Final answer:
The island commonwealth dealing with the issue of popular sovereignty with the United States and discussions around becoming the 51st state is Puerto Rico. Puerto Rico is a U.S. commonwealth and its status remains complex, influenced by history and political dynamics with the U.S.
Step-by-step explanation:
The island commonwealth in question, dealing with issues of popular sovereignty in relation to the United States and discussions around becoming the 51st state, is Puerto Rico. Puerto Rico is currently a U.S. commonwealth, and throughout its history has held several referendums to decide its future, with options including maintaining commonwealth status, pursuing statehood, or gaining independence. While it elects its own government and was granted U.S. citizenship to its residents in 1917, it does not have the right to vote in U.S. presidential or congressional elections. The status of Puerto Rico remains a complex issue influenced by its colonial past, aspirations for self-governance, and the interconnected political dynamics with the United States.