Independence of Irrelevant Alternatives under the Lens of Pairwise Distortion

We give a quantitative analysis of the independence of irrelevant alternatives (IIA) axiom. IIA says that the society's preference between x and y should depend only on individual preferences between x and y: we show that, in several contexts, if the individuals express their preferences about additional (or "irrelevant") alternatives, this information helps to estimate better which of x and y has higher social welfare. Our contribution is threefold: (1) we provide a new tool to measure the impact of IIA on social welfare (pairwise distortion), based on the well-established notion of voting distortion, (2) we study the average impact of IIA in both general and metric settings, with experiments on synthetic data, and its impact with real datasets; and (3) we study the worst-case impact of IIA in the 1D-Euclidean metric space.