MathDB

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

R

is also in a worse position than

a

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}.

Problem Statement