Related papers: An algebraic approach to revealed preferences

This paper studies choice situations in which a decision maker can choose multiple alternatives. Given a menu of available options, the decision maker selects a subset of the menu with certain probabilities. We employ an axiomatic approach…

When ranking big data observations such as colleges in the United States, diverse consumers reveal heterogeneous preferences. The objective of this paper is to sort out a linear ordering for these observations and to recommend strategies to…

Recent work on the logical structure of non-locality has constructed scenarios where observations of multi-partite systems cannot be adequately described by compositions of non-signaling subsystems. In this paper we apply these frameworks…

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…

Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…

There are countless sources of data available to governments, companies, and citizens, which can be combined for good or evil. We analyse the concepts of combining data from common sources and linking data from different sources. We model…

This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter…

Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…

Modeling the preferences of agents over a set of alternatives is a principal concern in many areas. The dominant approach has been to find a single reward/utility function with the property that alternatives yielding higher rewards are…

Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…

We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…

Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…

It is conventional wisdom in machine learning and data mining that logical models such as rule sets are more interpretable than other models, and that among such rule-based models, simpler models are more interpretable than more complex…

With the wide adoption of machine learning techniques, requirements have evolved beyond sheer high performance, often requiring models to be trustworthy. A common approach to increase the trustworthiness of such systems is to allow them to…

We introduce an Attention Overload Model that captures the idea that alternatives compete for the decision maker's attention, and hence the attention that each alternative receives decreases as the choice problem becomes larger. Using this…

This paper exhibits a duality between the theory of Revealed Preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat's theorem can be interpreted as a second welfare theorem in…

This article takes an oblique sidestep from two previous papers, wherein an approach to reformulation of game theory in terms of information theory, topology, as well as a few other notions was indicated. In this document a description is…

Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…

Preference modelling lies at the intersection of economics, decision theory, machine learning and statistics. By understanding individuals' preferences and how they make choices, we can build products that closely match their expectations,…

Humans use social context to specify preferences over behaviors, i.e. their reward functions. Yet, algorithms for inferring reward models from preference data do not take this social learning view into account. Inspired by pragmatic human…