Nationwide threshold of representation

How large must parties be to achieve minimal representation in a national assembly? The degree of institutional constraints is reflected indirectly by the number of seat-winning parties (n) and more directly by the threshold of representation (T), defined as the vote level at which parties have a 50-50 chance to win their first seat. The existing theoretical threshold formulas use district-level reasoning and therefore overestimate the nationwide threshold. This study extends the theory to the nationwide level. In addition to district magnitude (M), the number of electoral districts and hence assembly size (S) emerge as important variables. When all seats are allocated in M-seat districts, T=75%/[(M+1)(S/M)0.5] and n=(MS)0.25, T and n are connected by T=75%/[n2+(S/n2)]. These theoretical expectation values are tested with 46 durable electoral systems. © 2002 Elsevier Science Ltd. All rights reserved