Federal courts are authorized to hear cases when the case involves federal question jurisdiction. State courts, on the other hand, are authorized to hear civil cases when the case involves state law. Suppose one wishes to file a suit to compel arbitration in a matter that involves both state and federal law, can one submit overlapping lawsuit to federal & state court at the same time?
For example, suppose two parties have an executed contract with a binding arbitration clause. Party A believes that Party B is in violation of both federal and state law and wishes to force Party B to arbitrate both claims. Party B holds that the contract does not force them to arbitrate (let's say because it expired) and believes that they have not violated any laws.
Can Party A file a suit to compel arbitration in both federal and state court?
What if they file two lawsuits and the state court rules differently than the federal court?
Assuming Party A can only file one lawsuit at a time, what stops Party A from first filling a lawsuit in state court and if the court rules against them to file a suit in federal court on the federal question? Presumably, if the federal court rules in their favor it would override the state court's decision.
Note: Although the reason for each lawsuit is different (federal vs. state law), the underlying question of whether the parties are bound to arbitration is the same. In other words, if the federal court arrives at the conclusion that the parties are bound to arbitrate the federal question (for example, because they arrive at the conclusion that the contract didn't expire), the same logic would apply to the state question (and vice versa).