Evaluating Policy Effects through Network Dynamics and Sampling

In the process of enacting or introducing a new policy, policymakers frequently consider the population's responses. These considerations are critical for effective governance. There are numerous methods to gauge the ground sentiment from a subset of the population; examples include surveys or listening to various feedback channels. Many conventional approaches implicitly assume that opinions are static; however, in reality, the population will discuss and debate these new policies among themselves, and reform new opinions in the process. In this paper, we pose the following questions: Can we quantify the effect of these social dynamics on the broader opinion towards a new policy? Given some information about the relationship network that underlies the population, how does overall opinion change post-discussion? We investigate three different settings in which the policy is revealed: respondents who do not know each other, groups of respondents who all know each other, and respondents chosen randomly. By controlling who the policy is revealed to, we control the degree of discussion among the population. We quantify how these factors affect the changes in policy beliefs via the Wasserstein distance between the empirically observed data post-discussion and its distribution pre-discussion. We also provide several numerical analyses based on generated network and real-life network datasets. Our work aims to address the challenges associated with network topology and social interactions, and provide policymakers with a quantitative lens to assess policy effectiveness in the face of resource constraints and network complexities.