[Median Voter Theorem] In a small town, there are 100 voters, each with a distinct ideal point uniformly distributed along a one-dimensional political spectrum from 0 (most liberal) to 100 (most conservative). Three candidates, A, B, and C, are running for mayor and can choose their political positions (from 0 to 100) to gain votes. Each voter will choose the candidate with a political position closer to them. If candidates A and B choosed positions 50 and 70, respectively, they can now move their position after the candidate C decision. Assuming rationality and common knowledge, where should candidate C locate