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The effective number of parties, N = 1/Σp(i)2 (where p(i) is the fractional share of the ith party), usually suffices to describe adequately a constellation of parties of different strengths. Difficulties arise when disparity in party sizes is such that the largest share (p1) surpasses 0.50 (meaning absolute dominance), while N still indicates a multi-party constellation. In such cases N(∞) = 1/p1 is proposed as a supplementary indicator: a value less than 2 indicates absolute dominance. An 'NP' index proposed earlier is a combination of N and N(∞); its values are close of those of N(∞), but NP sometimes falls below 2 even when many parties are relevant for coalition formation. Appendix A offers an alternative approach based on indices of deviation from a norm, but it proves cumbersome.

In the presence of a large lumped category of 'Other' parties the effective number of parties cannot be known exactly. Some approaches used produce large discrepancies. This note shows how the effective number still can be estimated with fair accuracy. The same issue arises with the measures of disproportionality between seats and votes. © 1997 Elsevier Science Ltd.

This note helps to explain how cabinet-level concentration of power is constrained by party level concentration of seats. Arend Lijphart's Patterns of Democracy (1999) measures concentration of executive power by the frequency of minimal winning and one-party cabinets (MW/OP), and party concentration by the effective number (N) of legislative parties. In his factor analysis, these highly correlated indices are the central features that distinguish consensual from majoritarian systems. The present study establishes a quantitative logical relationship leading from N to the major component of MW/OP, so as to explain the reasons behind Lijphart's empirical observation. The note analyses separately the frequency of various types of cabinet coalitions that Lijphart's book has lumped together. It also offers a new way to visualize the effective number of legislative parties, as twice the minimal number of parties needed to form a minimal winning coalition. © 2002, Sage Publications. All rights reserved.

This paper proposes a new method to evaluate the number of relevant parties in an assembly. The most widespread indicator of fragmentation used in comparative politics is the "Effective Number of Parties", designed in 1979 by M. Laakso and R.Taagepera. Taking both the number of parties and their relative weights into account, the ENP is arguably a good parsimonious operationalization of the number of "relevant"parties. This index however produces misleading results in single-party majority situations as it still indicates that more than one party is relevant in terms of government formation. We propose to modify the ENP formula by replacing proportions of seats by voting power measures. This improved index behaves more in line with Sartori's definition of relevance, without requiring additional information (such as policy positions) in its construction. We thus advocate for the use of our "Effective Number of Relevant Parties"in future comparative research.

This paper proposes a new method to evaluate the number of relevant parties in an assembly. The most widespread indicator of fragmentation used in comparative politics is the "Effective Number of Parties", designed in 1979 by M. Laakso and R.Taagepera. Taking both the number of parties and their relative weights into account, the ENP is arguably a good parsimonious operationalization of the number of "relevant"parties. This index however produces misleading results in single-party majority situations as it still indicates that more than one party is relevant in terms of government formation. We propose to modify the ENP formula by replacing proportions of seats by voting power measures. This improved index behaves more in line with Sartori's definition of relevance, without requiring additional information (such as policy positions) in its construction. We thus advocate for the use of our "Effective Number of Relevant Parties"in future comparative research.

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. Copyright © 1985, Wiley Blackwell. All rights reserved

The mechanical effect of electoral systems, identified by Maurice Duverger, can be estimated by means of a quantitative model. The model predicts the range within which the effective number of parties in a district should fall for a given magnitude (number of seats) of the district. At the national level, a related model predicts the effective number of parties based on the effective magnitude and the number of seats in the national assembly. The institutional variables considered—magnitude and assembly size—define a great portion of the structural constraints within which a given country's politics must take place. The model developed provides a good fit to data in spite of its having been developed from outrageously simple starting assumptions. © 1993, American Political Science Association. All rights reserved.

What determines the number of parties in a national assembly? Previous work has emphasized either sociopolitical heterogeneity or electoral system permissiveness, or brought them together on an empirical basis. Here an equation is developed that satisfies two theoretical boundary conditions and expresses the effective number of assembly parties (N) in terms of both the number of politicized issue dimensions (I) and effective magnitude (M) of electoral system: N= I.6M.15 + 1. Actually, depending on circumstances, any of the three variables could become the dependent one, affected by the two others. Empirical evidence is presented, based on Lijphart's (1984) data on 22 stable regimes.

What determines the number of parties in a national assembly? Previous work has emphasized either sociopolitical heterogeneity or electoral system permissiveness, or brought them together on an empirical basis. Here an equation is developed that satisfies two theoretical boundary conditions and expresses the effective number of assembly parties (N) in terms of both the number of politicized issue dimensions (I) and effective magnitude (M) of electoral system: N= I.6M.15 + 1. Actually, depending on circumstances, any of the three variables could become the dependent one, affected by the two others. Empirical evidence is presented, based on Lijphart's (1984) data on 22 stable regimes.

Effective magnitude (M') and effective threshold (T') are important because they try to express quantitatively a major aspect of electoral systems, namely the degree of squeeze they put on representation of small parties. Three relationships have previously been proposed between M' and T'. Of these, T'=75%(M'+1) is found here to have the most desirable characteristics. However, regardless of the precise equation used, a disturbing discrepancy is observed in the case of single-member districts: the effective threshold predicted is much too high, if applied nationwide. This points out a more general need to keep district-level and nationwide indicators carefully separate. An appendix proposes a new formula to find effective magnitude when district magnitudes within a country vary.

We study a model of public decision-making in simple public goods economies with moral hazards and adverse selection. Economic agents must invest resources (or provide effort) to discover their own preferences. We consider direct revelation mechanisms based on sampling. A sample of agents is drawn in the population, and each member of the sample reports a preferences type to a Principal. The determinants of the "representative sample" size are studied. The structure and magnitude of effort and sampling costs affects the optimal number of representatives. If the net social value of the effort is high, first and second best optimality require a maximal sample (or "direct democracy"). If, on the contrary, effort is too costly, the recourse to samples ("representative democracy") is justified as a second best. To obtain the results, we not only take effort and revelation incentives into account, but also restrict decision rules to satisfy an additional property of robustness to opportunistic manipulation by the Principal, which forbids the use of a priori knowledge in public decision procedures.

The purpose of the study was to identify the components of an effective workplace mentorship. Twenty-five panelists participated in a three-round Delphi study to reach a consensus on these components. The panelists were (1) local school-site teachers and school-to-work coordinators, (2) community college school-to-work coordinators, (3) directors of tech-prep consortia, and representatives from (4) business and industry, (5) labor and management, (6) corporate rsearch, and (7) federal government. A two-round pilot study was conducted to test the initial open-ended questions for round 1 and to test the survey instrument developed for round 2. Feedback from the pilot study was used to develop the open-ended questionnaire instrument in round 1 and the Likert scale used in round 2 of the study. Criteria of an effective workplace mentorship were retained in both rounds 2 and 3 if 80% of the respondents rated them "important" or "very important." The study produced 93 criteria in five categories necessary for an effective workplace mentorship. The five categories were: (1) program structure; (2) recruitment, selection, and placement; (3) support activities; (4) program outcomes and evaluation; and (5) ethics. A sixth category, barriers and obstacles to an effective workplace mentorship, was included in the survey and contained four responses. These four responses were summarized along with the 93 criteria of an effective workplace mentorship. A checklist of criteria is included for the assessment of existing programs or to aid those implementing new programs. ; Ed. D.

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