The idea behind the word analogy task (Mikolov et al., 2013b) is that the "best" word embedding is the one that encodes linguistic relations in the most regular way: simple vector offset should be sufficient to capture semantic shifts such as F rance : P aris to Japan : T okyo.
this view of linguistic relations (and analogical reasoning) is oversimplified, and performance on word analogies has also been shown to depend on cosine similarity between source word vectors Linzen, 2016;Levy and Goldberg, 2014b).