Related papers: On Locally Rationalizable Social Choice Functions
We study measurable spaces equipped with a $\sigma$-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version -- a kind of fiber space that describes locally their directions -- defined by…
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
There is a well-known inclusion $\iota_\mathscr{E}$ of a topos $\mathscr{E}$ in the linguistic topos $\mathscr{T}(\Sigma)$ of its internal language $\Sigma$ that proves both toposes to be equivalent. There is also a canonical translation…
Local explainability methods -- those which seek to generate an explanation for each prediction -- are becoming increasingly prevalent due to the need for practitioners to rationalize their model outputs. However, comparing local…
Recent years have seen a boom in interest in machine learning systems that can provide a human-understandable rationale for their predictions or decisions. However, exactly what kinds of explanation are truly human-interpretable remains…
We consider classes of non-manipulable social choice functions with range of cardinality at most two within a set of at least two alternatives. We provide the functional form for each of the classes we consider. This functional form is a…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…
We offer a rationalization of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a…
In economic theory, an agent chooses from available alternatives -- modeled as a set. In decisions in the field or in the lab, however, agents do not have access to the set of alternatives at once. Instead, alternatives are represented by…
I consider decision-making constrained by considerations of morality, rationality, or other virtues. The decision maker (DM) has a true preference over outcomes, but feels compelled to choose among outcomes that are top-ranked by some…
We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives…
In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $\Sigma_n$-definable parameters,…
In this paper, we give a precise definition of an analytic $\gamma$-factor of an irreducible representation of a classical group over a local function field of odd characteristic so that it satisfies some notable properties which are enough…
Given a collection A of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from A. The notion of local definability of holomorphic functions was introduced by Wilkie, who gave a complete…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
We define notions of dominance between two actions in a dynamic game. Local dominance considers players who have a blurred view of the future and compare the two actions by first focusing on the outcomes that may realize at the current…
We determine the quality of randomized social choice mechanisms in a setting in which the agents have metric preferences: every agent has a cost for each alternative, and these costs form a metric. We assume that these costs are unknown to…