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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.

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.

Accurate evaluation of electoral systems requires precise measurement of both the disproportionality and the concentration of party systems. While the measurement of disproportionality has been investigated systematically and clear guidance for measurement exists, such treatment is lacking for the concentration dimension. This paper clarifies the theoretical concept of concentration in focusing on the directness of the voter-government link and differences between types of coalitions. In light of this concept, a new measure is introduced, and the different measures are compared theoretically as well as empirically. In conclusion, the effective number of parties measure provides a fruitful framework, but should be applied to the cabinet instead of the parliament level in order to clearly identify substantial features of party system concentration.

We illustrate the power of "logical models" (Taagepera, 2007) by offering a three-parameter model of the relationship between the effective number of parties and electoral turnout that makes use of the constraints on what parameter values are internally coherent given boundary conditions to specify functional form, and seeks not optimal curve fitting but rather a direct model testing. In our model, one parameter reflects an effect that generally acts to increase turnout as the effective number of parties increases, another an effect that generally acts to decrease turnout as the effective number of parties increases, while a third parameter allows for baseline variation in turnout across countries (or within countries across elections). We fit this model to district-level data from 237 elections held in 17 countries, representing a wide range of electoral system types generating multi-party contests, with over 20,000 district-election observations. The basic intuition, that turnout rises to a peak as the effective number of parties increases and then falls slowly, fits our data pretty well. © 2013 © 2013 Elections, Public Opinion & Parties.

This paper proposes a model of a legislature, formed by several parties, which has to vote for or against a certain bill in the presence of a lobbyist interested in a certain vote outcome. We show that the ease with which the lobbyist can manipulate a legislature decision increases with the number of elected parties, and, consequently, decreases with an electoral threshold. On the other hand, a lower electoral threshold increases the representativeness of a legislature. We combine these two effects in a notion of fairness. We show the existence of an electoral threshold that optimizes the fairness of a political system, which is close to 1–5%. Namely, the optimal threshold (in our sense) is close to thresholds that exist in most parliamentary democracies.

Altres ajuts: COST Action IC1205 on Computational Social Choice ; This paper proposes a model of a legislature, formed by several parties, which has to vote for or against a certain bill in the presence of a lobbyist interested in a certain vote outcome. We show that the ease with which the lobbyist can manipulate a legislature decision increases with the number of elected parties, and, consequently, decreases with an electoral threshold. On the other hand, a lower electoral threshold increases the representativeness of a legislature. We combine these two effects in a notion of fairness. We show the existence of an electoral threshold that optimizes the fairness of a political system, which is close to 1-5%. Namely, the optimal threshold (in our sense) is close to thresholds that exist in most parliamentary democracies.

This paper proposes a model of a legislature, formed by several parties, which has to vote for or against a certain bill in the presence of a lobbyist interested in a certain vote outcome. We show that the ease with which the lobbyist can manipulate a legislature decision increases with the number of elected parties, and, consequently, decreases with an electoral threshold. On the other hand, a lower electoral threshold increases the representativeness of a legislature. We combine these two effects in a notion of fairness. We show the existence of an electoral threshold that optimizes the fairness of a political system, which is close to 1-5%. Namely, the optimal threshold (in our sense) is close to thresholds that exist in most parliamentary democracies.

Political science knows a fair amount about the variables explaining party systems fragmentation or the constant in the equation of the number of parties. But we know much less about changes in the number of parties over time within countries or the slope in the equation of the number of parties. This paper fills this gap explaining the entry of new viable competitors in party systems after the founding election. Using empirical evidence from Spain, we show that when there is an electoral market failure and the higher the number of perfectly elastic voters, the higher the probability of new viable entrants. ; La ciencia política tiene un conocimiento bastante extenso de las variables que explican el sistema de fragmentación de partidos o de la constante en la ecuación del número de partidos. Pero, en cambio, se sabe mucho menos sobre los cambios en el número de partidos en el tiempo en los países o la pendiente de la ecuación en el número de los partidos. Este trabajo viene a cubrir esta carencia al explicar la entrada de los nuevos competidores viables en el sistema de partidos después de la elección fundacional. Utilizando la evidencia empírica de España, mostramos que cuando hay un fallo del mercado electoral y cuanto mayor es el número de votantes perfectamente elásticos, mayor es la probabilidad de nuevas entradas viables.

Political science knows a fair amount about the variables explaining party systems fragmentation or the constant in the equation of the number of parties. But we know much less about changes in the number of parties over time within countries or the slope in the equation of the number of parties. This paper fills this gap explaining the entry of new viable competitors in party systems after the founding election. Using empirical evidence from Spain, we show that when there is an electoral market failure and the higher the number of perfectly elastic voters, the higher the probability of new viable entrants. ; La ciencia política tiene un conocimiento bastante extenso de las variables que explican el sistema de fragmentación de partidos o de la constante en la ecuación del número de partidos. Pero, en cambio, se sabe mucho menos sobre los cambios en el número de partidos en el tiempo en los países o la pendiente de la ecuación en el número de los partidos. Este trabajo viene a cubrir esta carencia al explicar la entrada de los nuevos competidores viables en el sistema de partidos después de la elección fundacional. Utilizando la evidencia empírica de España, mostramos que cuando hay un fallo del mercado electoral y cuanto mayor es el número de votantes perfectamente elásticos, mayor es la probabilidad de nuevas entradas viables.

