  Can an agent's intelligence level be negative? We extend the Legg-Hutter
agent-environment framework to include punishments and argue for an affirmative
answer to that question. We show that if the background encodings and Universal
Turing Machine (UTM) admit certain Kolmogorov complexity symmetries, then the
resulting Legg-Hutter intelligence measure is symmetric about the origin. In
particular, this implies reward-ignoring agents have Legg-Hutter intelligence 0
according to such UTMs.
