Relaxation of the Condorcet and Simpson conditions in voting location

A Condorcet point, in voting location, is a location point such that there is no other closer to more than half of the users. However, such Condorcet solution does not necessarily exist. This concept is based on two assumptions. First, two locations are indifferent only if they are at the same distance from the voter. Second, the number of voters needed to reject a location is more than half of them. We relax the Condorcet condition in two ways. First, by considering that two locations are indifferent for every user if the difference of the distances to them is within a positive threshold. Secondly, by considering that the proportion of users needed to reject a location is not one half. We consider the resulting new solution concepts that arise by applying both relaxations at the same time and develop algorithms for obtaining them in the finite case.