  Voting is the aggregation of individual preferences in order to select a
winning alternative. Selection of a winner is accomplished via a voting rule,
e.g., rank-order voting, majority rule, plurality rule, approval voting. Which
voting rule should be used? In social choice theory, desirable properties of
voting rules are expressed as axioms to be satisfied. This thesis focuses on
axioms concerning strategic manipulation by voters. Sometimes, voters may
intentionally misstate their true preferences in order to alter the outcome for
their own advantage. For example, in plurality rule, if a voter knows that
their top-choice candidate will lose, then they might instead vote for their
second-choice candidate just to avoid an even less desirable result. When no
coalition of voters can strategically manipulate, then the voting rule is said
to satisfy the axiom of Strategy-Proofness. A less restrictive axiom is Weak
Strategy-Proofness (as defined by Dasgupta and Maskin (2019)), which allows for
strategic manipulation by all but the smallest coalitions. Under certain
intuitive conditions, Dasgupta and Maskin (2019) proved that the only voting
rules satisfying Strategy-Proofness are rank-order voting and majority rule. In
my thesis, I generalize their result, by proving that rank-order voting and
majority rule are surprisingly still the only voting rules satisfying Weak
Strategy-Proofness.
