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Do Electoral Laws Affect Women's Representation? Andrew Roberts, Jason Seawright and Jennifer Cyr Comparative Political Studies 2013 46: 1555 originally published online 19 November 2012 DOI: 10.1177/0010414012463906 The online version of this article can be found at: http://cps.sagepub.com/content/46/12/1555
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463906 6Comparative Political StudiesRoberts et al. © The Author(s) 2011
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Article
Do Electoral Laws Affect Women’s Representation?
Comparative Political Studies 46(12) 1555–1581 © The Author(s) 2012 Reprints and permissions: sagepub.com/journalsPermissions.nav DOI: 10.1177/0010414012463906 cps.sagepub.com
Andrew Roberts1, Jason Seawright1, and Jennifer Cyr2
Abstract Numerous studies have found that proportional electoral rules significantly increase women’s representation in national parliaments relative to majoritarian and mixed rules. These studies, however, suffer from serious methodological problems including the endogeneity of electoral laws, poor measures of cultural variables, and neglect of time trends. This article attempts to produce more accurate estimates of the effect of electoral rules on women’s representation by using within-country comparisons of electoral rule changes and bicameral systems as well as matching methods. The main finding is that the effect of electoral laws is not as strong as in previous studies and varies across cases. The policy implication is that changes in electoral laws may not provide a quick and consistent fix to the problem of low women’s representation. Keywords electoral systems, women’s representation, matching methods
One of the most important political developments of the past century has been the increasing representation of women in politics. At the turn of the 20th century, almost no women held national-level political positions. Today, women are represented to a nontrivial degree in all democratic parliaments. 1
Northwestern University, Evanston, IL, USA University of Arizona, Tucson, AZ, USA
2
Corresponding Author: Jason Seawright, Department of Political Science, Northwestern University, Evanston, IL 60208, USA. Email:
[email protected]
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There are nevertheless significant cross-national differences in the degree of women’s representation in national parliaments (International Parliamentary Union [IPU], 2011). Although women have achieved near parity with men in some Scandinavian countries, women still play a small role in other democracies. Even within countries, there are large differences in trends. In some countries, women’s representation has increased dramatically over a short period, in others it has increased at a slow but constant rate, and in yet others it has remained stagnant or even dropped (Paxton & Hughes, 2007; Studlar & McAllister, 2002). What explains these differences? A number of explanations have been advanced in existing works including cultural attitudes toward women, strength of women’s organizations, and levels of democracy, but one has stood out as particularly important (see Kenworthy & Malami, 1999, for a comprehensive list of causes). Most studies have found that countries with party-based proportional electoral systems elect far more women to parliament than countries with candidate-based plurality systems (Kenworthy & Malami, 1999; Matland, 1998; Norris, 2004; Paxton & Kunovich, 2003; Reynolds, 1999; Rule, 1987; Siaroff, 2000). This finding is important because, in contrast to most other causes of women’s representation, electoral systems can be consciously manipulated. But how robust is the finding that electoral rules affect women’s representation? There are a number of reasons to question existing studies (see also Salmond, 2006). Four shortcomings are particularly evident. First, researchers typically compare a set of countries at a single point in time, an approach that turns both country-specific and more universal time trends into potentially problematic omitted variables. Second, measurements of the cultural determinants of women’s representation are often crude, with the potential for serious omitted variable bias. Third, the problem of endogeneity—the fact that women’s representation and electoral rules are jointly determined—is usually ignored. Fourth, studies usually assume that the effect of electoral laws is constant across time and space when in fact the effect may depend on context. This article estimates the effect of institutional change on women’s parliamentary representation using three novel research designs to explore the importance of these methodological difficulties. In the first place, we look at electoral system changes to account for strong time trends in women’s representation. Second, we use within-country comparisons rather than crossnational comparisons to sidestep the difficulties in measuring cultural attitudes toward women. Finally, we employ matching methods as a way of dealing with the potential problem of causal heterogeneity.
