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Deciding about human lives: an experimental measure of risk attitudes under prospect theory

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Abstract

For public policies in the health, security or safety domains, the main consequences concern the number of human lives that are saved or lost, and are uncertain ex-ante. In classic economic evaluations of such policies, losses and gains of human lives are often monetized and aggregated with other costs and benefits. Uncertainty about human lives is thus treated as uncertainty about monetary consequences. In this paper, we question whether people risk human lives as they risk money. We present an experiment comparing risk attitudes towards human lives and towards money under prospect theory. The results show that respondents treat the two attributes differently when losses are involved. Specifically, the decisions involving human lives are characterized by less elevated probability weighting in the loss domain and higher loss aversion compared to decisions involving money. These findings suggest that public preferences may differ from the cost-benefit analysis recommendations.

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Notes

  1. The trade-off method measures the utility function through a series of successive trade-offs between the consequences of risky prospects. The aim is to build a standard sequence of consequences \(x_{1},x_{2},x_{3},\ldots ,x_{n}\) that are equally spaced in terms of utility: \(u(x_{n})-u(x_{n-1})=\ldots =u(x_{2})-u(x_{1})\). This method allows neutralizing the impact of probability weighting in the measure of the utility, which makes it compatible with PT. Note however that the method is sequential, and not robust to error propagation. A complete description of the method is provided in Wakker and Deneffe (1996).

  2. Several terms are used in the literature to designate probability distributions over gains and losses of human lives. For example, Fishburn and Straffin (1989) mention “group fatality profile”, “probability distribution over fatalities” or “lottery on total fatalities”. Bernard et al. (2015) use “distribution of fatalities”.

  3. Asking subjects to play the role of social decision makers is not unusual in this type of study. See for instance Fetherstonhaugh et al. (1997), Subramanian and Cropper (2000) and Rheinberger (2010).

  4. For decision experiments involving monetary amounts, real incentive procedures are sometimes implemented. In this study, the preference measurement method was incentive compatible; however, given the nature of the consequences under study, the choices were hypothetical.

  5. The bisection method was used to assess indifference values, through a series of binary choices that aim at reducing successively the interval containing the indifference value. In our experiment, the process started with a choice between a lottery and its expected value. If the expected value was selected (rejected), a lower (higher) value was proposed in the next iteration. The process was iterated until the CE was measured with a precision of 5 units. The bisection method has been used by, among others, Abdellaoui et al. (2008) who present a complete example in their appendix.

  6. Comparing the certainty equivalent CE with the expected value EV characterizes the risk attitude of the decision maker. A CE below (above) EV reflects risk aversion (risk seeking), while a CE equal to EV reflects risk neutrality.

  7. When measures consist of indifference values, the amplitude of behavioral errors can depend on the characteristics of the stimuli (Bruhin et al. 2010). To account for this possible source of heteroscedasticity, we allowed the standard deviation of errors \(\sigma \) to depend on the lotteries. More precisely, we considered the specification \(\sigma =\sigma _{d}|x-y|^{h}\) with \(d\in \{+,-\}\) for certainty equivalents, and \(\sigma =\sigma _{m}|x|^{h}\) for mixed lotteries. Therefore, the variance of errors was allowed to vary across domains (gains, losses, mixed) and to depend on the characteristics of the lotteries when \(h>0\). To account for heteroscedasticity between subjects, we assumed that \(log(\sigma _{t})\sim N(\bar{\sigma _{t}},\theta _{\sigma })\), with \(t\in \{+,-,m\}\). This specification encompasses the homoscedastic case when \(\bar{\sigma _{+}}=\bar{\sigma _{-}}=\bar{\sigma _{m}}\), \(h=0\) and \(\theta _{\sigma }=0\). According to the estimation results, \(\bar{\sigma _{+}},\bar{\sigma _{-}}\text { and }\bar{\sigma _{m}}\) had similar values, but \(\theta _{\sigma }\) and h were significantly larger than 0 (\(p<0.001\) for the two parameters).

  8. For both human lives and money, we used a precision of \(a=2.5\), corresponding to half of the step used for the choice list.

  9. Non-negative parameters (i.e., \(\lambda ,\delta ^{+},\delta ^{-},\gamma ^{+},\gamma ^{-})\) are assumed to follow a log-normal distribution and a normal distribution is assumed for the CARA utility parameters (\(\alpha ^{+}\)and \(\alpha ^{-}\)) that can take either positive or negative values.

  10. More precisely, \(\Theta \) is a vector of the diagonal elements of the variance-covariance matrix. Estimating the full variance covariance matrix of a multivariate distribution is computationally intensive. We therefore assume that the parameters are independently distributed and measure only their variance.

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Author information

Authors and Affiliations

  1. GREGHEC-CNRS, HEC-Paris, 1 rue de la Libération, 78350, Jouy-en-Josas, France

    Emmanuel Kemel

  2. Paris Descartes University, Institut Universitaire de France, 143 Avenue de Versailles, 75016, Paris, France

    Corina Paraschiv

Authors
  1. Emmanuel Kemel
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  2. Corina Paraschiv
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Corresponding author

Correspondence to Emmanuel Kemel.

