Voting by conforminy

A group of agents has to decide whether to accept or reject a proposal. Agents vote in favor or against the proposal and, if the number of agents in favor is greater to certain quota, the proposal is accepted. The \textit{socially optimal decision} is the one adopted when all agents vote truthfully. Conformist agents vote based not only on their opinion but also on the vote of other agents. Independent agents only care about their opinion. If all agents are conformists and vote simultaneously, for any quota there are undominated Nash equilibria where the socially optimal decision is not obtained. Next, we provide the number of independents needed for the socially optimal decision to be obtained in any equilibria. It depends on the total number of agents, the quota and the conformity measure. If agents vote sequentially, the socially optimal decision is obtained in any subgame perfect Nash equilibrium.