Recommendation by personalization is a hot research topic in the field of computer science. The global market cap for the field is approximately 20 billion USD with an annual growth rate of 40%. However, a debate on whether personalization or popularity is the best choice for online recommendation systems is still on-going, and most of the time there is no theoretical argument answering the question. In this paper, we apply Arrow’s Impossibility Theorem to the topic, and demonstrate that recommendation by personalization and recommendation by popularity are two entirely different algorithmic paradigms that are not equivalent to each other.