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Patience and time consistency in collective decisions

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Abstract

We present experimental evidence regarding individual and group decisions over time. Static and longitudinal methods are combined to test four conditions on time preferences: impatience, stationarity, age independence, and dynamic consistency. Decision making in groups should favor coordination via communication about voting intentions. We find that individuals are neither patient nor consistent, that groups are both patient and highly consistent, and that information exchange between participants helps groups converge to stable decisions. Finally we provide additional evidence showing that our results are driven by the specific role of groups and not by either repeated choices or individual preferences when choosing for other subjects.

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Notes

  1. Meier and Sprenger (2015) also report non-negligible time-variations in experimental measures.

  2. We could not completely rule out wealth effects. For individuals who are paid for real at \(\ell + \Delta \), those previous gains might have affected behavior in Session 3. Since only three subjects met this condition, it is reasonable to assume that wealth effects did not bias our results.

  3. That axiomatization is based on five axioms—three technical conditions (continuity, sensitivity and boundedness), stationarity and an independence axiom—applied to time sequences (non-complementarity). Bleichrodt et al. (2008) clarify Koopmans’ axioms, especially independence and stationarity, and propose a clean and complete preference axiomatization of discounted utility.

  4. In the discounted utility model, violations of stationarity are not compatible with an exponential discount function; hence they are represented by a wide range of alternative discount functions. Of these, the most widely used are hyperbolic discount functions (Phelps and Pollak 1968; Loewenstein and Prelec 1992). Yet violations of stationarity can be accommodated also by nonhyperbolic discount functions (Bleichrodt et al. 2009), which can more flexibly incorporate increasing impatience.

  5. Our “stationarity” is their “cross-sectional time consistency”.

  6. For example, age independence is violated by a man who prefers one apple on his 21st birthday to two apples the day after but in all other situations prefers two apples a day later. Such a decision maker exhibits dynamic consistency but not stationarity.

  7. The tables in Appendix 1 show the values of the indexes of stationarity, age independence, and dynamic consistency for both individuals and groups (and their significance levels).

  8. Two subjects dropped out after session 1 and two more after session 2. The resultant missing data precluded our simulating a utilitarian criterion for three of the groups, which is why the simulation results are given only for nine of the twelve groups.

  9. With regard to one of Session 1’s three tasks (viz., elicitation of \(x_1^3\)), we found that group decisions were more patient than individual decisions (\(p=0.04\)).

  10. Giné et al. (2014) find that 50 % of the choices satisfy stationarity and 35 % satisfy dynamic consistency. In Study 1 of Sayman and Öncüler (2009), the authors find no evidence favoring time inconsistency: 58 % of the choices were dynamically consistent. Halevy (2015) report that 48 % of time-consistent subjects and 56 % of all subjects exhibit stationary preferences.

  11. Rather than voting on a common decision, subjects could have coordinated on a sharing rule (Millner and Heal 2014). Because this alternative mechanism did not allowed for direct comparisons between individual and collective preferences, we opted for a political (voting) approach.

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Authors and Affiliations

  1. University Rennes 1 - CREM, Place Hoche, Rennes, France

    Laurent Denant-Boemont & Olivier l’Haridon

  2. INSEAD, Boulevard de Constance, Fontainebleau, France

    Enrico Diecidue

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  1. Laurent Denant-Boemont
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  2. Enrico Diecidue
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  3. Olivier l’Haridon
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Correspondence to Laurent Denant-Boemont.

Additional information

We thank Aurelien Baillon, Nicolas Houy, Vincent Merlin, Amnon Rapoport, Jeeva Somasundaram, Karine Van Der Straeten, Marie-Claire Villeval, Peter Wakker, the editor of this journal as well as two anonymous referees for helpful comments. We also thank Elven Priour for programming the script and organizing the sessions.

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Appendices

Appendix 1: Indexes

This appendix reports values of the indexes of violation of stationarity (Tables 4, 5, 6), dynamic consistency (Fig. 4), and age independence (Fig. 5).

Table 4 Violations of stationarity for individuals and groups
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Table 5 Violations of dynamic consistency and age independence for individuals and groups
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Table 6 Violations of stationarity, age independence and dynamic consistency—utilitarian criterion based on the sum of individual values
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Appendix 2: Results for the additional treatments

For the Repetition treatment, a decision maker was classified as impatient (resp. patient) if at least four of six indifference values yielded an impatient (resp. patient) answer; otherwise, the decision maker was classified as mixed. For the remaining additional treatments (Voting treatment, Informed planner treatment, Uninformed planner treatment), a decision maker was classified as impatient (patient) if at least two out of three indifference values yielded an impatient (patient) answer. The classifications are presented in Table 7. Tables 8, 9, 10 and 11 report additional results on stationarity, dynamic consistency, age independence, shape of impatience and distance to individual preferences.

Table 7 Classification of answers under the additional treatments
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Table 8 Violations of stationarity
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Table 9 Violations of dynamic consistency and age independence in the repeated treatment
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Table 10 Classification of individuals and groups by shape of impatience
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Table 11 Distance to individual preferences
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Denant-Boemont, L., Diecidue, E. & l’Haridon, O. Patience and time consistency in collective decisions. Exp Econ 20, 181–208 (2017). https://doi.org/10.1007/s10683-016-9481-4

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