There are n voters and m candidates. Every voter makes a certain arrangement list of all candidates (there is one person in every place 1,2,...m) and votes for the first k people in his/her list. The candidates with most votes are selected and say them winners. A poll profile is all of this n lists.
If a is a candidate, R and R′ are two poll profiles. R′ is a\minus{}good for R if and only if for every voter; the people which in a worse position than a in R is also in a worse position than a in R′. We say positive integer k is monotone if and only if for every R poll profile and every winner a for R poll profile is also a winner for all a\minus{}good R′ poll profiles. Prove that k is monotone if and only if k>\frac{m(n\minus{}1)}{n}. combinatorics unsolvedcombinatorics