Polling one´s friends: A graph theoretic view

Polling is an effective method to collect information from a population. However, pollsters are often concerned with unsatisfactory response rate. Incentive is sometimes used to boost response rate, but pollsters want to keep it low. In fact, when there is an underlying social network among responders, a pollster can elicit a high response rate while attempting to minimize polling costs via asking a friend of a user for the user´s response to a poll. In this paper, we frame the problem as one that minimizes (i) monetary cost, the money it takes to elicit a response from a potential respondent, and (ii) querying cost, the number of different individuals queried, when polling users of a social network while maximizing the information collected. We consider a variety of graphs and compute the monetary and querying costs of some natural greedy polling algorithms. Our approach allows to conduct a detailed analysis and obtain, sometimes explicit, results on the cost of polling. Empirical results on both synthetic data and real social network data validate our analytic models. In particular, we find out that in the 1.46-billion-edge Twitter social graph, only 22% of the users need to be queried to get information about all the users, while monetary cost of our algorithm can be as low as 38% of that for the strategy to poll every user.