A one-voter election cannot have a majority cycle because of the requirement that we've imposed that the voter's list must be rational.
(a) Show that a two-voter election may have a majority cycle. (We consider the group preference a majority cycle if all three group totals are nonnegative or if all three are nonpositive-that is, we allow some zero's in the group preference.)
(b) Show that for any number of voters greater than one, there is an election involving that many voters that results in a majority cycle.