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The main result of our analyses is that the effect of electoral laws is smaller and more variable than most existing studies claim (see Salmond, 2006, for similar findings about the size of the effect). Although a switch to a more proportional electoral system may improve women’s representation in some cases, the effect is sometimes absent or even negative and when present is usually not large. We believe these inconsistent results suggest that there is considerable causal heterogeneity at work. Electoral laws may have different effects in different times and places. As a result, the general policy prescription that countries should switch to proportional representation electoral systems to increase women’s representation is unsupported.
Theory Women’s representation has received considerable attention from political scientists and sociologists. Three classes of explanations for differences in levels of representation are common in existing studies: socioeconomic, political, and cultural. Socioeconomic variables include levels of economic development, the education levels of women, their position in the labor force, and the strength of women’s movements. Cultural factors encompass attitudes toward women and general egalitarianism but are typically measured by the dominant religion in a country or its geographic region. Finally, political factors include democracy, the representation of right or left parties, and the variable we are interested in, electoral laws. Although the results of existing studies are not entirely uniform, the most consistent effects are found for cultural and political variables. Among the cultural variables, a Muslim or Catholic heritage and less accepting attitudes toward women in politics have been shown in numerous studies to be associated with lower levels of women’s representation (Kenworthy & Malami, 1999; Norris, 2004; Paxton & Kunovich, 2003; Reynolds, 1999). By contrast, “Measures of social structure are inconsistent predictors of women’s representation in national politics” (Paxton & Hughes, 2007, p. 132). Politically, electoral rules emerge as the most important and consistent cause of women’s representation (Kenworthy & Malami, 1999; Matland, 1998; Norris, 2004; Paxton & Kunovich, 2003; Reynolds, 1999; Rule, 1987; Siaroff, 2000). As Paxton and Hughes (2007) put it, “It is generally accepted that women do better in gaining political office under PR electoral systems” (p. 137). The effects are also substantively large. According to Norris (2004), “Women proved almost twice as likely to be elected under proportional than under majoritarian electoral systems” (p. 187). She finds an average of 15.4% of members of parliament are women in proportional systems versus 8.5% in
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plurality ones. The type of proportional representation (PR) also appears to matter, with larger district sizes leading to higher percentages of women.1 Several mechanisms have been put forward to explain why PR systems advantage women, but none has been explicitly tested. Voters may be hesitant to choose women in head-to-head contests with men. This may lead parties to select fewer female candidates in plurality systems and fewer of the ones chosen to be elected.2 By contrast, in PR systems, “Rather than having to look for a single candidate who can appeal to a broad range of voters, party gatekeepers think in terms of different candidates appealing to specific subsectors of voters” (Matland, 2002, p. 6). The same logic applies to internal party politics. In plurality systems, candidates are often chosen at the local level, where balancing of men and women is impossible. In proportional systems, candidates are often chosen centrally where leaders can create balance. One aspect of the effect of electoral laws on women’s representation that has not been considered is the possibility of causal heterogeneity (though see Matland, 1998). The effect of electoral rules may differ across cases. Consider the following ideal-type countries. The first is a completely nonsexist country. Since citizens do not distinguish between the sexes in this country, the effect of electoral institutions is likely to be zero: Women are nominated and elected exactly as men are. The same goes for a completely sexist country. No voter would dream of voting for a female candidate, and no party would dream of nominating one. The causal effect of alternative institutions is again zero. Now consider a society divided into a majority of sexists and a minority of nonsexists with the nonsexists more prominent among the political elite. Under majoritarian rules, elites will offer a slate with some female candidates. Because the range of alternatives is limited, some voters will choose women because the male alternative is less appealing on some other dimension.3 More permissive electoral rules, by contrast, will allow the easy entry of potential elites who can win by offering all-male slates. The causal effect of moving from majoritarian to PR rules may be negative. Finally, consider a society that is also divided into a majority of sexists and a minority of nonsexists, but the two segments are equally represented among elites and masses. Nonsexist elites will have to bargain to place women on lists and the larger district magnitude of PR will make it easier for them to strike such bargains because it enables a larger range of log rolls. Fewer women will be nominated in majoritarian systems where such bargains are harder to strike. The causal effect of moving from majoritarian to PR rules would be positive in such a society. Though artificial, these comparisons remind us that the relationship between institutions and representation is conditional on a country’s social
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structure and configuration of gender ideologies. In other words, there is no good reason to believe that a single, universal causal effect of institutional change exists that could be statistically estimated.
