  We consider two-alternative elections where voters' preferences depend on a
state variable that is not directly observable. Each voter receives a private
signal that is correlated to the state variable. Voters may be "contingent"
with different preferences in different states; or predetermined with the same
preference in every state. In this setting, even if every voter is a contingent
voter, agents voting according to their private information need not result in
the adoption of the universally preferred alternative, because the signals can
be systematically biased.
  We present an easy-to-deploy mechanism that elicits and aggregates the
private signals from the voters, and outputs the alternative that is favored by
the majority. In particular, voters truthfully reporting their signals forms a
strong Bayes Nash equilibrium (where no coalition of voters can deviate and
receive a better outcome).
