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The Laakso-Taagepera index of the effective number of parties, while satisfying most of the requirements of this aggregate quantity, tends to produce unrealistically high scores for party constellations in which the shares of the largest parties exceed 50 percent, and can produce misleading results in several other situations. After reviewing the structural properties of the Laakso-Taagepera index and supplements or alternatives to it proposed in the literature, this article proposes a new index that eliminates several problems inherent in the mathematical form of indices using the Herfindahl-Hirschman measure of concentration as computational core. The proposed index is tested on a set of party constellations from recent elections in new democracies and non-democratic electoral regimes. The results confirm that the new index works better than earlier proposed alternatives in measuring the effective number of components in highly fragmented and highly concentrated party systems. [Reprinted by permission of Sage Publications Ltd., copyright holder.]

The Laakso—Taagepera index of the effective number of parties, while satisfying most of the requirements of this aggregate quantity, tends to produce unrealistically high scores for party constellations in which the shares of the largest parties exceed 50 percent, and can produce misleading results in several other situations. After reviewing the structural properties of the Laakso—Taagepera index and supplements or alternatives to it proposed in the literature, this article proposes a new index that eliminates several problems inherent in the mathematical form of indices using the Herfindahl—Hirschman measure of concentration as computational core. The proposed index is tested on a set of party constellations from recent elections in new democracies and non-democratic electoral regimes. The results confirm that the new index works better than earlier proposed alternatives in measuring the effective number of components in highly fragmented and highly concentrated party systems.

Polarization is a key characteristic of party systems, but scholars disagree about how polarization relates to the number of parties in a system. Different authors find positive, negative, or null relationships. This relationship is what one would expect if parties were drawn randomly from a super-population with an effective sample size somewhere between the effective and raw number of parties. I test this claim using multiple datasets which report party positions and seat shares, before extending my analysis to consider vote-level polarization, the range of positions, and polarization in presidential and parliamentary regimes. My work extends the Taageperaan research agenda of building interlocking networks of equations relating key quantities of electoral and party systems.

This paper develops a novel argument as to the conditions under which new political parties will form in democratic states. Our approach hinges on the manner in which politicians evaluate the policy implications of new party entry alongside considerations of incumbency for its own sake. We demonstrate that if candidates care sufficiently about policy outcomes, then the likelihood of party entry shouldincreasewith the effective number of status quo parties in the party system. This relationship weakens, and eventually disappears, as politicians' emphasis on "office-seeking" motivations increases relative to their interest in public policy. We test these predictions with both aggregate electoral data in contemporary Europe and a data set on legislative volatility in Turkey, uncovering support for the argument that party system fragmentation should positively affect the likelihood of entry when policy-seeking motivations are relevant, but not otherwise.

Different scholars count `the number of parties' in different ways, partly because they examine different parts of the political process and for different reasons. Sartori's qualitative approach focused mainly on competition for government, but is now largely supplanted by the quantitative `effective number of parties' index, which deals with votes and seats. But some quantitative research requires us to look beyond votes and seats. For example, testing proportional and pluralitarian models of democracy requires us to count parties not just in terms of votes and seats but also in terms of legislative and cabinet power. I estimate party shares of legislative and cabinet power to test democratic norms at British and German elections and parliaments. So, the effective number of parties index needs to be, and can be, extended beyond votes and seats alone.

Blais (2006) and Blais and Aarts (2006) in their review essays on voter turnout call attention to a striking puzzle about the link between electoral systems and turnout, namely that, ceteris paribus, proportional representation (PR) systems with many parties appear to have higher national-level turnout than single-member district (SMD) plurality systems with few parties, yet turnout does not increase with the (effective) number of parties (ENP) at the national level. To address this puzzle we turn to district-specific within-nation panel data from Switzerland and Spain. Our country-specific findings allow us to explain the national-level puzzle as essentially an ecological artefact, in that the multi-member districts found in proportional systems, on average, do exhibit higher turnout than SMDs, but turnout does not rise with district magnitude, m, once we move beyond the contrast between m = 1 and m > 1. Using a more sophisticated approach to measuring political competition that does not treat all PR systems as generating identical turnout incentives (Grofman and Selb, 2009), we seek to explain this puzzle by showing both empirically and theoretically that (1) proportionality does not necessarily increase with district magnitude, and (2) competition does not necessarily increase with district magnitude. [Reprinted by permission of Sage Publications Ltd., copyright holder.]

Blais (2006) and Blais and Aarts (2006) in their review essays on voter turnout call attention to a striking puzzle about the link between electoral systems and turnout, namely that, ceteris paribus, proportional representation (PR) systems with many parties appear to have higher national-level turnout than single-member district (SMD) plurality systems with few parties, yet turnout does not increase with the (effective) number of parties (ENP) at the national level. To address this puzzle we turn to district-specific within-nation panel data from Switzerland and Spain. Our country-specific findings allow us to explain the national-level puzzle as essentially an ecological artefact, in that the multi-member districts found in proportional systems, on average, do exhibit higher turnout than SMDs, but turnout does not rise with district magnitude, m, once we move beyond the contrast between m = 1 and m > 1. Using a more sophisticated approach to measuring political competition that does not treat all PR systems as generating identical turnout incentives (Grofman and Selb, 2009), we seek to explain this puzzle by showing both empirically and theoretically that (1) proportionality does not necessarily increase with district magnitude, and (2) competition does not necessarily increase with district magnitude.

Despite its conceptual centrality to research in comparative politics and the fact that a single measure—the Laakso-Taagepera index (LT)—is nearly universally employed in empirical research, the question of what is the best way to "count" parties is still an open one. Among other alleged shortcomings, LT has been criticized for over-weighting small parties, especially in the case of a one-party majority. Using seat-shares data from over 300 elections, I have calculated LT as well as an alternative measure (BZ) which employs normalized Banzhaf scores rather than simple party seat shares, as weights. The Banzhaf index is a voting power index which calculates a party's voting power as a function of its coalitional potential. Though the two measures are highly correlated, I identify three particular party constellations in which the differences between LT and BZ are systematic and statistically significant. In all of these cases, and especially in the case of a one-party majority, I argue that BZ is a more accurate representation of the actual party system, after any given election, while LT is perhaps better interpreted as a measure of the shape of the party system more generally. These findings have many implications, including with respect to the categorization of party systems and the empirical validity of Duverger's Law.