On the equivalence of simultaneous and sequential binary elections

We explore sequential voting in symmetric two-option environments. We show that the (informative) symmetric equilibria of the simultaneous voting game are also equilibria in any sequential voting structure. In unanimity games, (essentially) the whole set of equilibria is the same in all sequential structures. We also explore the relationship between simultaneous and sequential voting in other contexts. We illustrate several instances where sequential voting does no better at aggregating information than simultaneous voting. The inability of the sequential structure to use additional information in voting models is distinct from that in the herd-cascade literature