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Sequential Expected Utility Theory: Sequential Sampling in Economic Decision Making under Risk

University of Warwick, April 2012. Sequential Expected Utility Theory: Sequential Sampling in Economic Decision Making under Risk. Andrea Isoni (Warwick) Graham Loomes ( Warwick ) Daniel Navarro-Martinez (LSE). Introduction.

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Sequential Expected Utility Theory: Sequential Sampling in Economic Decision Making under Risk

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  1. University of Warwick, April 2012 Sequential Expected Utility Theory: Sequential Sampling in Economic Decision Making under Risk • Andrea Isoni(Warwick) • Graham Loomes(Warwick) • Daniel Navarro-Martinez(LSE)

  2. Introduction • Modern economics is largely silent about decision making processes (e.g., EUT, PT) • Psychologists have dedicated substantial efforts to study decision processes • Psychological process models: Decision Field Theory, Decision by Sampling, Query Theory, Elimination by Aspects, Priority Heuristic • Some of the models/evidence suggest the idea of a deliberation process • Sequential sampling models (e.g., Decision Field Theory, Decision by Sampling) • Explain decision times (e.g., decision time decreases significantly as choice probability approaches certainty) • Virtually all economic decision models are silent about deliberation processes and decision times

  3. Introduction • In this paper: We take EUT and introduce in it the idea of sequential sampling (deliberation). We show what such a model can do. We investigate experimentally some aspects of it. • Similarity to Decision Field Theory • Presentation: • Explain the Sequential EUT model • Illustrate its implications (simulation) • Show some experimental evidence

  4. The Model: Sequential EUT • Binary choice • Based on a random preference EUT specification:

  5. Introducing sequential sampling • People sample repeatedly from the choice options to accumulate evidence, until it is judged to be enough to make a choice • Usecertainty equivalent (CE) differences: • After each sample, individuals conduct a sort of internal test of the null hypothesis that D(L1, L2) is zero • If the hypothesis is not rejected, sampling goes on; if it’s rejected, sampling stops and the individual chooses the favoured option

  6. Introducing sequential sampling • After each sample k, an evidence statistic Ek is computed: • The null hypothesis of zero difference is rejected if: • Essentially a sequential two-tailed t-test of the null hypothesis that the difference in value between the options is zero • Sampling is psychologically costly, so CONF decreases with sampling: • We assume C = 1 • Only one additional free parameter (d)

  7. The model constructs • The model can address4 main behavioural constructs: • Choice probabilities: , probability that the null hypothesis is rejected with Ek > 0 instead of Ek < 0 • Response times (RTs): Increasing function of the samples taken to reach the threshold (n) and the number of outcomes: • Confidence (CONF): The desired level of confidence in the last test • Strength of preference (SoP): Absolute value of the average CE difference sampled:

  8. Illustration of the model’s implications • Simulation (50,000 runs per choice) • Three main aspects: • Comparing a risky lottery to an increasing sequence of sure amounts • Effects of changes in the three free parameters (α, β, d) • Behaviour in specific lottery structures (dominance, deviations from EUT)

  9. Increasing sure amount • Choosing between a fixed lottery and a series of monotonically increasing amounts of money

  10. Changing the free parameters (1) • Changing the location of the distribution of risk aversion coefficients (α)

  11. Changing the free parameters (2) • Changing the range of the distribution of risk aversion coefficients (β)

  12. Changing the free parameters (3) • Changing the confidence level decrease rate(d)

  13. Specific lottery structures • Dominance (α = 0.24, β = 1.00, d = 0.05)

  14. Specific lottery structures • Deviations from EUT (common ratio and common consequence effects) • Kahneman and Tversky (1979) • Common ratio (α = 0.24, β = 1.00, d = 0.05) • Common consequence (α = 0.26, β = 1.00, d = 0.05)

  15. Distribution of CE differences

  16. Experimental evidence • Focus on one experiment: 44 students, University of Warwick • Focus on subset of choice structures: • Common ratio • Dominance • 4 different tasks: • Binary choice (with response times) • Confidence • Strength of preference • Monetary strength of preference

  17. The choices • Common ratio: • Dominance:

  18. The tasks (1)

  19. The tasks (2)

  20. The tasks (3)

  21. The tasks (4)

  22. Results • Common ratio: • Dominance:

  23. Parameters α:0.27 β: 1.18 d:0.05

  24. Conclusions • We have introduced sequential sampling (deliberation) in a standard economic decision model (Sequential EUT) • Just one additional parameter • Can explain important deviations from EUT, by simply assuming that people sample sequentially from EUT • Makes predictions about additional behavioural measures related to deliberation (response times, confidence) • Experimental evidence shows that these measures follow quite systematic patterns • Sequential EUT can explain most of the patterns obtained • Potential to be extended to other economic decision models, and other types of tasks (e.g., CE valuation, multi-alternative choice)

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