This issue pops up now and then in Secured Transactions, when three (or more) creditors are fighting over a pool of collateral with a value that falls short of adequately securing repayment of all of the debts (creating a genuine priority dispute). The relevant legal rules may resolve the priority dispute as follows: A beats B, B beats C, and C beats A. Now what?
If this topic is of interest to you (it is, isn't it?!?!?!), you'll want to read Circular Priorities in Secured Transactions Law, authored by Roderick J. Wood (pictured), a professor on the law faculty at the University of Alberta. Here's the SSRN abstract:
Circular priority problems are endemic in secured transaction law. A circular priority situation arises when there are three or more parties with competing claims to the same asset and there is no clear ranking of priority among them. There are multiple approaches applied by courts or advanced by commentators to resolve circular priority problems. The different mechanisms used by the courts to resolve a circular priority problem are evaluated using criteria that reflect the general values and goals of commercial law, and the mechanism that best accords with this criteria is identified. Although consensus on the best way of breaking a circularity will reduce litigation costs, it does not provide a complete solution as it can be undermined by ex post bargaining among creditors. Given this instability, priority rules should be designed so as to minimize the occasions when such problems can arise.
The article appears at 47 Alberta Law Review 823-852 (2010).