  When applied to question answering and other text generation tasks, language
models (LMs) may be queried generatively (by sampling answers from their output
distribution) or discriminatively (by using them to score or rank a set of
candidate outputs). These procedures sometimes yield very different
predictions. How do we reconcile mutually incompatible scoring procedures to
obtain coherent LM predictions? We introduce a new, a training-free,
game-theoretic procedure for language model decoding. Our approach casts
language model decoding as a regularized imperfect-information sequential
signaling game - which we term the CONSENSUS GAME - in which a GENERATOR seeks
to communicate an abstract correctness parameter using natural language
sentences to a DISCRIMINATOR. We develop computational procedures for finding
approximate equilibria of this game, resulting in a decoding algorithm we call
EQUILIBRIUM-RANKING. Applied to a large number of tasks (including reading
comprehension, commonsense reasoning, mathematical problem-solving, and
dialog), EQUILIBRIUM-RANKING consistently, and sometimes substantially,
improves performance over existing LM decoding procedures - on multiple
benchmarks, we observe that applying EQUILIBRIUM-RANKING to LLaMA-7B
outperforms the much larger LLaMA-65B and PaLM-540B models. These results
highlight the promise of game-theoretic tools for addressing fundamental
challenges of truthfulness and consistency in LMs.
