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Table 3 Probabilities of proposals in the top four rank places based on the Mallows-Binomial (left) and Ratings-Only Binomial (right) models in toy example 2

From: A new approach to grant review assessments: score, then rank

Proposal

1

2

3

4

1

2

3

4

First

1

0

0

0

1

0

0

0

Second

0

0.48

0.52

0

0

0.48

0.26

0.26

Third

0

0.52

0.47

0.01

0

0.04

0.47

0.48

Fourth

0

0

0.01

0.99

0

0.48

0.27

0.26