Methodological Issues Although existing studies have accumulated substantial evidence that there is a statistical relationship between electoral rules and women’s legislative representation, conditional on a variety of factors, a number of methodological issues complicate interpreting these statistical relationships as causal. Most existing works have assessed the causes of women’s representation in roughly similar ways. The standard setup is to compare the percentage of women in the national legislature across a group of countries at a single moment in time. Scholars thus estimate women’s representation as a function of a set of covariates, usually using ordinary least squares (for examples, see Kenworthy & Malami, 1999; Matland, 1998; Norris, 2004; Paxton & Kunovich, 2003; Reynolds, 1999; Rule, 1987; Siaroff, 2000).4 Such regression estimates are common in the social sciences and provide a useful general summary of data. However, for purposes of causal inference, regression estimates involve a wide range of complexities. First, there are strong time trends in women’s representation. Not only has women’s representation been increasing in general over time, but the rates of increase have varied dramatically over countries. Paxton and Hughes (2007) identify five major patterns of changes that they call “flat,” “increasing,” “big jump,” “small gains,” and “plateaus” and three subgroups of “high,” “medium,” and “low” within each pattern. The timing of changes likewise varies across countries. For example, countries that experienced a “big jump” did so at different times. Given these patterns and the fact that there is no consensus on why time trends vary from country to country, estimating the effects of electoral systems at a single point in time is problematic. There is a good chance that the variation in time trends will be associated with the electoral system variable, confounding causal inference and making electoral systems seem more—or less—important than they are. Better strategies might include modeling the time trend or comparing countries with similar time trends. And in fact studies that have done this by using cross-sectional time series data sets find much smaller effects for electoral rules (Rosenbluth, Salmond, & Thies, 2006; Salmond, 2006). However, because the causal processes behind countries’ time trends are at best dimly understood, these possibilities present challenges of their own. Without a clear understanding of the dynamics driving time trends, it is difficult to specify a model that would fully account for them.
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A second problem is omitted variable bias. A consistent result of existing studies is that attitudes toward women are a key determinant of women’s representation. But these attitudes are difficult to measure. Most studies rely on dummy variables for religious traditions, but these variables are both crude and constant. Diverse countries are grouped together and attitudes are assumed to be unchanging over time. As a result, there is likely to be considerable measurement error. A recent work by Paxton and Kunovich (2003) has produced a far better measure by looking at attitudes toward women in the World Values Survey, but this survey is limited in its temporal and spatial coverage and was not designed to measure the willingness of voters to elect women. Omitted variable bias arises because these attitudes and electoral systems are correlated. In the first place, it is likely that electoral systems are chosen because of particular cultural, historical, and political characteristics and may influence them in turn. As mentioned above, the mechanism through which electoral systems affect women’s representation runs in large part through attitudes. Women do worse in plurality systems because voters prefer to elect a man in one-on-one contests but are more accepting of women if multiple positions are chosen. If attitudes are poorly measured, we can then expect bias in the estimated coefficients on electoral rules. A third concern is endogeneity. Electoral rules are not randomly assigned to countries. As Persson and Tabellini (2003) write, “It is quite possible that countries self-selected into [electoral systems] on the basis of cultural traits and historical experience, which also shape long-run collective preferences and thus influence policy and performance even today” (p. 114). Indeed, a common purpose in choosing electoral rules is to support or hinder the representation of specific groups, women potentially among them (Boix, 1999; Rokkan, 1970). It may also happen that women play a role in choosing or altering electoral rules. Fourth, it may further be the case that the effects of electoral rules differ across time and space. Proportional representation may encourage women’s representation in developed countries, but not in developing ones as Matland (1998) has found. Other works find that the effect of electoral rules depends on context (Amorim Neto & Cox, 1997; Ordeshook & Shvetsova, 1994). Although such effects could be modeled in the traditional framework—for example, with interaction terms—the relevant factors may not be fully observed and may interact in nonlinear ways. It may be better to engage in local comparisons of like with like to produce more reliable estimates, or alternatively to adopt methods of analysis that explicitly allow for heterogeneous causal effects.
