This paper explores the existence of structural state dependence in arbitration use where it is legally mandated to resolve labor-management bargaining disputes. Previous studies have found both positive state dependence (the narcotic effect) and negative state dependence. This paper reports a negative state dependence for the Minnesota public sector during the period 1973 to 1980. A weak positive trend in arbitration probabilities and a positive relationship between current arbitration probabilities and the proportion of bargainers engaging in arbitration during the same calendar year are also found. An analysis of the dynamic implications of these findings does not support fears that compulsory arbitration schemes are unstable or lead to arbitration as the dominant settlement mode.