The institute overall is run by co-directors in concert with an interdisciplinary steering group, a deliberate experiment with organisational structures, aiming to avoid excess hierarchy and to stimulate scholarly informality. The directors facilitate the Triple-I environment for innovative work and interaction, and collaborate with a group of academic and artist associates that contribute in an advisory capacity.

The two Triple-I directors are dr Frederick Whitling (historian) and dr David Horan (economist), both alumni of the European University Institute, Florence.