So, the judges each contribute a collection of ingredients using our own nefarious methods -- and typically we don't share our methods with each other, just our output.
There is nothing really all that secret or esoteric about my method of devising contributions to the list of ingredients. I just brainstorm a variety of things or creatures, and then try to apply an interesting adjective to each one. The nouns are generally just words that catch my fancy as I am brainstorming (mirror, kitten, triceratops), without much rhyme or reason except what pops into my brain. The adjectives are applied a bit more thoughtfully, but can be chosen for any number of reasons, depending... Sometimes the adjective will be chosen because of tradition (broken mirror), sometimes for whimsy (persistent kitten), and sometimes because it is somewhat incongruous (divine triceratops). I try not to think too hard about how it might be used in any given scenario.
With our list of 100 ingredients put together, I choose the first couple completely randomnly, the next couple semi-randomnly, allowing myself to veto rolls if I think they are too similar to something already chosen, and then less randomly for the last couple as I want to make sure there is a decent variety of types of ingredients (people, places, things, and so forth). For the later rounds, when each judge picks a couple, I will pick the first one randomnly, and may then scan the list to see if there is one that catches my eye so that I would like to see what someone might do with it. For the final round, I might add in one not on the list, if there is something I have thought of since. For this years final round, for instance, I have an ingredient in mind that I think I will toss into the pot when it comes time to put the last list of ingredients together because it tickled my fancy when I read about it somewhere else.