Chance Agreement for Fleiss Kappa In Measuring nominal scale agreement among many raters, where the authors define Fleiss kappa, the agreement by chance is defined as

where $p_j$ is defined as the proportion of ratings which were to the $j$th category.
Can someone explain how the authors arrived at this equation?
An additional reference for the equations can be found on Wikipedia

Say two raters respond randomly, with probability of yes = 0.9 and probability of no = 0.1, we can put the results into this table.
      Yes    |   No  
Yes          |        |  0.9 
 No          |        |  0.1
---------------------------
Total   0.9  |   0.1  |  1.0

Best case (perfect agreement):
            R1 
R2     Yes   |   No  
Yes    0.9   |   0.0  |  0.9 
 No    0.0   |   0.1  |  0.1
---------------------------
Total   0.9  |   0.1  |  1.0

Worst case (max disagreement):
            R1 
 R2    Yes   |   No  
 Yes   0.81  |   0.09  |  0.9 
 No    0.09  |   0.01  |  0.1
---------------------------
Total   0.9  |   0.1   |  1.0

How much disagreement do we have in the worst case? 0.9^2 + 0.1^2 = 0.82
That's the formula.
