1: for s ← 1 to S do

2:  (i, j) ← RandomChoose( )

3:  r ← logit−1 (η (θ, x) · Δi,jg(y, x)) {i.e. Prη,g(Yi,j = 1|x, Y(s−1) − (i, j) = y(s−1) − (i, j); θ)}

4:  u ← Uniform(0, 1)

5:  if u < r then

6:   ys ← y(s−1) + (i, j) {Have a tie at (i, j) with probability r.}

7:  else

8:   ys ← y(s−1) − (i, j) {Have no tie at (i, j) with probability 1 − r.}

9: return yS