A Model for Intransitive Preferences

It is known that humans form non-transitive preferences. We propose to model human preferences as a complete weighted directed graph where nodes are objects of preference, and an edge leading from one node to another has weight equal to the probability that the destination node will be preferred (or chosen) from the pair connected by the edge. We also propose that the most preferred object(s) might be modeled as the one that wins in a round-robin tournament played amongst the nodes. We discuss computations using this model and introduce a polynomial-time algorithm to bound the probability of selecting an object from a pool of objects with symmetric preferences.