arXiv subjects

Kemal Yildiz

Publications and source records attributed to Kemal Yildiz.

4 recordsLinked to original sources

arXiv2026

Self-ordered choice models

Consider an analyst who, for each menu of alternatives, observes a probability distribution over choices, reflecting heterogeneity in the population's choices. The analyst uses a choice model\textendash consisting of deterministic \textit{choice types} \textendash to explain the data, in the sense that mixtures over the admissible types reproduce the observed choice probabilities. A central difficulty is that such representations are typically non-unique. We introduce self-orderedness, a criterion ensuring that every probabilistic choice pattern the analyst can explain admits a unique and ordered representation. We show that self-ordered models are exactly those whose choice types form a \textit{lattice}. This equivalence provides a precise recipe to restrict or extend any choice model for unique ordered representation. Following this recipe, we identify the choice types that are essential for the unique ordered representation of random utility functions. This extension adds economically meaningful non-rational behaviors linked to choice overload and enables identification of the underlying order.

econ.TH↗

arXiv2026

Decomposition-Closed Sublattices as Minimizer Sets of Modular Functions over Distributive Lattices

We characterize the subsets of a finite distributive lattice that arise as the minimizer sets of modular functions. It is immediate that the minimizer set of any modular function is a decomposition-closed sublattice. Our main theorem establishes the converse: every decomposition-closed sublattice is the minimizer set of a modular function. Our proof is constructive. Using Birkhoff's representation, we decompose the problem along the intervals determined by an arbitrary maximal chain of the given sublattice. The key ingredient is a weight assignment on connected difference posets that yields local modular functions vanishing precisely at the endpoints of each interval. We also provide an example showing that this characterization fails for nondistributive lattices.

math.RA↗

arXiv2025

Ordered Probabilistic Choice

We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be associated with a copula, enabling the analysis of representations through established results from copula theory. We provide functional forms to describe the "extremal" representations of an ordered probabilistic choice behavior and their distinctive structural properties. The resulting functional forms act as an "identification method" that uniquely generates heterogeneous choice types and their weights. These results provide valuable tools for analysts to identify micro-level behavioral heterogeneity from macro-level observable data.

econ.TH↗

arXiv2019

Lexicographic Choice Under Variable Capacity Constraints

In several matching markets, in order to achieve diversity, agents' priorities are allowed to vary across an institution's available seats, and the institution is let to choose agents in a lexicographic fashion based on a predetermined ordering of the seats, called a (capacity-constrained) lexicographic choice rule. We provide a characterization of lexicographic choice rules and a characterization of deferred acceptance mechanisms that operate based on a lexicographic choice structure under variable capacity constraints. We discuss some implications for the Boston school choice system and show that our analysis can be helpful in applications to select among plausible choice rules.

econ.TH↗