The purpose of this research is to better understand the connections between dice and elections in voting theory. We explored the phenomenon of nontransitivity in dice and elections. In a set of 3 dice, labeled A, B, C, it is straightforward to designate sides such that, on average, A beats B, B beats C, and C beats A. Similarly, in an election of more than two candidates, where voters create a preference list for the set of candidates, it is simple to make nontransitive relationships in voter preference. Motivated by these situations, we aimed to find a correspondence between these two mathematical objects. Additionally, we defined the concept of an overall winner for a set of dice and an election, and explored the effects of nontransitivity in determining it. We used tournaments (from graph theory) as a tool to visualize the relationship structure among dice and elections. As a result of this work, we have shown that, from any dice set, an election can be constructed such that the dice possess the same winning-losing relationships. The converse is also true: given an election, a set of dice can be constructed with identical winning structure to the election. We defined the notion of a contest, which serves as a classification for both objects. Finally, we developed a triangular inequality for contests, and proved that dice and elections both satisfy this inequality.