  Possibility theory is proposed as an uncertainty representation framework for
distributed learning in multi-agent systems and robot swarms. In particular, we
investigate its application to the best-of-n problem where the aim is for a
population of agents to identify the highest quality out of n options through
local interactions between individuals and limited direct feedback from the
environment. In this context we claim that possibility theory provides
efficient mechanisms by which an agent can learn about the state of the world,
and which can allow them to handle inconsistencies between what they and others
believe by varying the level of imprecision of their own beliefs. We introduce
a discrete time model of a population of agents applying possibility theory to
the best-of-n problem. Simulation experiments are then used to investigate the
accuracy of possibility theory in this context as well as its robustness to
noise under varying amounts of direct evidence. Finally, we compare possibility
theory in this context with a similar probabilistic approach.
