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We provide a nonparametric revealed preference approach to demand analysis based on homothetic efficiency. Homotheticity is widely assumed (often implicitly) because it is a convenient and often useful restriction. However, this assumption is rarely tested, and data rarely satisfy testable conditions. To overcome this, we provide a way to estimate homothetic efficiency of consumption choices. The method provides considerably higher discriminatory power against random behavior than the commonly used Afriat efficiency. We use experimental and household survey data to illustrate how our approach is useful for different empirical applications and can provide greater predictive success.

We provide an efficient way to generate random choices which are consistent with utility maximisation. They are drawn from an approximate uniform distribution on the admissible region on each budget based on a Markovian Monte Carlo algorithm due to Smith (Oper Res 32(6):1296–1308, 1984 ). This can be used to extend Bronars’ (Econometrica 55(3):693–698, 1987 ) method by approximating the power of tests for conditions for which utility maximisation is necessary but not sufficient (e.g., homotheticity, separability, etc.). The approach can also be applied to production analysis.

It is shown that for two dimensional commodity spaces any homothetic utility function that rationalizes each pair of observations in a set of consumption data also rationalizes the entire set. The result is used to provide a simplified nonparametric test for homotheticity of demand and a measure for homothetic efficiency. The article thus provides a useful tool to screen data for severe violations of homotheticity before estimating parameters of homothetic utility functions. The new test and measure are applied to previously published data.

It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be of arbitrary length for more than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic ( L − 1 ) -polytope into a facet of a convex monotonic hull in L -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles.

This article explores rationalizability issues for finite sets of observations of stochastic choice in the framework introduced by Bandyopadhyay et al. (Journal of Economic Theory, 84(1), 95–110, 1999 ). It is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity bundles. A new rationalizability condition for stochastic choices, “rationalizable in terms of stochastic orderings on the normalized price space” ( rsop ), is defined. rsop is satisfied if and only if there exists a solution to a linear feasibility problem. The existence of a solution also implies rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here.

We provide a framework to decompose preferences into a notion of distributive justice and a selfishness part and to recover individual notions of distributive justice from data collected in appropriately designed experiments. \"Dictator games\" with varying transfer rates used in Andreoni and Miller (2002) and Fisman et al. (2007) can be used to assess individuals' preferences, but - with the help of simple new axioms - also to recover some part of individuals' notion of justice. \"Social planner\" experiments or experiments under a \"veil of ignorance\" (Rawls 1971) can be used to recover larger parts of the notion of justice. The axioms also allow a simple test for the validity of such an experimental approach, which is not necessarily incentive-compatible, and to recover a greater part of an individual's preference relation in dictator experiments than before. Interpersonal comparison of the individual intensity of justice (or fairness) similar to the suggestions in Karni and Safra (2002b) are possible, and we can evaluate the intensity based on an individual's own notion of justice. The approach is kept completely non-parametric. As such, this article is in the spirit of Varian (1982) and Karni and Safra (2002a).

We report the results of a combination of a dictator experiment with either a \"social planner\" or a \"veil of ignorance\" experiment. The experimental design and the analysis of the data are based on the theoretical framework proposed in the companion paper by Becker, Häger, and Heufer (BHH, 2013), in which we introduce a \"notion of distributive justice\" by which individuals trade off equality and efficiency. The purpose of the theoretical framework is to explain preferences in dictator experiments by a combination of selfishness and concerns for distributive justice. Most participants conform very well with the Agreement and Symmetry axioms proposed in BHH; we find that for 80% of participants the evidence is very strong. The experiment therefore demonstrates that most participants' behaviour in dictator experiments can be explained by a combination of selfishness and concerns for distributive justice. We also provide a rough classification of preferences and notions of distributive justice and show that participants' strength of the sense for justice (Karni and Safra 2002b) can be compared non- parametrically.

We propose an instrument to measure individuals' social preferences regarding equity and efficiency behind a veil of ignorance. We pair portfolio and wealth distribution choice problems which have a common budget set. For a given bundle, the distribution over an individual's wealth is the same for both problems. The portfolio choice serves as a benchmark to evaluate whether the wealth distribution choice exhibits equity or efficiency preferring tastes. We report experiments using a within-subject design testing the veracity of this instrument. We find clusters of equity preferring, efficiency preferring, and socially agnostic individuals through reduced form, revealed preference, and structural estimation analyses.

Fuels with high-knock resistance enable modern spark-ignition engines to achieve high efficiency and thus low CO2 emissions. Identification of molecules with desired autoignition properties indicated by a high research octane number and a high octane sensitivity is therefore of great practical relevance and can be supported by computer-aided molecular design (CAMD). Recent developments in the field of graph machine learning (graph-ML) provide novel, promising tools for CAMD. We propose a modular graph-ML CAMD framework that integrates generative graph-ML models with graph neural networks and optimization, enabling the design of molecules with desired ignition properties in a continuous molecular space. In particular, we explore the potential of Bayesian optimization and genetic algorithms in combination with generative graph-ML models. The graph-ML CAMD framework successfully identifies well-established high-octane components. It also suggests new candidates, one of which we experimentally investigate and use to illustrate the need for further auto-ignition training data.