Causal Razors

When performing causal discovery, assumptions have to be made on how the true causal mechanism corresponds to the underlying joint probability distribution. These assumptions are labeled as causal razors in this work. We review numerous causal razors that appeared in the literature, and offer a comprehensive logical comparison of them. In particular, we scrutinize an unpopular causal razor, namely parameter minimality, in multinomial causal models and its logical relations with other well-studied causal razors. Our logical result poses a dilemma in selecting a reasonable scoring criterion for score-based casual search algorithms.