The aim of this article is to present a critical overview of research methods (so called indexes) used for measuring different parameters of party systems. The starting point for further discussion is the semantic relevance theory developed by G. Sartori. In the next part of the article I will deal with the question whether this qualitative method can be quantified in any way. With this regard, I will analyse such indexes as: the effective number of parties index, the power indexes and the government relevance indexes. The article shows that despite many scholars' fears, political science has a large set of tools for making precise measurements of empirical data, which may be used for comparison. A theoretical concept of relevance, together with its "qualitative" test, combined with properly selected and configured quantitative techniques, guarantee the effective measurement of relevance also at the ordinal, or even the interval level. Thus, it is legitimate to refer to this approach as an "index method". ; Celem artykułu jest krytyczny przegląd popularnych technik badawczych (tzw. indeksów) wykorzystywanych do pomiaru różnych parametrów systemów partyjnych pod kątem ich użyteczności w badaniu relewancji partii politycznych. Punktem wyjścia dla dalszych rozważań jest nominalna koncepcja relewancji zaproponowana przez G. Sartoriego. W dalszej części podjęta zostanie próba odpowiedzi na pytanie czy ta jakościowa metoda może zostać w jakikolwiek sposób skwantyfikowana? W tym kontekście analizie poddane zostaną takie wskaźniki jak: indeks efektywnej liczby partii, indeksy siły i relewancji rządowej. Artykuł wykazuje, że wbrew obawom wielu badaczy, politologia dysponuje rozbudowanym zbiorem narzędzi umożliwiających dokonywanie precyzyjnych i komparatystycznie przydatnych pomiarów danych empirycznych. Teoretyczna koncepcja relewancji, wraz z jej jakościowym "testem", w połączeniu z odpowiednio dobranymi i skonfigurowanymi technikami ilościowymi gwarantują skuteczny pomiar relewancji również na poziomie porządkowym, a nawet interwałowym. Można zatem podejście to z powodzeniem nazwać "metodą indeksowa".

Despite secularisation, there is growing recognition that some religious parties continue to influence elections and the formation of policy in several countries. But what explains why religious parties persist in some countries but not others? This study tests an argument holding that religious diversification promotes political cooperation and therefore reduces the number of religious parties. Using a data set of religious parties across advanced industrial democracies between 1945 and 2011, this paper analyses this argument and finds that religious diversity puts downward pressure on the number of religious parties over time.

We consider alternative methods of measuring the competitiveness of a majoritarian electoral system in the context of an analysis of Indian State elections. Our analysis highlights a number of weaknesses in the construction and interpretation of commonly used measures such as the effective number of parties, the first versus second place vote margin and safe seats, while presenting these and their proposed alternatives for 14 major Indian states from 1952 to 2009. The alternative indexes we present are based in part on ideas that are longstanding in the literature but have not been fully adopted within the Indian context. These indexes incorporate vote volatility, allow for multi-party competition at the constituency level, and adjust for asymmetry among parties of safe seats in the legislature. We argue that these newly computed indexes capture distinct but related dimensions of electoral competition better than do the extant commonly used measures. The analysis of these indexes is then extended to consider the role of caste, class, regionalism and level of development to reveal interesting patterns of commonality and difference in electoral competition across the states.

Arguing that religious diversity creates incentives for political cooperation, recent research questions the assumption that religious diversity leads to more fragmented party systems and finds a negative association between religious diversity and the fragmentation of vote shares. Before this revisionist perspective can be believed, however, we need to observe the causal processes linking religious diversity and party system fragmentation. One of these is that religious diversity is negatively associated with the number of religious parties contesting elections. Using data counting the number of religious parties in elections around the world between 2011 and 2015, the analysis shows that religious diversity is negatively associated with the number of religious parties. In line with the revisionist perspective, these results suggest that religious diversity creates incentives for political cooperation that lead elites to cooperate across religious group lines in support of parties representing their shared political interests.

We investigate the measurement of three distinct, but related dimensions of electoral competition in a majoritarian electoral system: contestability in the struggle for governing power; competition among candidates at the constituency level; and competition among existing parties at the level of the legislature. At each step, the analysis is made concrete by calculating our preferred indexes of these dimensions of competitiveness for 14 major Indian states from 1972 to 2009 (and from 1952 in some cases), while comparing them to others that have been widely used, though not always calculated for Indian states. We also use our preferred indexes to study the importance of the level of development for an understanding of how competition has evolved across the states. The paper concludes by posing questions about the measurement of competitiveness, in general and in the Indian case, that arise in the course of our investigation.