Systems, methods, and other embodiments associated with multi-distance tri-point arbitration are described. In one embodiment, a method includes using a K different distance functions, calculating K per-distance tri-point arbitration similarities between a pair of data points with respect to an arbiter point. A multi-distance tri-point arbitration similarity S between the data points is calculated by determining that the data points are similar when a dominating number of the K per-distance tri-point arbitration similarities indicate that the data points are similar; and determining that the data points are dissimilar when a dominating number of the K per-distance tri-point arbitration similarities indicate that the data points are dissimilar. The multi-distance tri-point arbitration similarity is associated with the data points for use in future processing.