Totally! I am an ardent fan of Behavioral Economics and the psychology of illogical behavior — I have Kahneman and Tversky’s collected research on my shelf. :) Irrational behaviors are the key exploit used against us, most of the time.

I suppose that, if a provably fair protocol exists, then lawyers will advise you to only sign contracts which explicitly state that the cake-slicing protocol is used for arbitration — and, because the protocol has a guaranteed result, you can actually just write down how much you value each item, and feed that to a pair of autonomous agents, who do the iterated slicing for you, using your own stated values as their rewards. When they’re done, they spit out the result, and trash the valuations that they stored. So, humans only enter how much each item is worth, to them, while contract and algorithms take care of the rest. With luck, we can put a little toddler fence across the hallway of superstitions.