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Changes in Electoral Laws Our empirical strategy is to use three separate procedures, each of which solves some of these methodological problems. One way of partially addressing the problems of time trends and the lack of good measures of voters’ willingness to vote for women is to look at what happens when countries change their electoral laws. This allows us to deal with the average linear time trend—by comparing women’s representation before and after law changes— and also provides a degree of control for cultural factors that presumably remain relatively constant within countries at least over short time spans.5 An additional benefit of this method is that it gives us a sense of the actual consequences of the policy intervention that existing work recommends. We began by identifying all electoral law changes described in Golder (2005). His data set includes all postwar elections in countries that qualified as democratic according to Przeworski, Alvarez, Cheibub, and Limongi (2000). Following Lijphart (1984), he defines an electoral system change as a change in the district magnitude, assembly size, or electoral formula by more than 20%. We coded each change as more restrictive—leading to a more majoritarian system—or less restrictive—leading to a more proportional system. We also coded whether a change was major in the sense of fundamentally altering the electoral system—for example, from a plurality to PR system. Our search yielded 57 changes in electoral rules in 43 countries. Table 1 presents the countries, the direction of the change, and the years of the elections immediately before and after the change. A country with more than one electoral system change is listed as two separate cases in Table 1 (e.g., Argentina1, Argentina2). In all, 23 changes were more restrictive and 34 were less restrictive. Also, 25 changes were coded as major; of these, 17 were less restrictive and 8 more restrictive. Major changes are indicated in bold in the table. While they vary in scope, relatively few of these changes involve complete switches from plurality to PR, and none are complete switches from PR to plurality. Because of the small number of elections in each country, it is difficult to conduct country-by-country analyses of the effects of an electoral system change. Instead, we combined all of the countries in a single data set. We then added 53 comparable pairs of elections in 24 countries that did not change their electoral systems. These countries were chosen using full genetic matching (Diamond & Sekhon, 2005) to select the country-years that, on average, best correspond to the country-years where electoral system change took place. Matching was conducted on the variables of year of the last election, the percentage of women in the workforce as of the last election, the degree of democratization of the country, male and female life expectancies, GDP
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Table 1. Electoral Law Changes. More restrictive Albania (1992, 1996), Argentina2 (1983, 1985) Armenia (1995, 1999) Austria2 (1990, 1994) Barbados (1966, 1971) Belgium (1991, 1995) Benin (1991, 1995) Bolivia2 (1993, 1997) Cape Verde (1991, 1995) Colombia1 (1970, 1974) Colombia2 (1990, 1991) France1 (1946, 1951) France2 (1956, 1958) India (1957, 1962) Israel2 (1969, 1973) Italy2 (1992, 1994) Korea (1992, 1996) Nicaragua (1990, 1996) Poland (1991, 1993) Turkey1 (1983, 1987) Uruguay (1989, 1994) Venezuela1 (1988, 1993)
Less restrictive
Control cases
Argentina1 (1962, 1963) Australia (1946, 1949) Austria1 (1970, 1971) Bolivia1 (1989, 1993) Brazil1 (1950, 1954) Brazil2 (1994, 1998) Bulgaria (1990, 1991) Costa Rica (1958, 1962) Croatia (1995, 2000) Denmark1 (1953, 1953) Denmark2 (1968, 1971) Dom. Rep1 (1970, 1974) Dom. Rep2 (1978, 1982) Dom. Rep3 (1994, 1998) Ecuador (1996, 1998) El Salvador (1988, 1991) Guatemala (1995, 1999) Iceland1 (1959, 1959) Iceland2 (1983, 1987) Italy1 (1953, 1958) Japan (1993, 1996) Lebanon (1957, 1960) Macedonia (1998, 2002) Malta (1981, 1987) Mongolia (1992, 1996) Netherlands (1952, 1956) New Zealand (1993, 1996) Norway (1985, 1989) Philippines (1992, 1995) Sweden (1968, 1970) Turkey2 (1991, 1995) Ukraine1 (1994, 1998) Venezuela2 (1998, 2000) West Germany (1953, 1957)
Canada Chile Cyprus Czech Republic Fiji Guyana Honduras Ireland Jamaica Latvia Lithuania Malaysia Mauritius Moldova Peru Portugal Russian Federation Slovakia Solomon Islands Spain Sri Lanka Trinidad and Tobago United Kingdom Zimbabwe
Major changes in bold. Sometimes multiple election pairs from the control countries were used. Years in parentheses denote the election year prior to and the election year following the electoral system change.
