When does aggregation reduce uncertainty aversion?

We study the problem of uncertainty sharing within a household: "risk sharing," in a context of Knightian uncertainty. A household shares uncertain prospects using a social welfare function. We characterize the social welfare functions such that the household is collectively less averse to uncertainty than each member, and satises the Pareto principle and an independence axiom. We single out the sum of certainty equivalents as the unique member of this family which provides quasiconcave rankings over risk-free allocations

Spherical Preferences

We introduce and study the property of orthogonal independence, a restricted additivity axiom applying when alternatives are orthogonal. The axiom requires that the preference for one marginal change over another should be maintained after each marginal change has been shifted in a direction that is orthogonal to both. We show that continuous preferences satisfy orthogonal independence if and only if they are spherical: their indifference curves are spheres with the same center, with preference being "monotone" either away or towards the center. Spherical preferences include linear preferences as a special (limiting) case. We discuss different applications to economic and political environments. Our result delivers Euclidean preferences in models of spatial voting, quadratic welfare aggregation in social choice, and expected utility in models of choice under uncertainty

Ordinal notions of submodularity

We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to Kreps [Kreps, D.M., 1979. A representation theorem for “Preference for Flexibility”. Econometrica 47 (3), 565–578] and one is a weakening of a notion due to Milgrom and Shannon [Milgrom, P., Shannon, C., 1994. Monotone comparative statics. Econometrica 62 (1), 157–180]. We show that any reflexive binary relation satisfying either of Kreps’s definitions also satisfies Milgrom and Shannon’s definition, and that any transitive and monotonic binary relation satisfying the Milgrom and Shannon’s condition satisfies both of Kreps’s conditions

Profit maximization and supermodular technology

A dataset is a list of observed factor inputs and prices for a technology; profits and production levels are unobserved. We obtain necessary and sufficient conditions for a dataset to be consistent with profit maximization under a monotone and concave revenue based on the notion of cyclic monotonicity. Our result implies that monotonicity and concavity cannot be tested, and that one cannot decide if a firm is competitive based on factor demands. We also introduce a condition, cyclic supermodularity, which is both necessary and sufficient for data to be consistent with a supermodular technology. Cyclic supermodularity provides a test for complementarity of production factors

Supermodularity and preferences

We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that supermodularity is a weak property, in the sense that many preferences have a supermodular representation

Feral objects and acts of domestic piracy: sculpture, secular magic, and strategies of feminist disruption

This practice-­led doctoral project is a material investigation of the potential for sculptural artworks to perform disruptive, dissenting and resistant narratives of women and girls’ intersubjective relationship with the material culture of feminine domesticity. I argue for the entanglement of objects, ideas, bodies and artwork as a material-­led encounter and ask, what might a feminist new materialism look like when the focus is on domestic objects, and how can we draw meaning from these objects when they perform as sculpture? I propose a category of material culture I call ‘feral objects’, the overlooked and undervalued materiality of consumer culture as identified by Attfield (2000), objects that perform in the threshold spaces of society and culture (Crewe and Gregson, 2003). I analyse feral objects in their role as sculpture to argue for a feminist new materialism that disrupts subject/object hierarchies (Boscagli, 2014). Developing Eckstein and Schwarz’s (2014) identification of piracy as a boundary practice, I introduce the term ‘domestic piracy’ to identify material-­led strategies of feminist disruption as activism materialised as sculptural artworks. Drawing upon Bennett’s (2010) vital materialism and Pil and Galia Kollectiv’s (2010) proposition that sculpture and installations made from found objects are performative in and of themselves, I argue that the embodied encounter with sculpture and installation made from found domestic objects materialises the agency of objects to perform an inter-­relationality that is agentic of corporeal feminism (Meskimmon, 2019). I analyse poltergeist phenomena as ‘secular magic’, the sleight-­of-­hand of conjuring (During, 2002), proposing that secular magic materialises feminine domestic disruption as the embodied encounter between (feminine) subject and (domestic) object. I argue that the trickery or sleight-of-­hand required to construct sculptural artworks performs feminist strategies of domestic dissent enacted by women and girls through feminine material culture (Owen, 1989)

On behavioral complementarity and its implications

We study the behavioral definition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize those data sets which can be generated by rational preferences exhibiting complementarities. The class of preferences that generate demand complements has Leontief and Cobb–Douglas as its as extreme members

The Axiomatic Structure of Empirical Content

In this paper, we provide a formal framework for studying the empirical content of a given theory. We define the falsifiable closure of a theory to be the least weakening of the theory that makes only falsifiable claims. The falsifiable closure is our notion of empirical content. We prove that the empirical content of a theory can be exactly captured by a certain kind of axiomatization, one that uses axioms which are universal negations of conjunctions of atomic formulas. The falsifiable closure operator has the structure of a topological closure, which has implications, for example, for the behavior of joint vis a vis single hypotheses. The ideas here are useful for understanding theories whose empirical content is well-understood (for example, we apply our framework to revealed preference theory, and Afriat's theorem), but they can also be applied to theories with no known axiomatization. We present an application to the theory of multiple selves, with a fixed finite set of selves and where selves are aggregated according to a neutral rule satisfying independence of irrelevant alternatives. We show that multiple selves theories are fully falsifiable, in the sense that they are equivalent to their empirical content

Inefficiency

We introduce an ordinal model of efficiency measurement. Our primitive is a notion of efficiency that is comparative, but not cardinal or absolute. In this framework, we postulate axioms that we believe an ordinal efficiency measure should satisfy. Primary among these are choice consistency and planning consistency, which guide the measurement of efficiency in a firm with access to multiple technologies. Other axioms include symmetry, which states that the names of commodities do not matter, scale-invariance, which says that units of measurement of commodities does not matter, and strong monotonicity, which states that efficiency should decrease if the inputs and outputs remain static when the technology becomes unambiguously more efficient. These axioms characterize a unique ordinal efficiency measure which is represented by the coefficient of resource utilization. By replacing symmetry (the weakest of our axioms) with a very mild continuity condition, we obtain a family of path-based measures.Efficiency Measurement, Coefficient of Resource Utilization, Ordinal, Choice Consistency, Planning Consistency, Path-based

On Behavioral Complementarity and its Implications

We study the behavioral denition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize those data sets which can be generated by rational preferences exhibiting complementarities. In a model in which income results from selling an endowment (as in general equilibrium models of exchange economies), the notion is surprisingly strong and is essentially equivalent to Leontief preferences. In the model of nominal income, the notion describes a class of preferences whose extreme cases are Leontief and Cobb-Douglas respectively.Afriat's Theorem, Weak Axiom of Revealed Preference, Complementary goods.