Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues
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چکیده
n (M)} denote its ordered eigenvalues. A.1. Proof of Proposition 1 We will show that the matrix M⇤ specified in Figure 1a satisfies the conditions required by the proposition. It is easy to verify that M⇤ 2 CSST, so that it remains to prove the approximation-theoretic lower bound (4). In order to do so, we require the following auxiliary result: Lemma 1. Consider any matrix M that belongs to CPAR(F ) for a valid function F . Suppose for some collection of four distinct items {i
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