Reach maximization for social lotteries

•We offer a new approach to control social influence driven by expansion of reach, rather than by direct diffusion.•We guarantee fairness in the randomized distribution of incentives, while maximizing the impact of a social influence program.•We formulate and solve the reach maximization problem, without exhaustive exploration of the solution space.•We demostrate the application of our work to a social lottery for fostering pro-environmental (energy-saving) behavior at households. Social influence programs promoting behavior change have shown that people are more likely to adjust their behavior when simple information on the benefits of a targeted behavior is followed by “social proof” that referent others have already adopted this behavior. We argue that the impact of such programs, in particular those that promote a pro-environmental behavior, can be enhanced with direct incentives (e.g., monetary prizes) distributed in a random manner to adopters of the favored behavior according to their efforts. We formally model “social lottery” as a type of social influence program, and solve the problem of maximizing its expected impact. A social lottery rewards the promoted behavior and distributes the incentives fairly—based mainly on the individuals’ verifiable commitment to the program (e.g., their achievements in energy-saving) as opposed to their network positions. We define “reach” as a measure of exposure of individuals to Word-of-Mouth spread of information, and explain that the impact of a social influence program on a population (the conversion rate of non-adopters to adopters) can be viewed as a direct consequence of enhancing its reach. We then introduce reach maximization as a fundamental approach to maximizing the impact of social influence programs, where the influence spread is not driven by direct diffusion and where influence is delivered over multiple rounds. We show how our methodology can be applied to design each individual round of a social lottery. Further, we illustrate how our methodology can be used to design a social lottery program for fostering energy-conscious behavior, and perform computational experiments to showcase its effectiveness and scalability.