Election Inversions,Coalitions and Proportional Representation: Examples of Voting Paradoxes in Danish Government Formations

When collective choices are made in more than one round and with different groups of decision makers, so‐called ‘election inversions’ may take place, where each round produces different majority outcomes. In this article, two versions of such compound majority paradoxes are identified that are particularly, but not exclusively, relevant for systems of proportional representation with governing coalitions: the ‘Threshold Paradox’ and the ‘Federal Paradox’. The empirical relevance of the paradoxes is illustrated with examples from two Danish elections (in 1971 and in 1990), where a majority of the voters voted for one bloc of parties, but a majority of the seats fell to another.     

Balancing district and party seats: The arithmetic of mixed-member proportional electoral systems

Mixed-member proportional electoral systems (MMP) are widely praised because they combine the direct, personal election of MPs from single-seat constituencies with a proportional seat allocation. However, the size of the proportional tier matters for the question of whether the system's overall proportionality is preserved. Hence, a key challenge for constitution-makers and scholars is finding the right balance between district and proportional seats, so as to maximise district representation and guarantee proportional representation.This paper develops the first theoretical model that helps to locate this sweet spot for district and party seats. The novel solution builds on Taagepera's “logical models” about party sizes. The model is tested on 58 national parliamentary elections under MMP rules.     

Election Inversions under Proportional Representation

It has been shown by Peter Kurrild‐Klitgaard, using several empirical examples under the Danish electoral system, that proportional representation (PR) can produce ‘election inversions’ such that a coalition of parties collectively supported by a majority of voters fails to win a majority of parliamentary seats. However, Kurrild‐Klitgaard's examples result from imperfections in the Danish PR system introduced to serve goals other than proportionality. In this article, Kurrild‐Klitgaard's analysis is carried a step further by showing that election inversions can occur even under the purest type of PR – namely, one with (i) a single national constituency, (ii) no explicit seat threshold, and (iii) a highly proportional electoral formula. Inversions result from the unavoidable ‘whole number problem’. Recent election data from Israel and the Netherlands is examined and examples of inversions under their relatively pure PR systems are found. Inversions are also found after recalculating seat allocations without a threshold, and on the basis of the most proportional electoral formulas and when the analysis is restricted to seat‐winning parties. Kurrild‐Klitgaard's Danish data is then re‐examined in the same fashion, as is the most recent apportionment of seats in the United States House of Representatives, and more examples of inversions are found.     

Empirical evidence of paradoxes of voting in Dutch elections

In this paper we analyze four national elections held in 1982, 1986, 1989 and 1994 in the Netherlands on the occurrence of the Condorcet paradox. In addition, we investigate these elections on the occurrence of three so-called majority-plurality paradoxes. The first paradox states that a party having a majority over another party may receive less seats. The second states that a Condorcet winner may not receive the largest number of seats and even may not receive a seat at all. The third says that the majority relation may be the reverse of the ranking of parties in terms of numbers of seats.     

Towards a Gender-Equal Bundestag? The Impact of Electoral Rules on Women’s Representation

Cross-sectional research designs show that proportional representation (PR) tends to produce more equitable outcomes in terms of gender representation. While existing research provides valuable insights into the covariates of gender representation, such cross-sectional designs fail to provide a definitive test of the influence of electoral rules both over time and in the case of mixed systems. Addressing this gap, this article proposes a longitudinal research design using the case of Germany, because half the Bundestag’s seats are allotted through majoritarian first-past-the-post methods, while the other half are allotted through proportional methods. The main findings point towards heavy interaction between the two electoral tiers that becomes visible in party quotas, double nominations and increased competitiveness of female candidates.     

The strategic determinants of legislative malapportionment in new democracies

When the number of seats to be elected in the districts of an electoral system is not proportional to their population, the cost of seats in raw votes tends to vary across districts. Malapportionment generates partisan bias when some parties do better (worse) in the districts where seats are cheaper (costlier) than in other districts. While existing research has focused on the exogenous determinants of malapportionment, in this article we argue that malapportionment also derives from the strategic decisions of ruling elites to maximize their legislative representation. The degree of malapportionment in newly democratized countries increases when ruling policymakers have reliable ex ante information about the geographical distribution of partisan support, and the authoritarian incumbent, at the moment of democratic transition, is strong. Our arguments are tested with original data from 60 third and fourth-wave democracies at national and district levels.     

Is there an incumbency advantage or cost of ruling in proportional election systems?

This paper investigates the effects of political representation on electoral outcomes at the party and coalition levels in proportional election systems using data from Swedish local government elections. There are two notions of representation, namely, to hold seats and to belong to the ruling coalition. I refer to the effect of the former as the incumbency effect and the effect of the latter as the ruling effect. The discontinuous variation in the seat share as the vote share varies for parties is used to isolate exogenous variation in incumbency. The discontinuous variation in ruling at the 50% seat share cutoff for coalitions is used in order to exogenous variation in ruling. I find that incumbency determines the distribution of 12% of the total vote, which is similar to the advantage found in majoritarian systems. I find no ruling effect, contrary to the commonly found cost of ruling in proportional systems.     

