Leave No Winner
Close the ring so nothing is unbeaten; then work on the one you would have discarded first.
Formerly Unrank
Non-transitive dice: whoever picks second wins.
Seen in Game Freak, Pokémon Red and Blue, Generation 1, 1996
Try it on your work
Lay out five versions of the thing you're working on. For each, name one other it is better than and one it is worse than, by different criteria, until the five form a closed cycle with no winner. Stop when the cycle closes. Work on the one you would have discarded first.
Write five one-line arguments for your project. Arrange them so each defeats the next and the last defeats the first. Stop when the ring holds. Notice which argument you had been treating as the strongest, and why the ring did not let it be.
List the five ways you could spend next month on the project. Refuse to rank them; instead, for each, state one respect in which it beats one other and one in which it loses to another. Stop when no option is unbeaten. Choose by coin.
How it has been used
Preferences can run in circles: rock beats scissors, scissors beat paper, paper beats rock. Mathematicians have built dice that do the same. Once options form a ring, there is no best one, and the question changes from which wins to what each is for.
Where it leads
Grouped under Push me beyond what I’d normally do