Final answer:
Balance of power theory is limited in explaining alliance decisions because it overlooks factors like shared culture or religion, fails to recognize that not all strong powers are opposed, and incorrectly suggests that alliances are rare when they are not. The correct option is 4.
Step-by-step explanation:
The balance of power theory does not fully account for all alliance decisions in international relations for several reasons. Firstly, not all alliances form with balance of power as a goal. States often form alliances for a variety of reasons including political, strategic, and ideological motives that transcend mere power balancing.
For instance, shared culture, religion, or political ideologies can be substantial factors in alliance formations. Secondly, the balance of power theory suggests that strong powers should universally trigger balancing against them, which isn't always the case.
Certain powerful states may not be perceived as threats due to their relationships or behavior, which may lead to bandwagoning rather than balancing.
Lastly, the assumption that alliances rarely form in the international system is incorrect, as history shows multiple instances of alliances being a common feature in global politics for mutual security and strategic advantages. The correct option is 4.