There are several mathematical results and theorems concerning electoral processes. I'll cover the two most important theorems in voting theory: May's theorem, which shows the strength of first-past-the-post in the setting of a two-candidate election, and Arrow's theorem, which shows a weakness of all voting systems for elections with more than two candidates. I'll discuss some applications of the theory to two voting systems: First-Past-The-Post and the Alternative Vote, discussing their strengths and weaknesses.