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Choice Functions, Digraphs, and Balanced Allocations

Electronic Theses and Dissertations

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abstract
In this thesis, we consider broadly the concept of choice in a variety of settings, focusing on equity in selection. In particular, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges, and are interested, for instance, in minimal numbers of edges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge) domination graphs are presented. In addition, we consider fairness for choice functions, from a sequential perspective, prove existence of fair choice, and consider connections with balanced allocation, path-connected directed graphs and cyclic preference. Several open questions are posed.
subject
Choice function
Digraphs
Domination
Fair choice
Hypergraphs
Hypertournaments
contributor
Lidral-Porter, Brendan (author)
Berenhaut, Kenneth S. (committee chair)
Mason, Sarah K. (committee member)
Gemmer, John (committee member)
date
2017-06-15T08:36:13Z (accessioned)
2017 (issued)
degree
Mathematics and Statistics (discipline)
2022-06-01 (liftdate)
embargo
2022-06-01 (terms)
identifier
http://hdl.handle.net/10339/82247 (uri)
language
en (iso)
publisher
Wake Forest University
title
Choice Functions, Digraphs, and Balanced Allocations
type
Thesis

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