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Measuring the impact of uncertainty resolution

Measuring the impact of uncertainty resolution. Mohammed Abdellaoui CNRS-GRID, ESTP & ENSAM, France Enrico Diecidue & Ayse Onçüler INSEAD, France. ESA conference, Roma, June 2007. Research question & motivations.

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Measuring the impact of uncertainty resolution

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  1. Measuring the impact of uncertainty resolution Mohammed Abdellaoui CNRS-GRID, ESTP & ENSAM, France Enrico Diecidue & Ayse OnçülerINSEAD, France ESA conference, Roma, June 2007

  2. Research question & motivations • How does the evaluation of prospects change when they are to be resolved in the future? Examples: • Lottery ticket to be drawn today versus in a month • End-of-year bonus as a stock option or cash • New product development • Medical tests

  3. Research question & motivations • Intuition: sooner rather than later uncertainty resolution is preferred. • Motivations: • i) value of perfect information cannot be negative (Raiffa 1968) • ii) psychological disutility for waiting (Wu 1999) • iii) opportunity for planning and budgeting.

  4. Related literature • Markowitz (1959), Mossin (1969), Kreps & Porteus (1978), Machina (1984), Segal (1990), Albrecht & Weber (1997), Smith (1998), Wakker (1999), Klibanoff & Ozdenoren (2007) • Wu (1999): • model for evaluating lotteries with delayed resolution of uncertainty. Model is rank-dependent utility with time dependent probability weighting functions.

  5. Background and notation • Interested in (x, p; y)tuncertainty resolved att in [0, T], (temporal prospects) • Outcomes received at T, expressed as changes wrt status quo • Prospects rank-ordered

  6. Background and notation (cont.) • Value of the temporal prospect (x, p; y)t wit(p)U(x) + (1-wit(p))U(y), where i = + for gains & i = - for losses. • The decision maker selects the temporal prospect that has the highest evaluation.

  7. Background and notation • Interested in 3 functions: wit(p) and U(·) • The utility function U reflects the desirability of outcomes and satisfies U(0) = 0. • Outcomes received at the same T, we consider the same utility function U. • Probability weighting functions strictly increasing satisfy w+t(0) = w-t(0) = 0w+t(1) = w-t(1) = 1 for all t in [0, T]. • The impact of uncertainty resolution at a resolution date t for an event of probability p can be quantified through the comparison of wit(p) and wi0(p).

  8. Background and notation • Preferences for two temporal prospects (either gain prospects or loss prospects) with common outcomes but different resolution dates depend only on the probabilities and resolution dates, and not the common outcomes. • The usefulness of this condition is also emphasized in Wu (1999, p. 172): “weak independence” and formulated as follows: if a temporal prospect (x, p; y)t is preferred to the temporal prospect (x, q; y)t’ for x > y > 0 [x < y < 0] then, for all x’ > y’ [x’ < y’ < 0], the prospect (x’, p; y’)t should be preferred to the prospect (x’, q; y’)t’.

  9. Measuring the impact of uncertainty resolution • 56 individual interviews, instructions, training sessions, random draw mechanism, hypothetical questions • Task: choice between two temporal prospects • Six iterations (i.e. choice questions) to obtain an indifference • Iterations generated by a bisection method. • Counterbalance; control for response errors: repeated the third choice question of all indifferences at the end of each step described in Table 1.

  10. The stimuli

  11. The stimuli

  12. The method: 4 steps

  13. On step 2 • U and w0+(.) known. • wT+(.) can be elicited from the indifferences (1000, i/6; 0)0 ~ (gi, i/6; 0)T, i = 1,…,5 • From these indifferences wT+(i/6) = w0+(i/6)[U(1000)/U(gi)], i = 1, …, 5.

  14. Results

  15. Results NS

  16. Results

  17. Results

  18. Results

  19. Results NS

  20. Results

  21. Results

  22. Conclusions • First individual elicitation of utility and pwf to understand the impact of delayed resolution: measured decision weights for immediate and delayed resolution of uncertainty • Observed temporal dimension of the uncertainty; pwf depends on the timing of resolution of uncertainty • Gains: detected difference for small probabilities • Losses: detected no significant difference • Found U for “more convex” (consistent with recent study by Noussair & Wu)

  23. end

  24. Roadmap • Research question + motivating examples • Measurement: method and results

  25. Remark • Transformation of probabilities is robust phenomenon in decision under risk • Kahneman & Tversky 1979 • Empirically: Inverse-S shape for probability weighting function • Abdellaoui 2000, • Bleichrodt & Pinto 2000, • Gonzalez & Wu 1999.

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