  We study two models of the Majority problem. We are given n balls and an
unknown coloring of them with two colors. We can ask sets of balls of size k as
queries, and in the so-called General Model the answer to a query shows if all
the balls in the set are of the same color or not. In the so-called Counting
Model the answer to a query gives the difference between the cardinalities of
the color classes in the query. Our goal is to show a ball of the larger color
class, or prove that the color classes are of the same size, using as few
queries as possible. In this paper we improve the bounds given by De Marco and
Kranakis for the number of queries needed.
