Deliberation for Social Choice

In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard voting methods of social choice may be impractical. In such circumstances, one would like to have a general way of discovering socially preferable outcomes without relying on an understanding of the fundamental structure of the space. We propose deliberation, modeled by many bargaining scenarios among small sets of agents, as a natural solution to this problem. We describe the general method and analyze its outcomes in canonical spaces; our main result is that deliberation finds a 1.207-approximation to the social welfare optimum in median graphs. Introduction. Suppose you are a city council member in Urbanopolis, a large city offering a complex variety of public services. You are in charge of transportation services and have been tasked to (i) choose a set of 5 new projects out of 10 proposed for the city to initiate before the next fiscal year and (ii) determine the allocation of existing transportation funds to 20 ongoing transportation initiatives and services. Mindful of the public interest, you decide to elicit the best way forward based on the consensus of the citizens of Urbanopolis. This example highlights two problems in social choice theory. In (i), the decision space is combinatorial; there are 252 possible sets of projects, far too many to put to any ordinal vote. Furthermore, projects likely exhibit substitutions or complements, so any assumption of additive utility for cardinal utility elicitation and subsequent welfare optimization seems ill founded. In (ii), the decision space is continuous, at least within some range, and multidimensional. Assuming that utility is some metric over the space seems reasonable enough, but the imposition of any particular model of utility seems arbitrary. Intuitively, neither of these problems are hard for humans. That is to say, if any small set of interested agents look at the proposals, think for a bit, and discuss with one another, we suspect that agents can determine reasonable socially preferable outcomes. We seek to develop practical mechanisms based on this insight. We propose a mechanism that we term sequential deliberation. Sequential Deliberation. There is a decision space S of feasible outcomes (these may be projects, sets of projects, or continuous allocations) called decision points or alternatives and a set N of agents. We assume each agent has a hidden cardinal utility for each outcome. Sequential deliberation proceeds for T rounds and each round can be viewed as bargaining between the agents with a disagreement outcome. ∗Department of Computer Science, Duke University, 308 Research Drive, Durham, NC 27708. [email protected]. Supported by NSF grants CCF-1408784 and IIS-1447554. †Supported by the Army Research Office Grant No. 116388, the Office of Naval Research Grant No. 11904718, and by the Stanford Cyber Initiative. Author’s Address: Management Science and Engineering Department, Stanford University, Stanford CA 94305. Email: [email protected] ‡Department of Computer Science, Duke University, Durham NC 27708-0129. [email protected]. Supported by NSF grants CCF-1408784 and IIS-1447554.