In the 1984 case of Arkansas v. Mississippi, the Supreme Court ruled on a dispute between these two states regarding their shared border along the Mississippi River. The controversy arose due to changes in the river's course over time, which led to uncertainty about where exactly state lines should be drawn. The court had previously established that when a river serving as a boundary shifts gradually through erosion and deposition processes (a process known as accretion), state boundaries shift with it; however, if it moves suddenly due to an event like flooding or an earthquake (avulsion), borders remain fixed at their pre-event location. In this case, Arkansas claimed that gradual changes had moved its border eastward into what is now considered part of Mississippi while Mississippi argued that avulsive events kept the boundary at its old location. After reviewing evidence including historical maps and documents, expert testimony from geologists and hydrologists among others -the Supreme Court sided with Arkansas' interpretation of events ruling in favor of them by stating that most recent alterations were indeed caused by slow accretion rather than sudden avulsion.

In the dissenting opinion for Arkansas v. Mississippi, it was argued that the majority's decision to apply a new standard of proof in original jurisdiction cases involving boundary disputes between states was unjustified and inconsistent with prior case law. The dissent contended that there was no compelling reason to depart from the preponderance-of-the-evidence standard traditionally used in such cases, which requires only that one side's evidence be more convincing than the other's. They believed this change would make resolving state boundary disputes unnecessarily difficult and complex by requiring clear and convincing evidence instead. Furthermore, they disagreed with how the majority interpreted previous rulings on similar issues, arguing their interpretation did not align with past decisions or legal principles established by those precedents.