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

TL;DR

This paper introduces a novel neighborhood expectation polling method leveraging the friendship paradox to efficiently estimate election outcomes in social networks, with algorithms suited for unknown or partially known network structures.

Contribution

The paper proposes three new NEP algorithms utilizing the friendship paradox for network polling, applicable when the network graph is unknown or partially known, with theoretical analysis and empirical validation.

Findings

Algorithms reduce mean squared error in network polling

Performance depends on network properties like degree distribution

Numerical results demonstrate effectiveness on real and synthetic data

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 case (i) and (ii), two 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.