Appendices

Appendix A: Instructions

Upon arrival in the lab, subjects received instructions individually from the experimenter. The instructions consisted in three parts:

  • a 10 min presentation with a beamer,

  • reading and signing a consent form,

  • practice questions on the software used to collect the answers.

This appendix presents the material used for these three parts.

1.1 Presentation

Figures 3 and 4 show the slides used for the beamer presentation.

Fig. 3
figure 3

Slides used for the instructions

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Fig. 4
figure 4

Slides used for the instructions (continued)

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1.2 Consent form

A translation of the consent form for the experiment is presented in Fig. 5.

Fig. 5
figure 5

Consent form

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Fig. 6
figure 6

Screenshot of practice questions involving lives. Translation: “Vies” is the French word for “lives”. The text appearing on the top of the screen translates as: “The project’s consequences for society are expressed in terms of HUMAN LIVES”. Subjects were asked to click on the preferred option

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1.3 Practice questions

The practice questions included six questions, corresponding to the different types of experimental tasks used during the experiment. Each question measured an indifference value for a given prospect, corresponding to either a certainty equivalent assessment (for gain and loss prospects), or to a loss equivalent assessment (for mixed prospects). Three questions concerned human lives, and three concerned public money. We only present hereafter the questions for human lives (the questions for monetary consequences were similar). The three questions about human lives (see Fig. 6) concerned the gain prospect \(50_{0.50}0\), the loss prospect \(-50_{0.50}0\) and the mixed prospect \(20_{0.50}l\) , respectively. The answers given to these practice questions were not recorded.

Appendix B: Illustration of the two-step process for the choice lists: bisection and confirmation steps

Choice lists contained up to 20 choices. In order to speed up the completion of the choice lists, a first step based on the bisection method was implemented to pre-fill the list, followed by a confirmation step. These two steps are illustrated hereafter for the certainty equivalent of the prospect \(100_{0.5}0\) with monetary consequences.

1.1 Bisection step

The bisection method consists in a series of binary choices that aims at searching an indifference value by iterative bisection of the interval that contains it. The method is initiated with a choice between the prospect and its expected value. Figure 7 shows the first two iterations. Figure 7a shows the first choice, between the prospect and its expected value. The second choice depended on the choice observed in the first step. If the subject chose the sure outcome of 50, this means that the sure outcome would also be selected for amounts larger than 50 and that the CE was located in the interval [0, 50]. Therefore, the second iteration of the bisection consisted in a choice between the prospect and a sure outcome of 25 (Fig. 7b), to further refine the interval. Likewise, if the subject declined the sure amount of 50 and chose the prospect, this means that the sure amount would be also declined for amounts lower than 50 and that the CE was in the interval [50, 100]. In this case, the second iteration consisted in a choice between the prospect and a sure outcome of 75 (Fig. 7c). The bisection was iterated until the certainty equivalent was assessed with a precision of 5 units. At each step, the sure outcome was rounded to be a multiple of 5 units. This level of precision was obtained in 5 or 6 iterations depending on the questions.

Fig. 7
figure 7

First two steps of the bisection for the prospect \(100_{0.5}0\) with monetary consequences. The text appearing on the top of the screen translates as: “The project’s consequences for society are expressed in terms of “Monetary AMOUNTS”. Subjects were asked to click on the preferred option

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1.2 Confirmation step

The bisection was followed by a confirmation step. A scrollbar appeared at the bottom of the screen (Fig. 8a). Each position of the scrollbar corresponded to a choice of the list, i.e. to a possible value of the sure outcome. The subject had to scroll the bar from one side to another in order to scan all the choices. For each choice, the selected option, determined from the bisection process, was highlighted in black. In the example in Fig. 8, the subject selected the sure outcome when higher or equal to 40 (Fig. 8b), and selected the prospect for outcomes lower than 35 (Fig. 8c). For each choice, the subject was offered the possibility to change the selected option. When all the choices were scanned, a confirmation button appeared (Fig. 8d). Clicking the confirmation button validated all the choices of the choice list and moved the subject to the next choice list. In order to access the confirmation button and be allowed to go to the next choice list, the subject had to scan the list entirely.

Fig. 8
figure 8

Illustration of the confirmation step. The text appearing on the top of the screen translates as: “The project’s consequences for society are expressed in terms of “MONETARY AMOUNTS”. Subjects were asked to click on the preferred option

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1.3 Appendix C: Additional descriptive statistics on the measured indifference values

Median and interquartile intervals of measured indifference values are reported in Tables 6 and 7.

Table 6 Interquartiles of certainty equivalents for money and lives non-mixed prospects
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Table 7 Interquartiles of loss equivalents for money and lives mixed prospects
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Kemel, E., Paraschiv, C. Deciding about human lives: an experimental measure of risk attitudes under prospect theory. Soc Choice Welf 51, 163–192 (2018). https://doi.org/10.1007/s00355-018-1111-y

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