Japan's new electoral system:: la plus ça change . . .

We examine the impact on parties and candidates of Japan's new electoral rules, first used in the 1996 House of Representatives election. We argue that the Japanese rules, which not only permit dual candidacy but also allow votes cast in the single member district (SMD) portion of the race to allocate proportional representation (PR) seats to dual candidates, effectively defeat the purposes of electoral reform. The new arrangement transforms PR representatives into locally-based politicians who will rely on personalistic rather than party-based or programmatic campaigning, effectively converts single-member districts back into the multi-member districts of the past, enhances incumbency advantage, and will push the ratio of candidates to seats down as low or even lower than before.     

Self-exclusion as a strategy of inclusion: the case of Shas

Among the many paradoxes of Israeli politics, there are the strategies of political inclusion used by organizations and parties representing groups that reject the universalism which Israeli democracy is heir to. This paper develops a model of ‘political inclusion Israeli-style’, illustrated by one party, Shas, which since 1984 proclaims itself the voice of the socially and culturally excluded Sephardi population of north African and Middle Eastern Jews, who represent over 40% of the Jewish population. Shas is also a movement of religious and ethnic revival which, by adopting a social strategy of self-exclusion grounded in strict religious observance, and of independence vis-à-vis established Ashkenazi ultra-Orthodox politics, has gained 11 out of 120 Knesset seats, inclusion in government, and control over a share of educational and welfare expenditure. The paper raises the issue whether such less-than-perfectly universalistic practices are not a variety of corporatism and possibly, for the parties concerned, a more effective strategy of incorporation than the classic social democratic path.     

Proportional representation: An empirical evaluation of single-stage,non-ranked voting procedures

Rapoport, Felsenthal and Maoz (1988) have proposed three alternative methods to discern the fair proportion of seats that a party in a representative assembly ought to receive as a function of voters' preference orderings. All three methods assume that the ratio between the number of voters preferring party i over j to the number of voters preferring party j over i can be tested for consistency, and, if sufficiently consistent, can be appropriately scaled to discover the proportion of seats each party ought to receive. Using these methods as standards, we use exit-poll data gathered during the 1985 elections to the general convention of the Israeli General Federation of Labor (Histadrut) to examine the extent to which plurality- and approval-voting procedures provide a fair allocation of seats. The findings indicate that: (a) all three methods yield sufficiently consistent matrices of preference ratios; (b) the plurality- and the approval-voting procedures yielded significantly different proportional representations; (c) the proposed proportion of seats according to the three aggregation methods fall midway between the proportion of seats that the plurality and the approval procedures allocate. We discuss practical implications of these findings. Requests for reprints should be sent to: Professor Amnon Rapoport, Department of Psychology, University of North Carolina, Davie Hall 013A, Chapel Hill, NC 27514.     

Raising the Threshold,Fighting Fragmentation? Mechanical and Psychological Effects of the Legal Electoral Threshold in Belgium

Many proportional representation systems are characterised by a legal electoral threshold. Such a threshold reserves the allocation of seats for those parties that reach a minimum share of the votes. In order to fight fragmentation, a 5 per cent threshold has been introduced for both federal and regional elections in Belgium. This article seeks to explore the mechanical and psychological effects of this legal threshold after five elections. It is shown that the threshold has had limited mechanical and psychological effects on voters but some psychological effects on party elites. Moreover, while in the short term the average number of lists dropped and several pre-electoral coalitions formed, in the longer term the legal threshold has not prevented further fragmentation.     

Why Geographically-Targeted Spending Under Closed-List Proportional Representation Favors Marginal Districts

Research on geographically-targeted spending under closed-list proportional representation (CLPR) is characterized by debate over whether ruling parties target core supporters or swing voters. We show that when CLPR is used in multiple districts and separate competitions are conducted in each, parties can reverse the formula through which votes are converted into seats to calculate how many additional votes they need to capture an additional seat. This enables parties to rank districts according to how close they are to winning an additional seat. We then show that under divisor-based formulae, parties will find they need fewer additional votes to capture another seat in districts where they captured fewer seats (‘marginal districts’). We posit that in these systems, ruling parties will steer geographically-targeted spending toward marginal PR districts and we present evidence of this from Japan.     

