In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem as a distributed constraint optimization problem (DCOP), in which each agent can communicate with other agents that share an interest in one or more variables. Whereas existing DCOP algorithms can be easily manipulated by an agent, either by misreporting private information or deviating from the algorithm, we introduce M-DPOP, the first DCOP algorithm that provides a faithful distributed implementation for efficient social choice. This provides a concrete example of how the methods of mechanism design can be unified with those of distributed optimization. Faithfulness ensures that no agent can benefit by unilaterally deviating from any aspect of the protocol, neither information-revelation, computation, nor communication, and whatever the private information of other agents. We allow for payments by agents to a central bank, which is the only central authority that we require. To achieve faithfulness, we carefully integrate the Vickrey-Clarke-Groves (VCG) mechanism with the DPOP algorithm, such that each agent is only asked to perform computation, report information, and send messages that is in its own best interest. Determining agent i's payment requires solving the social choice problem without agent i. Here, we present a method to reuse computation performed in solving the main problem in a way that is robust against manipulation by the excluded agent. Experimental results on structured problems show that as much as 87% of the computation required for solving the marginal problems can be avoided by re-use, providing very good scalability in the number of agents. On unstructured problems, we observe a sensitivity of M-DPOP to the density of the problem, and we show that reusability decreases from almost 100% for very sparse problems to around 20% for highly connected problems. We close with a discussion of the features of DCOP that enable faithful implementations in this problem, the challenge of reusing computation from the main problem to marginal problems in other algorithms such as ADOPT and OptAPO, and the prospect of methods to avoid the welfare loss that can occur because of the transfer of payments to the bank.