and logged GDP, and the geographical region of the country. Balance tests indicate satisfactory comparability between the treatment and control groups for each conditioning variable. Although matching was used to select a control group, the estimates in this section report the results of applying a
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Roberts et al. Table 2. Effects of Electoral Law Changes. Model Intercept Change Major change Major × change Quota Multiple imputation R2 N
(1)
(2)
(3)
(4)
1.552** (0.544) -0.409 (0.535)
1.460** (0.545) -0.336 (0.583)
-0.132 (0.776)
1.515** (0.554) 0.482 (0.711) -0.506 (0.973) -2.121 (1.096) -0.026 (0.794)
.006 103
.042 103
1.562** (0.543) 0.521 (0.749) -0.475 (1.038) -2.158 (1.174) -0.133 (0.809) Yes 118
0.085 (0.805) Yes 118
Dependent variable is change in the percentage of women elected to the national legislature. Standard errors in parentheses. Multiple imputation in Models 3 and 4 uses a procedure developed by Gelman and Pittau (n.d.). **Significant at p < .05.
statistical model to the combined matched and control groups, as recommended by Ho, Imai, King, and Stuart (2007). To estimate the effects of electoral system changes, we conducted differencein-differences estimations. The dependent variable is the difference between the percentage of women elected in the election after the electoral change and the percentage of women elected prior to the change.6 The difference-indifferences method eliminates the effects of any country-specific omitted variables such as culture or social structure that are constant between the two elections. Furthermore, the matching technique used to select the nonchange comparison cases means that the results control for the variables used to choose the matching cases. The main independent variable is whether there was an electoral system change: More restrictive changes were coded as 1, no change as 0, and less restrictive as –1. The intercept estimates the universal time trend toward increased women’s representation from one election to the next in the absence of institutional change. We also added a control variable to our models that indicated whether a country had a binding national-level quota on the number of women a party must nominate.7 Since quotas force parties to nominate more women, they may obscure the effect of electoral laws on women’s representation.8 Table 2 presents the results of these estimates. Model 1 looks at all electoral system changes, whereas Model 2 interacts these changes with a variable indicating whether the change was major or not. For both regressions, the only significant coefficient involves the general time trend. None of the institutional-design-related coefficients can be statistically differentiated
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from zero at the standard .05 level. Models 3 and 4 extend these results by using imputation to account for missing data (Gelman & Pittau, n.d.). This procedure does not alter the results. Alternative estimates—removing the quota variables or creating separate dummy variables for more and less restrictive changes—also yield equivalent results. Even if these insignificant coefficients were treated as meaningful, they almost all indicate incredibly small effects. In Model 1, the effect of a move toward more restrictive institutions is associated with a decrease of about half a percentage point in women’s representation. For a legislature like the U.S. House of Representatives with 435 members (itself a very large legislature), these results suggest that a move in the direction of proportionality would be expected to produce an increase of about 1.8 female representatives. Even a major change toward less restrictive institutions would produce an increase of about 9.3 elected women. Although this result is not trivial, it is still small enough to suggest that such electoral changes are not a general answer to female legislative representation. Also worth noting is that the coefficients for minor changes in Models 2 and 4 are in the opposite direction of predictions and that an F test comparing the interactive model with the purely linear specification shows that the more complex model is not statistically preferred. One possible issue with these results is the relatively short time frame we used in the analysis—the elections immediately before and after the change. We believe this is the appropriate time frame for changes to occur, but to confirm this, we also extended the above analyses to two and three elections surrounding the change. These results are presented in Online Appendix 1 (available at https://sites.google.com/site/robertspolisci/published-papers). They confirm the previous results. The electoral system change variables continue to be indistinguishable from zero and in fact shrink while the secular trend variable (the intercept) grows larger. To give some concreteness to these results, it may be worth looking at some of the more visible changes in electoral systems in recent years. These cases are chosen not for their representativeness but because they are likely to be familiar to readers. Three developed democracies dramatically changed their electoral systems in the early 1990s and adopted mixed electoral systems. This might have been expected to increase women’s representation in New Zealand, where the status quo ante was a plurality system, and decrease it in previously proportional Italy. Japan is a trickier case as its previous system, single nontransferable vote (SNTV), combined the high district magnitude of PR and the candidate-centered elections of plurality systems. In fact, only one of these cases had an unequivocal effect. Figure 1 shows the trends in women’s representation for the three countries, with the vertical
