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

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