Defining Privacy for Weighted Votes, Single and Multi-voter Coercion

Most existing formal privacy definitions for voting protocols are based on observational equivalence between two situations where two voters swap their votes. These definitions are unsuitable for cases where votes are weighted. In such a case swapping two votes can result in a different outcome and both situations become trivially distinguishable. We present a definition for privacy in voting protocols in the Applied π-Calculus that addresses this problem. Using our model, we are also able to define multi-voter coercion, i.e. situations where several voters are attacked at the same time. Then we prove that under certain realistic assumptions a protocol secure against coercion of a single voter is also secure against coercion of multiple voters. This applies for Receipt-Freeness as well as Coercion-Resistance.