The question is long, so I will paraphrase it briefly
Q: There are n people voting to choose the chair of the committee. Each person can vote for one person that has unique id (it is positive integer and vote will be stored in array). Chair will be the one with the most vote. Design algorithm to determine who is the chair and what would be the time complexity? Then if there are m < n candidates for the chair and we know value of m, what would be the algorithm to determine who is the chair and its time complexity?
(Edit: okay so no boyer-moore algorithm)
For the second part, I'm not sure why the fact that I know the value of m makes a difference. The last part of the question sounds like there are more efficient way of solving the problem when m is known.