View Proposal #531
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| ID | 531 |
|---|---|
| First Name | Alvaro |
| Last Name | Carbonero |
| Institution | University of Nevada, Las Vegas |
| Speaker Category | undergraduate student |
| Title of Talk | Exploring Preference Orderings Through Discrete Geometry |
| Abstract | Consider $n + 1$ points in the plane: a set $S$ consisting of $n$ points along with a distinguished vantage point $v$. By measuring the distance from $v$ to each of the points in $S$, we generate a preference ordering of $S$. This work is motivated by a voting theory application, where an ordering corresponds to a preference list. The maximum number of orderings possible is given by a fourth-degree polynomial (related to Stirling numbers of the first kind), found by Good and Tideman (1977), while the minimum is given by a linear function. We investigate intermediate numbers of orderings achievable by special configurations $S$. We also consider this problem for points on the sphere, where our results are similar to what we found for the plane. A variant of the problem that uses two vantage points is also developed. |
| Subject area(s) | Discrete Geometry |
| Suitable for undergraduates? | Y |
| Day Preference | SaturdayStrong |
| Computer Needed? | Y |
| Bringing a laptop? | N |
| Overhead Needed? | Y |
| Software requests | Just a projector for a beamer presentation. |
| Special Needs | |
| Date Submitted | 09/12/2019 |
| Year | 2019 |