Category-theoretic approach to social choice theory

It is known (see, for example, this paper) that certain aspects of social choice theory can be reframed in category theory, a powerful and abstract field that unifies and encodes many different concepts and ideas in mathematics. For example, Arrow and Gibbard-Satterthwaite Impossibility Theorems can both be phrased in this context.

With all the recent advances in category theory, it seems that a new and broader look at the relationship between category theory and social choice theory is warranted. Is there a way to axiomatize social choice theory in category-theoretic language so that the notions such as voting, conflict, bargaining, fairness, and manipulation have a common foundation in this field? This would of course be useful since the full power of category theory could be brought to bear on social choice theory, expanding and enriching it. These are some of the questions Prof. Ismar Volić has been investigating in this research that bridges abstract mathematics and game theory.