  How to distribute welfare in a society is a key issue in the subject of
distributional justice, which is deeply involved with notions of fairness.
Following a thought experiment by Dworkin, this work considers a society of
individuals with different preferences on the welfare distribution and an
official to mediate the coordination among them. Based on a simple assumption
that an individual's welfare is proportional to how her preference is fulfilled
by the actual distribution, we show that an egalitarian preference is a strict
Nash equilibrium and can be favorable even in certain inhomogeneous situations.
These suggest how communication can encourage and secure a notion of fairness.
