Decentralized Polling with Respectable Participants

We consider the polling problem in a social network where participants care about their reputation: they do not want their vote to be disclosed nor their misbehaving, if any, to be publicly exposed. Assuming this reputation concern, we show that a simple secret sharing scheme, combined with verification procedures, can efficiently enable polling without the need for any central authority or heavyweight cryptography. More specifically, we present DPol, a simple and scalable distributed polling protocol where misbehaving nodes are exposed with a non-zero probability and the probability of dishonest participants violating privacy is balanced with their impact on the accuracy of the polling result. The trade-off is captured by a generic parameter of the protocol, an integer k we call the privacy parameter, so that in a system of N nodes with $B