Logic and Philosophy of Science Group Talk (Eric Pacuit, Maryland)

This talk will discuss axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. In a recent paper, we proposed a weakening of Kenneth Arrow’s famous condition of the Independence of Irrelevant Alternatives (IIA), called Coherent IIA. We showed that five well-known axioms  of voting  plus Coherent IIA single out a voting procedure studied in other  recent work called Split Cycle. The main objective of this talk is to explain how Split Cycle escapes Arrow’s Impossibility Theorem and related impossibility results. This work is part of a larger project focused on identifying voting methods that respond reasonably to the addition of new candidates and new voters to an election: If a voting method selects candidate $x$ as a winner, then $x$ should not become a loser by the addition of a new candidate to whom $x$ is majority preferred or the addition of a new voter who ranks $x$ in first place. We are interested both in characterizing voting methods that satisfy this and related principles and using computer simulations to assess the frequency and severity of violations to this principle for different voting methods.

This is joint work with Wes Holliday.