Final answer:
Great Britain and the United States opted for joint occupation of the Oregon Country to foster peace and improve economic relationships after the War of 1812, balancing British and American claims based on discovery, exploration, treaty rights, and settlement activity.
Step-by-step explanation:
Great Britain and the United States agreed to share possession of the Oregon Country to address unresolved issues following the War of 1812. Joint occupation of the Oregon territory was established in 1818, renewed in 1827, with both nations recognizing the need to improve relations and trade. British claims were associated with discovery, exploration, and trade via the Hudson Bay Company, while U.S. claims involved discovery, exploration, and increasing settlement by Americans, particularly during the 1840s 'Oregon Fever' westward migration. The treaty rights and increasing population in the territory exerted by the United States eventually strengthened its claim to Oregon, reinforcing notions such as Manifest Destiny.
It is also important to note that the agreement to share possession of the Oregon Country came in the wake of the War of 1812, during which both Great Britain and the United States sought ways to improve their relationship. The agreements reached during this period, including the Rush-Bagot Agreement and the Congress of 1818, helped to improve foreign trade and economic health between the two nations.