Which factor is essential in rendering an ally's nuclear arsenal redundant?

The correct choice focuses on the concept of a "nuclear umbrella," which refers to a security arrangement where a nuclear-armed state extends its deterrence capabilities to an ally that does not possess its own nuclear weapons. This arrangement can significantly reduce the perceived need for the ally to maintain its own nuclear arsenal, as they rely on the protective capabilities of their ally to deter potential threats.

In the context of international security, a nuclear umbrella provides reassurance and stability, allowing allied nations to feel secure from external aggression without developing their own nuclear capabilities. This can lead to a more cooperative relationship among nations, fostering stronger alliances and potentially leading to non-proliferation as nations feel less compelled to pursue their own nuclear programs.

The other options, while they may contribute to international relations, do not directly address the concept of nuclear deterrence in the same way. Geographic isolation may limit threats but does not eliminate the need for a nuclear arsenal. Strong diplomatic relations can foster cooperation and peace, but they do not inherently provide the security that a nuclear umbrella offers. Economic incentives can encourage alliances and cooperation but do not directly influence the need for nuclear weapons in the same way that a nuclear umbrella does.