Daniel Halpern
Harvard University
Computer Science
Social Choice Under Uncertainty
This talk will touch on a few projects in social choice under uncertainty. Social choice theory gives a variety of tools for making a decision for a group of people based on the individuals’ heterogeneous preferences. These solutions often enjoy provable mathematical guarantees about the quality of the outcome. However, in many cases, we will not have enough data on people’s preferences in order to make the recommended decision. The question guiding this research agenda is what kind of theoretical guarantees can we make using this limited information?
We then focus on one project inspired by the opinion aggregation website pol.is. On pol.is, participants submit free-text opinions on a topic and then vote on other users’ submitted opinions, either indicating agreement or disagreement. The platform’s goal is to collect enough of this agreement/disagreement data in order to output a summary of the populations’ preferences. If we knew all participants’ opinions on all submitted opinions, tools from social choice theory would allow us to select a diverse subset of opinions that “represent” the entire population in a formal sense. However, in this practical scenario, people will only feasibly be able to respond to 20 of other users’ opinions, even though thousands have been submitted. We show that if this data is collected in the canonical way of showing random opinions from other users, finding a representative set will, in some cases, be impossible. On the other hand, we devise an adaptive sampling method that, provably, will be able to find a representative set with high probability.