Backward induction in the wild? evidence from sequential voting in the US senate

In the US Senate, roll calls are held in alphabetical order. We document that senators early in the order are less likely to vote with the majority of their own party than those whose last name places them at the end of the alphabet. To speak to the mechanism behind this result, we develop a simple model of sequential voting, in which forward-looking senators rely on backward induction in order to free ride on their colleagues. Estimating our model structurally, we find that this form of strategic behavior is an important part of equilibrium play. We also consider, but ultimately dismiss, alternative explanations related to learning about common values and vote buying.