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Figure 1. Selected electoral system changes.
Vertical lines represent the last election under the old electoral rules for New Zealand, Italy, and Japan, and the single proportional representation (PR) election in France.
line representing the last election under the old system. Although women’s representation did rise in New Zealand, there is little difference in the trend before and after the change. Contrary to expectation, women’s representation in Italy increased along with the trend line even as institutions became more restrictive. Only Japan shows a clear change—women’s representation rose dramatically (from a very low baseline) after the switch—but this is a difficult case to generalize from because of the unique nature of the status quo ante.9 Another widely discussed case is France’s single election experiment with PR (for most of the postwar period it has used a two-round system) in 1986. As Figure 1 shows, this experiment had exactly no effect on women’s representation (here the vertical line represents the single election conducted under PR rules). What about recent significant changes in less developed countries? Several of these countries have also switched recently to mixed systems (Shugart & Wattenberg, 2001). In Bolivia, there was little deviation from the trend when the country switched away from PR; in the Philippines, women’s representation actually declined when the majoritarian system was replaced with a mixed
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system; Venezuela’s switch from PR to mixed and then back to PR seemed to have the expected effect in the first case but the opposite effect in the second. To summarize, there is little strong evidence that adjusting the restrictiveness of electoral systems affects the representation of women. The dominant impression is of strong secular trends in women’s representation that overwhelm whatever effect electoral laws have. The challenge then is to explain the forces underlying these trends rather than the relatively minor alterations in these trends caused by electoral systems.
Bicameral Systems Although changes over time are one source of within-country leverage, another source is the diversity of electoral rules used within a single country. Since many countries elect numerous offices at a single point in time and use different rules for different offices, one can compare women’s representation in a fixed cultural and temporal context while varying electoral rules.10 The obvious place to conduct such comparisons is in bicameral systems where voters typically elect members to both chambers at a single point in time under different electoral rules. Such comparisons minimize worries about time trends, endogeneity, and omitted variable bias, the main problems we identified earlier. Cox (1997) has utilized this natural experiment to compare the effects of electoral rules on the number of parties elected to the legislature and found that a modified version of Duverger’s law does predict the differences he finds. In this section, we conduct a similar analysis, but focus instead on women’s representation. We expand Cox’s analysis in two ways. First, we look at multiple elections in each country because of the strong time trends in the data. (Cox considers only a single election.) Second, we consider the size of the effect. (Cox generates and tests only directional predictions.) Specifically, we look at all democratic elections in national bicameral systems around the world from the 1970s to the present (the period of the largest expansions in women’s representation). We ignore bicameral systems where the majority of one house is appointed or indirectly elected or where elections were not generally free and fair. Figure 2 presents the percentage of women elected in the upper and lower houses for the 19 countries that meet these conditions and where there were significant differences in the electoral rules of the two houses.11 Table 3 lists all countries and the dates of democratic elections covered. If a country experienced a significant electoral system change (again using the 20% rule), it is listed as two separate cases (e.g., Japan1, Japan2). The next two columns
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Figure 2. Bicameral differences.
