pairwise choices

39

• Tversky, Slovic, and Kahneman (1990) AER
• Procedure invariance over-pricing of -bet
  organizes data better than intransitivity
• Using a Dichotomous Choice DC design
• Cox and Grether (1991)
• Economic Theory
• Replicates this
• Loomes, Starmer, and Sugden (1989, 1991)
• Economic Journal, Econometrica
• Dispute these results more evidence of
  intransitivities using similar DC design
• Loomes and Taylor (1992) Economic Journal
• More evidence of procedural invariance rather
  than intransitivities
• Bostic, Herrnstein, and Luce (1990) JEBO
• Loomes (1991c) Oxford Economic Papers
• Process evidence
• Schkade and Johnson (1989) traced information
  search, Organizational Behavior and Human
  Decision Processes
• Johnson, Payne, and Bettman (1988) made
  calculating probabilities harder, Organizational
  Behavior and Human Decision Processes

40
Summary of recent evidence

• Support for Slovic and Lichtenstein
• Weight attached to a dimension (consequence or
  probability) increases when dimension is
  psychologically compatible with the response mode
• Choice probability
• Price consequence

41
New approaches

• What does it take to make subjects stop
  displaying reversals?

42
Arbitrage

• Chu and Chu (1990) AER
• money pump
• Going through the steps of switches and trades to
  make subject end with same bet but having lost
  money
• Stated preferences P-bet over -bet in choice but
  c() c(P)
• Sell - bet to subjects for c() their stated
  valuation
• Allow them to switch to P-bet according to stated
  choice preferences
• Buy the P-bet for c(P)
• Subject ends up holding neither P- nor -bet as
  before but has given up c() c(P) and is worse
  off
• Berg, Daley, Dickhaut and O-Brien (1985)
• Research in Experimental Economics

43
Incentives

• Bohm (1994)
• Empirical Economics
• cars
• Harrison (1994)
• Empirical Economics
• Increased expected value difference
• Berg, Dickhaut and Rietz (2003)
• Journal of Risk and Uncertainty
• Error-rate model testing
• Different errors in choice expression and pricing
  allowed

44
Markets

• Knez and Smith (1987)
• Between period trading of the bets
• Cox and Grether (1991)
• BDM, Vickrey, English
• Asymmetric reversals disappeared in English
• Bids are correlated with last market price

45
Summary

• Increased incentives
• Lower error rates but do not always remove
  reversals
• Arbitrage
• Reduces magnitude but not frequency of reversals
• Trading bets
• Reduce reversals
• Procedural invariance violations
• Should we model preferences as varying with
  procedures?
• What happens to our ability to do comparative
  statics if we allow preferences to be procedure
  contingent?
• State contingent preferences
• Alternative perception of opportunities may be
  varying with procedures

46

• Judgment
• Allais paradox
• Preference reversals
• Cognitive production and capital
• Decision theories

47
Cognitive Production and Capital

• Camerer and Hogarth (1999), The effects of
  financial incentives in experiments A review and
  capital-labor-production framework, Journal of
  Risk and Uncertainty
• Feldman Barrett, Tugade, and Engle (2004),
  Individual Differences in Working Memory Capacity
  and Dual-Process Theories of Mind, Psychological
  Bulletin
• Harrison, Hofler, and Rutstrom, Characterizing
  Cognitive Production Frontiers (ongoing research
  project)
• McDaniel and Rutstrom (2001), Decision Making
  Costs and Problem Solving Performance,
  Experimental Economics.

48
Financial Incentives and Cognitive Capital

• Camerer and Hogarth (1999)
• Procedural knowledge as cognitive capital
• Not just effort (labor) in cognitive production
• Incentived improve mean performance
• Incentives hurt mean performance
• Incentives do not hurt mean behavior
• Incentives do not hurt mean performance
• Incentives affect behavior, but no performance
  standard
• Incentive effects are confounded with effects of
  other treatments

49
Cognitive capital

• Experience with task in the lab
• Contextual labeling of actions or consequences
• Triggers use of field heuristics
• Cognitive capital generated in the lab is often
  task specific and does not transfer to other
  tasks

50
Relationship between cognitive capital and
incentives

• Experience and incentives are often substitutable
• Feedback and incentives like wise
• Instruction on optimal responses as well

51
Incentive effects

• Strongest in moderately easy tasks that are
  effort responsive
• Judgment, prediction, problem solving, recall,
  clerical
• If tasks are very easy performance will not be
  affected by incentives
• Variance is often reduced in
• Auctions, games, risky choices
• These tasks may be too difficult to generally
  generate performance improvement from incentives

52
Working memory capacity and dual-process theories
of Mind

• Two types of cognitive processes
• Automatic
• Attention based
• If automatic processes lead to conflicting
  evaluations
• Need for attention is triggered
• The ability to trigger and control attention may
  be related to working memory capacity

53
Working Memory Capacity task

• Read and recall lists of words
• While working on arithmetic task
• 6/3 14 -12? curve
• 49/7 10 19? file
• 28/7 8 -5? dance
• 27/3 11 2? dust
• 15/3 14 -9? guy

54
Recall the 5 words
55
Cognitive Reflection Test
56

• A bat and a ball cost 1.10. The bat cost 1 more
  than the ball. How much does the ball cost?

57

• If it takes 5 machines 5 minutes to make 5
  widges, how long would it take 100 machines to
  make 100 widgets?

58

• In a lake there is a patch of lily pads. Every
  day the patch doubles in size. If it takes 48
  days for the patch to cover the entire lake, how
  long would it take for the patch to cover half
  the lake?

59

• Judgment
• Allais paradox
• Preference reversals
• Cognitive production and capital
• Decision theories

60
Various Decision Theories

• Hey, John D., and Orme, Chris, Investigating
  Generalizations of Expected Utility Theory Using
  Experimental Data, Econometrica, 62(6), November
  1994, 1291-1326.

61
Hey and Orme

• 100 Circles pairwise lottery choices
• Include a Dont care option for indifference
• Cannot rule out that Left or Right still reflect
  indifference
• 4 sets of 25 questions
• Prizes 0, 10, 20, 30
• Models will be estimated for each subject
  individually based on the 100 observations

62
Models estimated
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Estimation

• Theory is deterministic
• Pick L, R, or Indifferent with p1 or 0
• Incorporate some error
• VVe
• Recognize that some models are nested
• Risk neutral is a special case of Expected
  Utility (and Yaari Dual)
• Expected Utility and Yaari are special cases of
  all the others
• Nested tests based on testing the parameter
  restrictions required for the special cases

66

• Risk neutrality is rejected for majority of
  subjects
• About 85 reject RN in favor of EUT
• Heterogeneity
• Reject EUT in favor of more general model for
  almost 60 of subjects

67
Mixture models

• Expected Utility Theory and Prospect Theory A
  Wedding and a Decent Funeral
• Pairwise lottery choices
• Hey-Orme lotteries
• EUT assuming CRRA
• U(sx)(sx)r
• EU?piu(sxi)
• Stochastic property added using logistic function
• ?(EU(R)-EU(L))e(EU(R)-EU(L))/(1e(EU(R)-EU(L)))
• Prospect Theory
• U(x)xa for x0 and U(x)-?(-x)ß
• W(p)p?/(p?(1-p)?)
• PT ?w(p)U(x)
• Logistic function
• Mixing probability p
• ln L(r, a, ß, ?, ?, pEUT y,X) ?i ln (pEUT
  l iEUT ) (pPT l iPT )