I was reading this old paper, doesn't matter why, but I stumbled on a funny little bit in the section about the mathematical model. Consider:
Let us consider t treatments in an experiment involving paired comparisons. We shall first consider that these treatments have true ratings (or preferences) on a particular subjective continuum throughout an experiment. The continuum is specialized by the requirements that every T[i] >= 0 and that [they sum to one], the latter condition being added for convenience. Further definition follows with the assumption that, when treatment i appears with treatment j in a block, the probability that treatment i obtains top rating (or a rank of 1) is T[i]/(T[i] + T[j]). Later generalization will require the addition of a second subscript on the parameters indicative of judges or time.
Reasonable enough model to play with. What's the part that's farcically mathematical?
Now r[i][j][k] will designate the rank of the ith treatment in the kth repetition of the block in which treatment i appears with treatment j. Clearly r[j][i][k] = 3 - r[i][j][k].
I think the term "trivially" is better here. Trivially, r[j][i][k] = 3 - r[i][j][k]. That is the least clear way to describe this I can imagine, although I will avoid the spoiler of explaining what absurdly simple statement that formula encodes, as decoding it was a true amusement to me, easily the funniest 45 seconds of my day so far.
This (trivial) mathematical statement forms the basis of even crazier descriptions, but the authors explain how they're massively over-complicating some of those, at least. And I'm not trying to typeset them, I'd have to do it in LaTeX and export and upload something here – just go look at the paper. It is a pretty interesting paper, and not all of the math is irrelevant or farcical (or, if it is, I have no decoded the farce sufficiently to find the humor).