  Some distinguished types of voters, as vetoers, passers or nulls, as well as
some others, play a significant role in voting systems because they are either
the most powerful or the least powerful voters in the game independently of the
measure used to evaluate power. In this paper we are concerned with the design
of voting systems with at least one type of these extreme voters and with few
types of equivalent voters, with this purpose in mind we enumerate these
special classes of games and find out that its number always follows a
Fibonacci sequence with smooth polynomial variations. As a consequence we find
several families of games with the same asymptotic exponential behavior
excepting of a multiplicative factor which is the golden number or its square.
From a more general point of view, our studies are related with the design of
voting structures with a predetermined importance ranking.
