  In experiments that study social phenomena, such as peer influence or herd
immunity, the treatment of one unit may influence the outcomes of others. Such
"interference between units" violates traditional approaches for causal
inference, so that additional assumptions are often imposed to model or limit
the underlying social mechanism. For binary outcomes, we propose new estimands
that can be estimated without such assumptions, allowing for interval estimates
assuming only the randomization of treatment. However, the causal implications
of these estimands are more limited than those attainable under stronger
assumptions, showing only that the treatment effects under the observed
assignment varied systematically as a function of each unit's direct and
indirect exposure, while also lower bounding the number of units affected.
