Decentralized polling with respectable participants

We consider the polling problem in a social network: participants express support for a given option and expect an outcome reflecting the opinion of the majority. Individuals in a social network care about their reputation: they do not want their vote to be disclosed or any potential misbehavior to be publicly exposed. We exploit this social aspect of users to model dishonest behavior, and show that a simple secret sharing scheme, combined with lightweight verification procedures, enables private and accurate polling without requiring any central authority or cryptography.