  Methods of statistical physics have proven valuable for studying the
evolution of cooperation in social dilemma games. However, recent empirical
research shows that cooperative behavior in social dilemmas is only one kind of
a more general class of behavior, namely moral behavior, which includes
reciprocity, respecting others' property, honesty, equity, efficiency, as well
as many others. Inspired by these experimental works, we here open up the path
towards studying other forms of moral behavior with methods of statistical
physics. We argue that this is a far-reaching direction for future research
that can help us answer fundamental questions about human sociality. Why did
our societies evolve as they did? What moral principles are more likely to
emerge? What happens when different moral principles clash? Can we predict the
break out of moral conflicts in advance and contribute to their solution? These
are amongst the most important questions of our time, and methods of
statistical physics could lead to new insights and contribute towards finding
answers.
