Rankings
Chair: Gara Pruesse (Vancouver Island University)
[PDF]

ANDREW BEVERIDGE, Macalester College
Constructing Admissible Voter Preferences with the Voter Basis  [PDF]

When making simultaneous decisions, our preference for the outcomes on one subset can depend on the outcomes on a disjoint subset. In referendum elections, this gives rise to the separability problem, where a voter must predict the outcome of one proposal when casting their vote on another. A set $A \subset [n]$ is separable for preference order $\succeq$ when our ranking of outcomes on $A$ is independent of outcomes on its complement $[n] \backslash A$. The admissibility problem asks which subsets $S \subset \mathcal{P}({[n]})$ can arise as the collection of separable subsets for some preference order. We introduce the $2^n$-dimensional voter basis, and use it to construct voter preferences whose Hasse diagram of separable sets has a tree-like structure, or is closed under intersections and unions.

DONOVAN HARE, University of British Columbia
Dual-Sport-Venue Sports Scheduling, Constraint Programming and Global Constraints - Part 2  [PDF]

Canada West oversees the administration of all sports of its 17 university members from British Columbia to Manitoba. The organization is responsible for scheduling the regular season games of the sports of its members and currently does this by hand using ad-hoc methods. Of particular difficulty is the dependency between the basketball and volleyball schedules of universities whose venues only support one of the sports on any given weekend. Also contributing to the difficulty of this dual-sport-venue sports scheduling problem is the desire to balance the home/away status of the teams, to minimize the breaks in the schedules, and to respect the size of local referees pools. In this talk, a solution for this problem using constraint programming is presented along with a discussion of graph factor algorithms used for filtering in global constraints relevant to this problem.

This is joint work with Charles Jolin-Landry.

CHARLES JOLIN-LANDRY, University of British Columbia
Dual-Sport-Venue Sports Scheduling, Constraint Programming and Global Constraints - Part 1  [PDF]

Canada West oversees the administration of all sports of its 17 university members from British Columbia to Manitoba. The organization is responsible for scheduling the regular season games of the sports of its members and currently does this by hand using ad-hoc methods. Of particular difficulty is the dependency between the basketball and volleyball schedules of universities whose venues only support one of the sports on any given weekend. Also contributing to the difficulty of this dual-sport-venue sports scheduling problem is the desire to balance the home/away status of the teams, to minimize the breaks in the schedules, and to respect the size of local referees pools. In this talk, a solution for this problem using constraint programming is presented along with a discussion of graph factor algorithms used for filtering in global constraints relevant to this problem.

This is joint work with Donovan Hare.

SARAH WOLFF, Denison University
Inferring Rankings From First Order Marginals  [PDF]

Motivated by applications in ranked-choice voting, we consider the problem of recovery of election results---encoded by a function $f$ on the symmetric group---given only partial data. In particular, we investigate the combinatorial structure of the matrix of first order marginals, which gives the number of voters who ranked each candidate in each position. We investigate conditions on $f$ that allow us to exploit this combinatorial structure in order to provide an algorithm to recover the original function $f$. As the matrix of first order marginals is the Fourier coefficient of the permutation representation of the symmetric group, this work sits within the context of algebraic compressed sensing, which tackles the question of how to recover a sparse function $f$ on a finite group given only a subset of the Fourier coefficients of $f$.