  Power-law distributions are common, particularly in social physics. Here, we
explore whether power-laws might arise as a consequence of a general
variational principle for stochastic processes. We describe communities of
'social particles', where the cost of adding a particle to the community is
shared equally between the particle joining the cluster and the particles that
are already members of the cluster. Power-law probability distributions of
community sizes arise as a natural consequence of the maximization of entropy,
subject to this 'equal cost sharing' rule. We also explore a generalization in
which there is unequal sharing of the costs of joining a community.
Distributions change smoothly from exponential to power-law as a function of a
sharing-inequality quantity. This work gives an interpretation of power-law
distributions in terms of shared costs.
