# The Cost of Risk Aversion

### Eliciting risk preferences and re-evaluating flood protection standards in the Netherlands

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## Abstract

Where water flows, prosperity follows.

Many prosperous areas around the world are situated near large bodies of water such as oceans, seas, and rivers. These bodies of water play a vital role in enhancing the prosperity of societies through various means. They provide convenient access to transportation, food, recreation, and many other benefits. However it is not only prosperity that follows, but also risk. This risk, defined as the product of probabilities and outcomes, is an inherent price that has to be paid to enjoy the social and economic fruits that are provided by these oceans, seas or rivers. As whenever one is close to a body of water, there exists a probability of a devastating outcome: A flood.

In order to effectively minimize and handle risks, the field of Flood Risk Management has naturally evolved. Within this field numerous decisions need to be made, such as determining an acceptable probability of flooding for a particular area or deciding when to evacuate if a flood is imminent. These decisions involve individuals who process information and make judgments under risk. However, it has been observed that the decision-making process is vulnerable to the influence of risk preferences. The St. Petersburg Paradox provides an illustrative example of how risk preferences can affect behavior, as individuals are only willing to pay a limited amount of money for an expected outcome of an infinite sum. By considering risk preferences, researchers were able to explain the observed mismatch between the expected value and the willingness-to-pay. This example raises the question of whether similar discrepancies between willingness to pay and expected outcomes can also arise in flood risk management, and whether the inclusion of these risk preferences can aid in the decision-making process under risk.

This research looks at ways of incorporating risk preferences into the field of Flood Risk Management. A stated preferences method is used to uncover the risk preferences of individuals for flood risk related problems, consisting of a series of flood related choice problems. The subsequent results are fitted to several commonly used risk preference models, which consist of a utility- and probability weighting function. A modified version of Prospect Theory by Tversky and Kahneman (1992) is found to best describe the risk preferences of individuals towards flood risk related problems. This research shows that individuals have similar risk preferences for flood risk related choice problems as for general (behavioural) economic choice problems. The found utility function shows that individuals have a diminishing sensitivity for outcomes that are larger in magnitude, with a greater diminishing effect for positive outcomes than for negative outcomes. Additionally, it became apparent that individuals experience flood-related losses around 1.5 times more intensely than equal gains, aligning with the current understanding of behavioural economics. The identified probability weighting function indicates that individuals overestimate small probabilities, perceiving them as greater than their actual value, while simultaneously underestimating large probabilities. The point where overestimation switches to underestimation occurs around probabilities of 0.3, in line with the results found in behavioural economics. Special attention was given to probabilities between one in a hundred thousand and one in a hundred where, instead of assuming a functional form for the probability weighting function, an additional elicitation was performed. This elicitation revealed that individuals perceive probabilities below one in a hundred as largely the same. Suggesting that people are unable to distinguish between very small probabilities, such as one in a thousand and one in ten thousand. This finding carries significant implications for the perceived level of safety in flood risk management, considering that flood safety standards typically fall below one in a hundred.

The found risk preferences are subsequently used to reevaluate the Statistical Value of Life (VOSL), previously found to be around €6.7 mln. by by de Blaeij (2003) and Bockarjova et al. (2009). Based on the found risk preferences and answers to the choice problems a new value of €11.8 mln. is found. Adjusted for inflation this value is around 1.18 to 1.33 higher than the previous found values. This research further looked at the influence of the additional risk premium in the Dutch discount rate for infrastructure projects and its effect on the safety standard in flood protections. Including a positive risk premium, which increases the overall discount rate, leads to a decrease in safety standards. This is the logical result of discounting future benefits in the form of reduced risk, while the incurred costs are borne in the present and are therefore not discounted. This decrease in safety standard is indicative of a risk seeking approach, which contradicts the risk-averse nature of the risk premium in the discount rate. To resolve this contradiction and adopt a risk-averse approach, several options for incorporating the risk-averse premium in the discount rate are proposed.

All the previous insights are used in a case study, which consists of the reevaluation of Dutch safety standards for all dike sections along rivers and coasts. The evaluation of optimal flooding probabilities for the Local Individual Risk (LIR) and the Social Cost-Benefit Analysis (SCBA) is modified to include the found risk preferences, along with the adjusted values for the discount rate and VOSL. The resulting criteria are then used to reassess the optimal classified flooding probabilities for various dike sections in the Netherlands. This adjusted evaluation shows that the ratio between the leading principles in the flood safety standards remains largely the same, but the optimal flood probabilities associated with these principles do change. Generally, these probabilities are reduced by approximately one order of magnitude when the best estimates found in this research are included, leading to a stricter safety standard for flooding. An analysis is conducted to examine the sensitivity of the different changes. This analysis demonstrates that the inclusion of risk preferences has the most significant impact on the optimal flooding probability for both the LIR and SCBA, with the probability weighting function exerting the most influence. When the best estimates for the adjusted evaluation are used, the additional costs for each resident of the Netherlands that are the result of risk aversion amount to €37 per year.

This research is concluded with the remark that the insights found in behavioural economics are useable and of value in the field of flood risk management. People tend to show the same degree of risk aversion when presented with an uncertain choice about flooding as they do when they are presented with an uncertain choice about economics, such as the problem posed in the St. Petersburg Paradox. Taking these risk preferences into account can help to better distribute the scarce resources such as time and money to where they are of most utility to society.