At a high level, the tidyverse is a language for solving data science challenges with R code. Its primary goal is to facilitate a conversation between a human and a computer about data. Less abstractly, the tidyverse is a collection of R packages that share a high-level design philosophy and low-level grammar and data structures, so that learning one package makes it easier to learn the next.

Although reference dependence plays a central role in explaining behavior, little is known about the way that reference points are selected. This paper identifies empirically which reference point people use in decision under risk. We assume a comprehensive reference-dependent model that nests the main reference-dependent theories, including prospect theory, and that allows for isolating the reference point rule from other behavioral parameters. Our experiment involved high stakes with payoffs up to a week's salary. We used an optimal design to select the choices in the experiment and Bayesian hierarchical modeling for estimation. The most common reference points were the status quo and a security level (the maximum of the minimal outcomes of the prospects in a choice). We found little support for the use of expectations-based reference points.

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Proper scoring rules serve to measure subjective degrees of belief. Traditional proper scoring rules are based on the assumption of expected value maximization. There are, however, many deviations from expected value, primarily due to risk aversion. Correcting techniques have been proposed in the literature for deviations due to nonlinear utility. These techniques still assumed expected utility maximization. More recently, corrections for deviations from expected utility have been proposed. The latter concerned, however, only the quadratic scoring rule, and could handle only half of the domain of subjective beliefs. Further, beliefs close to 0.5 could not be discriminated. This paper generalizes the correcting techniques to all bounded binary proper scoring rules, covers the whole domain of beliefs and, in particular, can discriminate between all degrees of belief. Thus, we fully extend the properness requirement (in the sense of identifying all degrees of subjective beliefs) to virtually all models that deviate from expected value.

Preference foundations give necessary and sufficient conditions for a decision model, stated directly in terms of the empirical primitive: the preference relation. For the most popular descriptive model for decision making under risk and uncertainty today, prospect theory, preference foundations have as yet been provided only for prospects taking finitely many values. In applications, however, prospects often are complex and involve infinitely many values, as in normal and lognormal distributions. This paper provides a preference foundation of prospect theory for such complex prospects. We allow for unbounded utility and only require finite additivity of the underlying probability distributions, leaving the restriction to countably additive distributions optional. As corollaries, we generalize previously obtained preference foundations for special cases of prospect theory (rank-dependent utility and Choquet expected utility) that all required countable additivity. We now obtain genuine generalizations of de Finetti's and Savage's finitely additive setups to unbounded utility.

This paper provides necessary and sufficient preference conditions for average utility maximization over sequences of variable length. We obtain full generality by using a new algebraic technique that exploits the richness structure naturally provided by the variable length of the sequences. Thus we generalize many preceding results in the literature. For example, continuity in outcomes, a condition needed in other approaches, now is an option rather than a requirement. Applications to expected utility, decisions under ambiguity, welfare evaluations for variable population size, discounted utility, and quasilinear means in functional analysis are presented.

We introduce a new type of preference condition for intertemporal choice, which requires present values to be independent of various other variables. The new conditions are more concise and more transparent than traditional ones. They are directly related to applications because present values are widely used tools in intertemporal choice. Our conditions give more general behavioral axiomatizations, which facilitate normative debates and empirical tests of time inconsistencies and related phenomena. Like other preference conditions, our conditions can be tested qualitatively. Unlike other preference conditions, our conditions can also be directly tested quantitatively, and we can verify the required independence of present values from predictors in regressions. We show how similar types of preference conditions, imposing independence conditions between directly observable quantities, can be developed for decision contexts other than intertemporal choice and can simplify behavioral axiomatizations there. Our preference conditions are especially efficient if several types of aggregation are relevant because we can handle them in one stroke. We thus give an efficient axiomatization of a market pricing system that is (i) arbitrage-free for hedging uncertainties and (ii) time consistent.

This paper presents preference axiomatizations of expected utility for nonsimple lotteries while avoiding continuity constraints. We use results by Fishburn (1975), Wakker (1993), and Kopylov (2010 to generalize results by Delbaen, Drapeau, and Kupper (2011). We explain the logical relations between these contributions for risk versus uncertainty, and for …nite versus countable additivity, indicating what are the most general axiomatizations of expected utility existing today.