Attempts to predict the number of political parties emerging in democracies have usually been based on one of two seemingly incompatible approaches: (1) the ‘institutional’ approach (e.g., Duverger's Law and Hypothesis) focuses on the nature of the electoral system and also on the number of seats per district; (2) the ‘ideological’ approach stresses the nature and extent of social cleavages. This article attempts a synthesis by showing that election system and cleavage type interact to affect the number of parties, with the former factor determined in part by the latter. Our most striking finding, however, is that the effective number of parties tends to be obtained by adding ‘one’ to the number of issue dimensions. Within this broader framework, Duverger's Law emerges as a special case for polities with a single issue dimension, and Duverger's Hypothesis is replaced by a much more quantitative prediction as to the effective number of parties.

Following Duverger, low district magnitude (low number of seats per electoral district) produces a mechanical effect, the underrepresentation of small parties, and a psychological effect, discouraging voters from voting for small parties. The two effects usually occur together and cannot be tested separately. However, in Venezuela an experimental ‘control’ is provided by the requirement that voters simultaneously cast a vote for the same party in each of three legislative tiers (Senate, Chamber of Deputies, and State Assembly), each with a different district magnitude. Hence the psychological effect can exert itself on only one tier. In the other tiers exceptionally high or low deviations from proportional representation are observed. The separate effects of district magnitude are analysed by their consequences on the number of electoral parties and the deviation from proportional representation.

The electoral law in many European countries permits voters to indicate preferred candidates within a party list rather than to make a choice only between parties. This paper examines briefly the various voting arrangements which allow this and considers in some detail the patterns of their utilization and their possible consequences. Whilst such behaviour can be understood as a form of political participation, it is evident that patterns vary and consequences are uncertain due to the complex interrelationship between the different elements in the electoral situation.

By ‘Time-Democracy’ is understood a system of representation and government formation in which the relative strength of a party or a coalition determines the fraction of an election period during which the party/coalition will be in executive office. This system is based upon the assumption that the structure of the legislative body as well as the length of the electoral period will be laid down in the constitution. Some questions related to the applicability and practical implementation of the system are discussed.

The argument for proportional representation (PR) rests on the assumption that the legislature should accurately reflect the opinions of the voters as a whole. An alternative, and more compelling, argument is that the government (executive) should faithfully reflect the voters’ opinions. When we apply this proportional tenure (PT) criterion to 87 political parties in 18 countries from 1945 to 1980, we find that neither PR nor plurality-majority systems have performed very well. In PR systems, small centrist parties tend to be favoured, and large parties, especially those that are ideologically ‘extreme’, are discriminated against. Three types of constitutional-electoral arrangements may be introduced in order to make government tenure more proportional: PT in each government that is formed: PT by consecutive governments; and majoritarian PT in which the largest party forms the government for a period proportional to the size of its share of the popular vote.

Considerable attention has been paid to the properties of electoral mechanisms used in Western democracies to determine who formally exercises political power. However, attempts to justify preferences among different electoral mechanisms are generally underdeveloped and piecemeal. What is needed is an explicit emphasis on procedural justice as a benchmark for determining the most appropriate means of electing democratic governments. In this paper, concepts of procedural justice are described and applied to electoral systems. It is argued that procedural justice demands recognition of the criteria of representativeness, proportionality, unbiasedness, correctability, and initiative. These criteria imply that constituencies for the election of legislators should be territorial, and that they should be drawn in accordance with communities of conflict, which afford candidates strong incentives to seek and articulate imaginative solutions to major conflicts. These properties of procedural justice are consistent with empirical evidence that citizens demand more decentralized and participation-oriented approaches to representative democracy.

The problem of fair representation is studied in the case of cleavage according to one or two criteria. In the latter case we show that with minimal requirements of equity, a solution exists only if the two criteria are binary. This might explain an observed tendency to political bipolarization.