I have 10 independent samples of ordinal data ranked 1-3. I also have predicted ranks for the same data set. I want to test if the predicted ranking matches the observed ranking at a rate better than chance.

I know for a single paired ordinal sample the Wilcoxon signed-rank test would be used, but I am not sure what to do with multiple samples. Would this be a good application of Fisher's method? Also with only 3 values to rank, my Wilcoxon test only returns p-values of 1 or NaN, is there another test that would be more appropriate here?