Contributed Paper Session
Saturday 2:00 – 2:50
2:00 - 2:15 Annela Kelly,
Title: Active Learning Innovations for Liberal Arts
Mathematics Class
Abstract: I will introduce several new ideas that were used in my liberal arts mathematics class last academic year. We will talk about implementing games and their strategies as an aid to learn mathematics. Moreover, we will discuss how check-digits and codes provide captivating applications of mathematics.
2:20 - 2:35 Robert Z. Norman,
Title: Some Comparisons of Voting Systems (Preliminary Report)
Abstract: The purpose of voting can be expressed as a function from voters’ preferences among candidates to a decision. The mechanism for doing this is for voters to cast ballots. The voting system then transforms the ballots into a decision. Voting thus becomes a compound of two functions, the first from each voter’s preferences to a ballot, and the second from ballots to a decision. The second function is determined by the voting system. The first is at the discretion of the voter, who knows the nature of the second function, and can take that information into account in adopting a voting strategy.
Several electorates have adopted or are considering IRV (Instant Runoff Voting) as an alternative to the traditional plurality system. We examine some of the properties of these systems, concentrating competitive elections and on elections containing polarizing candidates, noting that three simpler alternatives to IRV, Borda Count, Approval Voting, and Majoritarian Compromise, do better in both cases.
It is known that under IRV, ranking a candidate higher can reduce the candidate’s chances of winning (thus producing a violation of monotonicity). Also, IRV sometimes fails to take into account critical preferences of some of its voters, marginalizing a significant proportion of the electorate. We explore the likelihood of these transgressions. Proponents of IRV claim that strategic (manipulative) voting seldom occurs. We offer evidence to the contrary from Australian elections. We compare with the three simple alternative voting systems.