Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

It has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types. We present a parsimonious characterization of risk taking behavior by estimating a finite mixture regression model for three different experimental data sets, two Swiss and one Chinese, over a large number of real gains and losses. We find two distinct types of individuals: In all three data sets, the choices of roughly 80% of the subjects exhibit significant deviations from rational probability weighting consistent with prospect theory. 20% of the subjects weight probabilities linearly and behave essentially as expected value maximizers. Moreover, the individuals are assigned to one of these two groups with probabilities of close to one resulting in a low measure of entropy. The reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling.individual risk taking behavior, latent heterogeneity, finite mixture regression models

Topomap: Topological Mapping and Navigation Based on Visual SLAM Maps

Visual robot navigation within large-scale, semi-structured environments deals with various challenges such as computation intensive path planning algorithms or insufficient knowledge about traversable spaces. Moreover, many state-of-the-art navigation approaches only operate locally instead of gaining a more conceptual understanding of the planning objective. This limits the complexity of tasks a robot can accomplish and makes it harder to deal with uncertainties that are present in the context of real-time robotics applications. In this work, we present Topomap, a framework which simplifies the navigation task by providing a map to the robot which is tailored for path planning use. This novel approach transforms a sparse feature-based map from a visual Simultaneous Localization And Mapping (SLAM) system into a three-dimensional topological map. This is done in two steps. First, we extract occupancy information directly from the noisy sparse point cloud. Then, we create a set of convex free-space clusters, which are the vertices of the topological map. We show that this representation improves the efficiency of global planning, and we provide a complete derivation of our algorithm. Planning experiments on real world datasets demonstrate that we achieve similar performance as RRT* with significantly lower computation times and storage requirements. Finally, we test our algorithm on a mobile robotic platform to prove its advantages.Comment: 8 page

Rationality on the Rise: Why Relative Risk Aversion Increases with Stake Size

How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that, contrary to gains, no coherent change in relative risk aversion is observed for losses. The increase in relative risk aversion over gains cannot be captured by the curvature of the utility function. It is driven predominantly by a change in probability weighting of a majority group of individuals who exhibit more rational probability weighting at high stakes. These results not only challenge expected utility theory, but also prospect theory.Risk Aversion, Stake-Size Effect, Prospect Theory, Latent Heterogeneity

Fiat–Shamir Transformation of Multi-Round Interactive Proofs (Extended Version)

The celebrated Fiat–Shamir transformation turns any public-coin interactive proof into a non-interactive one, which inherits the main security properties (in the random oracle model) of the interactive version. While originally considered in the context of 3-move public-coin interactive proofs, i.e., so-called Σ-protocols, it is now applied to multi-round protocols as well. Unfortunately, the security loss for a (2μ+1)-move protocol is, in general, approximately Q$^μ$, where Q is the number of oracle queries performed by the attacker. In general, this is the best one can hope for, as it is easy to see that this loss applies to the μ-fold sequential repetition of Σ-protocols, but it raises the question whether certain (natural) classes of interactive proofs feature a milder security loss. In this work, we give positive and negative results on this question. On the positive side, we show that for (k$_1$,…,k$_μ$)-special-sound protocols (which cover a broad class of use cases), the knowledge error degrades linearly in Q, instead of Q$^μ$. On the negative side, we show that for t-fold parallel repetitions of typical (k$_1$,…,k$_μ$)-special-sound protocols with t≥μ (and assuming for simplicity that t and Q are integer multiples of μ), there is an attack that results in a security loss of approximately $\frac{1}{2}$Q$^μ$/μ$^{μ+t}$

Risk in Time: The Intertwined Nature of Risk Taking and Time Discounting

Standard economic models view risk taking and time discounting as two independent dimensions of decision making. However, mounting experimental evidence demonstrates striking parallels in patterns of risk taking and time discounting behavior and systematic interaction effects, which suggests that there may be common underlying forces driving these interactions. Here, we show that the inherent uncertainty associated with future prospects together with individuals’ proneness to probability weighting generates a unifying framework for explaining a large number of puzzling behavioral findings: delay-dependent risk tolerance, aversion to sequential resolution of uncertainty, preferences for the timing of the resolution of uncertainty, the differential discounting of risky and certain outcomes, hyperbolic discounting, subadditive discounting, and the order dependence of prospect valuation. Furthermore, all these phenomena can be accommodated by the same set of preference parameter values and plausible levels of inherent uncertainty

The missing type: where are the inequality averse (students)?

The empirical evidence on the existence of social preferences—or lack thereof—is predominantly based on student samples. Yet, knowledge about whether these findings can be extended to the general population is still scarce. In this paper, we compare the distribution of social preferences in a student and in a representative sample. Using descriptive analysis and a rigorous clustering approach, we show that the distribution of the general population’s social preferences fundamentally differs from the students’ distribution. In the general population, three types emerge: an inequality averse, an altruistic, and a selfish type. In contrast, only the altruistic and the selfish types emerge in the student population. The absence of an inequality averse type in the student population is particularly striking considering the fact that this type comprises about 50 percent of the individuals in the general population sample. Using structural estimation, we show that differences in age and education are likely to explain these results. Younger and more educated individuals—which typically characterize students— not only tend to have lower degrees of other-regardingness but this reduction in other-regardingness basically nullifies behindness aversion among students. Differences in income, however, do not seem to affect social preferences. These findings provide a new cautionary tale that insights from student populations might not extrapolate to the general population

The fundamental properties, stability and predictive power of distributional preferences

Parsimony is a desirable feature of economic models but almost all human behaviors are characterized by vast individual variation that appears to defy parsimony. How much parsimony do we need to give up to capture the fundamental aspects of a population’s distributional preferences and to maintain high predictive ability? Using a Bayesian nonparametric clustering method that makes the trade-off between parsimony and descriptive accuracy explicit, we show that three preference types—an inequality averse, an altruistic and a predominantly selfish type—capture the essence of behavioral heterogeneity. These types independently emerge in four different data sets and are strikingly stable over time. They predict out-of-sample behavior equally well as a model that permits all individuals to differ and substantially better than a representative agent model and a state-of-the-art machine learning algorithm. Thus, a parsimonious model with three stable types captures key characteristics of distributional preferences and has excellent predictive power

Performance Pay and Multidimensional Sorting - Productivity, Preferences and Gender

This paper studies the impact of incentives on worker self-selection in a controlled laboratory experiment. Subjects face the choice between a fixed and a variable payment scheme. Depending on the treatment, the variable payment is a piece rate, a tournament or a revenue-sharing scheme. We find that output is higher in the variable pay schemes (piece rate, tournament, and revenue sharing) compared to the fixed payment scheme. This difference is largely driven by productivity sorting. In addition personal attitudes such as willingness to take risks and relative self-assessment as well as gender affect the sorting decision in a systematic way. Moreover, self-reported effort is significantly higher in all variable pay conditions than in the fixed wage condition. Our lab findings are supported by an additional analysis using data from a large and representative sample. In sum, our findings underline the importance of multi-dimensional sorting, i.e., the tendency for different incentive schemes to systematically attract people with different individual characteristics