"What Do Your Friends Think?": Efficient Polling Methods for Networks Using Friendship Paradox

Abstract

This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for? Expectation polling asks: who do you think will win? In this paper, we propose a novel neighborhood expectation polling (NEP) strategy that asks randomly sampled individuals: what is your estimate of the fraction of votes for A? Therefore, in NEP, sampled individuals will naturally look at their neighbors (defined by the underlying social network graph) when answering this question. Hence, the mean squared error (MSE) of NEP methods rely on selecting the optimal set of samples from the network. To this end, we propose three NEP algorithms for the following cases: (i) the social network graph is not known but, random walks (sequential exploration) can be performed on the graph (ii) the social network graph is unknown. For both cases, algorithms based on a graph theoretic consequence called friendship paradox are proposed. Theoretical results on the dependence of the MSE of the algorithms on the properties of the network are established. Numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms.

Adaptive Polling in Hierarchical Social Networks Using Blackwell Dominance

“…The proposed adaptive polling mechanism for hierarchical social networks also takes this into account. We formulate adaptive generalizations of the Intent Polling and Expectation Polling methods 3 [18] in Sec.III-A and Sec.III-B, and Neighbourhood Expectation Polling [19] based on Friendship Paradox 4 in Sec.III-C. (ii) Blackwell Dominance in Hierarchical Networks: As mentioned above, in general, solving a POMDP is computationally intractable (see Footnote 1). A key property of our adaptive polling POMDP is that it exhibits a Blackwell dominance structure.…”

“…The formulations in this section are adaptive (feedback control based) generalizations of the intent and expectation polling [18], [22], and the recently proposed Neighbourhood Expectation Polling [19] mechanisms, to account for the time varying state and the hierarchical influence structure present in social networks.…”

Friendship paradox biases perceptions in directed networks

“…This is because in expectation polling, an individual names the candidate more popular among her friends, thus summarizing a number of individuals in the social network, rather that provide her own voting intention. Our polling algorithm is motivated by [20,19,21], which show that polling methods asking individuals to summarize information in their neighborhood outperform polling methods that ask only about the attribute of each individual. [20] studied the polling problem analytically in the context of an undirected network and, proposed a method to obtain an unbiased estimate of the global prevalence with bounds on its variance.…”

“…The analysis of Algorithm 1 for directed graphs is motivated by these results in [20] for undirected social networks. [21] proposed to ask the simple question "What fraction of your neighbors have the attribute 1?" (neighborhood expectation polling) from randomly sampled neighbors (instead of random nodes) on undirected social networks.…”

Diffusion in Social Networks: Effects of Monophilic Contagion, Friendship Paradox, and Reactive Networks

“…Friendship paradox, which in essence is a sampling bias observed in undirected social networks has gained attention as a useful tool for estimation and detection problems in social networks. For example, [18] proposes to utilize friendship paradox as a sampling method for reduced variance estimation of a heavy-tailed degree distribution, [19], [20], [21] explore how the friendship paradox can be used for detecting a contagious outbreak quickly, [22], [23], [24], [25], [26] utilizes friendship paradox for maximizing influence in a social network, [27] proposes friendship paradox based algorithms for efficiently polling a social network (e.g. to forecast an election) in a social network, [28] studies how the friendship paradox in a game theoretic setting can systematically bias the individual perceptions.…”