A ranking procedure based on a natural monotonicity constraint

We formulate a new ranking procedure in the traditional context where each voter has expressed a linear order relation or ranking over the candidates. The final ranking of the candidates is taken to be the one which best adheres to a natural monotonicity constraint. For a ranking a ≻ b ≻ c, monotonicity implies that the strength with which a ≻ c is supported should not be less than the strength with which either one of a ≻ b or b ≻ c is supported. We investigate some properties of this ranking procedure and encounter some surprising preliminary results.