This paper considers coercion contracts in voting systems with
end-to-end (E2E) veriability. Contracts are a set of instructions that
an adversary can dictate to a voter, either through duress or by
offering payment, that increase the probability of a compliant voter
constructing a vote for the adversary's preferred candidate. Using a
representative E2E system, we place the attacks in game-theoretic
terms and study the effectiveness of three proposed contracts from the
literature. We offer a definition of optimality for contracts, provide
an algorithm for generating optimal contracts, and show that as the
number of candidates increases, the adversary's advantage through the
use of contracts decreases. We also consider the use of contracts in a
heterogeneous population of voters and for financially constrained
adversaries.