  Berkovitz (1998b, section 3.2, 2002, section 4) argues that Arntzenius's line of reasoning fails because it is based on untenable assumptions about the nature of probabilities in closed causal loops—assumptions that are very natural in linear causal situations (where effects do not cause their causes), but untenable in causal loops. (For an analysis of the nature of probabilities in causal loops, see Berkovitz 2001 and 2002, section 2.) Thus, he concludes that the consistency of relativistic parameter-dependent theories cannot be excluded on the grounds of causal paradoxes. He also argues that the real challenge for relativistic parameter-dependent theories is concerned with their predictive power. In the causal loops predicted by relativistic parameter-dependent theories in Arntzenius's suggested experiment, there is no known way to compute the frequency of events from the probabilities that the theories prescribe. Accordingly, such theories would fail to predict any definite statistics of measurement outcomes for that experiment. This lack of predictability may also present some new opportunities. Due to this unpredictability, there may be an empirical way for arbitrating between these theories and quantum theories that do not predicate the existence such causal loops in Arntzenius's experiment. 