the fifty percent threshold. Against the previous hypothesis, this pattern suggests that the
larger the size of the chamber, the easier it is to form a majority to alter the status-quo.
Figure 3 illustrates the overall decline of the effective majority as a function of N.
The effective majority threshold is not only asymptotic on N; it also displays a cycling
pattern by which an increase in N from an odd to an even number locally raises the
threshold. An odd number of legislators allows for the formation of a majority with fifty
percent of the votes plus “half” of a legislator. With an even number of legislators, a
minimal winning coalition can only be achieved with literally fifty percent of the votes
plus one. For example, if the size of a committee expands from three to four, the number
of members needed to form a majority grows from two to three, so that 2/3<3/4.
Figure 3
Political Parties
For the most part, cross-national comparative studies do not focus on individual
legislators (who are hard to pin-down) but on legislative parties. It is now common
wisdom that an increase in the number of legislative parties breeds greater policy stability.
Because a majority party is less likely to exist in a fragmented legislature and the costs of
collective action are presumably greater, the ability of any group to challenge the status-
quo is expected to decline (Cox and McCubbins 2001; Johnson and Crisp 2003;
Mainwaring 1993; Stein, Talvi, and Grisanti 1999, 111).
In order to model the impact of legislative parties on policy stability, we introduce
two additional concepts, the (raw) number of parties in congress (J) and their legislative
weight (w) or share of the seats. Given a legislature with N seats where s
j
is the number
of seats held by the j-th party, w
j
=s
j
/N. The effective number of parties, conventionally
8
Convention