## Problem of the week

### 2022-09 A chaotic election

Let $$A_1,\dots, A_k$$ be presidential candidates in a country with $$n \geq 1$$ voters with $$k\geq 2$$. Candidates themselves are not voters. Each voter has her/his own preference on those $$k$$ candidates.

Find maximum $$m$$ such that the following scenario is possible where $$A_{k+1}$$ indicates the candidate $$A_1$$: for each $$i\in [k]$$, there are at least $$m$$ voters who prefers $$A_i$$ to $$A_{i+1}$$.