I voted for "Other", by which I mean the European Union. As a matter of fact, I do not consider it the most likely candidate for being the strongest power, but it should be on the list nevertheless. The Gross Domestic Product of the European Union as it is now in our timeline is bigger than that of the United States. If the EU were a unified country with a unified government and armed forces it would be the number one power on Earth (although, in the future, it might still lose this status to others, probably China or India). With earlier economic integration its strength would be even greater, and with earlier integration and no World Wars it would be stronger still. A European Union that begins to integrate earlier and is still more wealthy than in OTL might attract and admit still more members within Europe, at Europe's borders or even on other continents.
Having said all that, a POD that leads to an integration that makes the EU a unified country and the strongest power is difficult to find, but it is certainly not impossible.
So here is my personal choice of alternate Twentieth Century Number One Powers:
There are ten items on Anaxagoras' list, including "Other", for which I substitute "European Union". Liechtenstein must be removed because its inclusion is meant as a joke, leaving nine entities. I remove Italy from the list, if I remember correctly it has the smallest population base at the beginning of the Twentieth Century, and, at that time it is not even industrialized to the degree that the US, Britain and Germany are, and does not have valuable colonies. I also remove France from the list, it is far more industrialised than Italy and has valuable colonies. On the other hand, most of these colonies have populations that do not feel as French and the population of metropolitan France is small even compared to that of Germany. This leaves seven entities on the list.
I would like to group the remaining seven entities into two groups:
the most promising candidates: Russia, China, India, European Union
the outsiders with a chance: Britain, Germany, Japan
The difference between the two groups is the size of the "core group" - I do not know whether there is a scholarly name for this. With "core group" I mean those parts of the population of these entities that identify themselves with this entitiy - Russia, the European Union, the British Empire and so on. The members of the core group want the existence of the nation or Empire to continue, feel that the government of this entity represents at least partly their own interests, see each other as belonging to one of the same group and would, if the need arose, fight for this entity - not as mercenaries, but as patriots.
During large parts of the Twentieth Century the British Empire is the entity with the largest population, but its core group is only a small fraction of this - roughly the population of Britain, Irish Protestants and the white population of the Dominions and the British colonies. In China this group would be the Han Chinese, in India the Hindus, in Germany the Germans and in Japan the Japanese. If one makes the assumption (perhaps unfounded, criticism is welcome) that under other circumstances than those extreme ones that prevailed in the OTL Soviet Union, the Ukrainians, Byelorussians and the Russian population of Kazakhstan would see themselves as citizens of the same state as the Russians in Russia then one gets a much bigger core group for Russia than for either Britain, Germany or Japan. It needs no special comment that the core groups of China and China are also much bigger than those in the "outsider" group. In the case of the European communitiy I would say the core group would be much bigger than that of the British Empire, Germany or Japan, if the EU were one country.