Repression and reaction: militant democracy and the radical right in Germany and France

The June 2004 elections offered the British National Party unique opportunities for growth. There were three different elections being held at once: for seats on local councils, for the London mayor and the London Assembly, and for members of the European parliament (MEPs). Following boundary changes, the local council election was being conducted on a three-candidates-per-seat basis. The London and European elections were being run according to the rules of proportional representation. Both systems favour minor parties. The BNP went into the elections buoyed up by almost four years of considerable success. However, the party failed to achieve the gains anticipated. After several years that witnessed increasing votes, this was the first instance of the BNP vote stagnating. Renton explains the BNP's failure in terms of a series of factors: poor leadership, tactical errors, the hardening of Conservative anti-BNP voters, the press publicity garnered by the UK Independence Party, and the successful intervention of anti-BNP campaigners.     

Social representation

This paper examines social representation in the European Parliament using a model which uses the demand, the supply and the structure of opportunities as factors explaining differential recruitment. Analysis of the experiences of candidates suggest that supply–side factors proved more strongly related to candidates gaining winnable seats than demand–side factors. Results also confirm the importance of institutional structures in widening or narrowing opportunities, and suggest the European Parliament will remain social unrepresentative in the foreseeable future, a characteristic that serves only to add to the already considerable problems of legitimacy in the European Union.     

Gendered electoral systems in the French Sénat

A longstanding but contested hypothesis in political science suggests that proportional (rather than majoritarian) electoral systems tend to increase the share of legislative seats held by women. While scholars have used a variety of empirical methodologies to test this hypothesis, they have mostly neglected legislatures where different parts of the country use different electoral systems. This note looks at women’s election to the longest-established legislative body using such a mixed electoral system: the upper house of the French parliament, the Sénat, where high-population constituencies use proportional elections but low-population constituencies use a majoritarian system. Among elections to the Sénat from 1959 to 2014, regression estimates indicate that women’s share of seats is approximately 10 percentage points higher in proportionally allocated elections, all else being equal. This finding both contributes to the literature linking gender to electoral systems and shows the potential value of considering understudied institutions.     

Engineering inclusion: Assessing the effects of pro-minority representation policies

In democracies, a constant tension exists between the stability and integrity of the community as a whole, and the desire to ensure minorities a voice in politics. Reserved seats and reduced thresholds are two common means by which ethnic minorities gain legislative seats, though little or no empirical work exists testing their efficacy in this regard. Combining multivariate analysis with in-depth case studies, this article shows that both reserved seats and lower thresholds increase minority representation, though reserved seats accomplish that goal more consistently. Reduced thresholds tend to increase the share of votes and seats won by ethnoregional parties but reserved seats do not. Additionally, Mauritius' unusual best-loser system aids both minorities and ethnoregional parties.     

Assessing the psychological and mechanical impact of electoral rules: A quasi-experiment

The paper assesses the influence of electoral rules on vote choice and election outcomes using a quasi-experiment conducted during a recent Canadian provincial election. Respondents were invited to vote under three voting systems (first past the post, alternative voting and proportional representation) and to answer a short questionnaire. We examine how the distribution of votes and seats is affected, and we ascertain how much of the total difference is due to psychological and mechanical effects. We find that a PR system would have increased legislative fractionalization by the equivalent of one effective party and that the mechanical effect is much more important than the psychological effect. As for AV, its mechanical and psychological effects act in opposite directions.     

Social representation

Abstract This paper examines social representation in the European Parliament using a model which uses the demand, the supply and the structure of opportunities as factors explaining differential recruitment. Analysis of the experiences of candidates suggest that supply–side factors proved more strongly related to candidates gaining winnable seats than demand–side factors. Results also confirm the importance of institutional structures in widening or narrowing opportunities, and suggest the European Parliament will remain social unrepresentative in the foreseeable future, a characteristic that serves only to add to the already considerable problems of legitimacy in the European Union.     

The Worst of All Worlds? Electoral Reform and Britain's 2009 European Elections

At the 2009 European elections, Britain again elected its MEPs under the 'closed list' system of proportional representation (PR)—the third time it had done so since 1999. This article looks at claims that these elections vindicated PR by producing a 'fairer' relationship between the parties' share of votes and their share of seats, a truer reflection of diverse political allegiance in modern Britain, and (thanks to multi-member constituencies) a more efficient and sensitive system for representing voters. However, the article will also inspect the idea that the case for electoral reform was gravely weakened by the 2009 Euro elections. It will recall how PR again failed to boost turnout, again employed a method of counting that most voters did not understand, and again involved constituencies too large for meaningful representation. Furthermore, it will recall that PR allowed the election of two MEPs from the far-right British National Party. (With just 6% of votes, it is unlikely that the BNP would have secured seats under Britain's traditional electoral system.) The article will argue that, as a result, PR has had a centrifugal effect on the British party system and, potentially, a polarising effect on our political culture. Consequently, the article will assert that, owing to the success of the BNP in 2009, arguments about PR for Westminster have been 'ideologically neutralised'. The article will thus suggest that we can now take a more objective view of hung Parliaments and coalitions (the likely effects of PR at general elections), free from the assumption that they entrench centrist governments and progressive politics.