Calculating Expected Risk for a Candidate Output

In a system that selects an output by minimizing an expected cost, the cost for a candidate output y_A is calculated by summing the pairwise costs between y_A and every possible reference output y_r, with each cost weighted by the probability of that reference output. The pairwise cost function is designed to be high for dissimilar outputs and low for similar outputs.

Suppose you are calculating the expected cost for candidate y_A. The probability of a very dissimilar candidate y_B increases, while the probability of a very similar candidate y_C decreases by an identical amount. All other probabilities and pairwise costs remain constant. What is the most likely effect on the expected cost of y_A?

When calculating the expected cost for a candidate output, a reference output that is very dissimilar to the candidate (resulting in a high pairwise cost) will always have a large impact on the final calculated expected cost, even if that reference output has a very low probability of being correct.