The main insight to solve this is to levage the 2d wedge product as to capture oriented rotation. Imagine you have a circle and you place three points equally spaced apart. Now choose one of those points and measure the rotation between the other two points. For one of the points it will be +2/3 PI whereas the other point would be −2/3PI. This property is true for all 3 of the points… Which encodes a rock/paper/scissors relationship.
At a high-level a multidimension elo could be constructed via a scalar component and a vector of position (x,y).
or elo(a) = (aS, aV_i), where the logit is calculated via
z(a, b) = (aS—bS) + K * sum_i ( aV_i ^ bV_i), where (aS—bS) was the standard elo logit and
K * sum_i ( aV_i ^ bV_i) is a weighted wedge sum across the vectors of position.
The main insight to solve this is to levage the 2d wedge product as to capture oriented rotation. Imagine you have a circle and you place three points equally spaced apart. Now choose one of those points and measure the rotation between the other two points. For one of the points it will be +2/3 PI whereas the other point would be −2/3PI. This property is true for all 3 of the points… Which encodes a rock/paper/scissors relationship.
At a high-level a multidimension elo could be constructed via a scalar component and a vector of position (x,y).
or elo(a) = (aS, aV_i), where the logit is calculated via
z(a, b) = (aS—bS) + K * sum_i ( aV_i ^ bV_i), where (aS—bS) was the standard elo logit and
K * sum_i ( aV_i ^ bV_i) is a weighted wedge sum across the vectors of position.