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EvaluationHard· Fairness· Mathematics· Ranking

Why is a doubly stochastic matrix, rather than a single...

A hard ranking is a 0/1 permutation matrix, which creates a discontinuous step function for exposure. By relaxing this to a doubly stochastic matrix (where probabilities are between 0 and 1), exposure becomes continuous and differentiable. This mathematical shift is required to optimize for fairness constraints.

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