Maximizing the Spread of Stable Influence: Leveraging Norm-driven Moral-Motivation for Green Behavior Change in Networks

In an effort to understand why individuals choose to participate in personally-expensive pro-environmentalbehaviors, environmental and behavioral economists have examined a moral-motivation model in whichthe decision to adopt a pro-environmental behavior depends on the society-wide market share of thatbehavior. An increasing body of practical research on adoption of pro-environmental behavior empha-sizes the importance of encouragement from local social contacts and messaging about locally-embracednorms: we respond by extending the moral-motivation model to a social networks setting. We obtaina new decision rule: an individual adopts a pro-environmental behavior if he or she observes a certainthreshold of adoption within their local social neighborhood. This gives rise to a concurrent updateprocess which describes adoption of a pro-environmental behavior spreading through a network. Theprocess evolves according to a set of difference equations in an exponentially large space that describesall possible patterns of adoption. The original moral-motivation model corresponds to the special caseof our network version in a complete graph.In parallel with the original moral-motivation work, we examine issues of stability of adoption (whichnow depends intimately on the spatial distribution of adoption within the network), bounds on the conver-gence time of the process, and the implications of the model on potential impacts of periods of temporarysubsidy. In particular, we are interested in the planning question of how periods of temporary subsidymay be targeted in the network in order to ensure migration to a stable equilibrium with a high rate ofparticipation in the pro-environmental behavior. At such a green equilibrium, stability is enforced byegoistic utility benefits individuals experience from conforming to a locally-embraced green norm (andwhere positive externalities associated with high environment quality accrue to the entire society). Toexamine this issue, we create a time-indexed Integer Program Model (which has modest size due to newgeneral theorems we prove on convergence times) that allows practically-efficient measurement of theexact optimal set of individuals to target with subsidy. Making a connection to the theoretical computerscience literature, we prove that no rigorously-efficient method exists to compute such a set. Our resultsare general and do not require that the network have any specific topological properties.The qualitative predictions of the network moral-motivation model can depart strongly from thepredictions of the original moral-motivation model: for certain classes of networks, careful targetingof subsidy within a network can greatly reduce the number of subsidized individuals required to reachthe green equilibrium. Asymptotic classes of examples demonstrate that such departures can be severe.Further, computational experiments show substantial departures for networks that resemble real socialnetworks: we deploy our IP model with off-the-shelf solvers in modestly-sized highly-clustered small-world networks related to the famous small-world networks of Watts and Strogatz.∗Neukom Postdoctoral Fellow, Neukom Institute for Computational Science, Dartmouth College.†Dartmouth College. 1arXiv:1309.6455v1[cs.SI]25Sep2013