Date Thesis Awarded

12-2022

Access Type

Honors Thesis -- Open Access

Degree Name

Bachelors of Arts (BA)

Department

Mathematics

Advisor

Charles Johnson

Committee Members

Gregory Hunt

Robert Hicks

Abstract

This thesis composes of two chapters. Chapter one considers the higher order of Borda Rules (Bp) and the Perron Rule (P) as extensions of the classic Borda Rule. We study the properties of those vector-valued voting rules and compare them with Simple Majority Voting (SMV). Using simulation, we found that SMV can yield different results from B1, B2, and P even when it is transitive. We also give a new condition that forces SMV to be transitive, and then quantify the frequency of transitivity when it fails.

In chapter two, we study the `protocol paradox' of approval voting. In approval voting, the outcome is not a function of the profile of individual preferences of voters alone, but also of the preference protocols chosen by voters. By a protocol, we mean the number of alternatives an individual voter approves. We quantify the differences in outcome that result from this ambiguity in several ways regarding hypotheses about individual preferences. We refer to this ambiguity as the 'protocol paradox .'We find the paradox quite substantial in that the protocol rivals preferences as a determinant of the outcome.

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