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Table 3. Effects of Bicameralism. Country Argentina Australia Belgium1 Belgium2 Bolivia1 Bolivia2 Brazil Chile Colombia1 Colombia2 Czech Dom. Rep. Italy1 Italy2 Japan1 Japan2 Mexico Paraguay Philippines Poland Romania Spain Switzerland US Uruguay Venezuela1 Venezuela2
Years
Lower house rule
Upper house rule
2001-2005 1975-2004 1977-1987 1991-2007 1980-1993 1997-2005 1982-2006 1990-2005 1974-1990 1991-2006 1992-2006 1978-2006 1976-1992 1994-2005 1983-1993 1996-2005 1982-2006 1989-2003 1987-2007 1991-2005 1990-2004 1977-2004 1971-2003 1974-2006 1984-2004 1973-1988 1993-1998
PR, DM = 5.5 STV, DM = 8, 9.5 PR, DM = 7.1 PR, DM = 7.5 PR, DM = 14.4 Mixed PR, DM = 19 PR, DM = 2 PR, DM = 7.6 PR, DM = 4.4 PR, DM = 25, 14 PR, DM = 3, 6 PR, DM = 20 Mixed SNTV, DM = 4 Mixed Mixed PR, DM = 4.4 Plurality, DM = 1 PR, DM = 7, 10 PR, DM = 8, 9 PR, DM = 7 PR, DM = 7.7 Plurality, DM = 1 PR, DM = 5 PR, DM = 8 Mixed
Partial PR, DM = 3 STV, DM = 1 PR, DM = 5.3 PR, DM = 13.3 Partial PR, DM = 3 Partial PR, DM = 3 Plurality, DM = 1.5 PR, DM = 2 PR, DM = 4.4 PR, DM = 100 TRS, DM = 1 Plurality, DM = 1 Plurality/PR Mixed Mixed Mixed Partial PR, DM = 3 PR, DM = 30, 45 PR, DM = 12 Plurality, DM = 2 PR, DM = 3 PR, DM = 4 (3 votes) Plurality, DM = 1 or 2 Plurality, DM = 1 PR, DM = 30 PR, DM = 2 PR, DM = 2
Average Fitting Predicted difference elections + + + ? + ? + + + + ? ? + + + + + ? + +
-5.35 -11.7 -1.6 -6.4 +0.4 +8.2 +0.3 +4.0 +3.7 +1.0 +3.3 +8.5 +3.3 +3.8 -8.9 -8.2 +1.4 -5.8 -1.4 +1.6 +3.5 +2.4 +3.4 +2.8 +2.9 +2.5 +1.1
0/2 12/12 1/5 3/5 2/4 3/7 5/5 2/5 4/4 8/8 4/5 5/5 4/6 2/4 4/7 4/6 5/5 6/8 9/9 0/5 4/4 1/2
Fit Poor Strong Poor Good Weak Weak Good Poor Good Strong Good Strong Weak Weak Weak Weak Good Strong Good Poor Good Weak
DM = district magnitude; PR = proportional representation; SNTV = single nontransferable vote; STV = single transferable vote; TRS = two-round system.
describe the electoral rule and average district magnitude for the upper and lower house. The “Predicted” column shows the theoretical prediction. Positive signs indicate that the lower house should feature higher percentages of women because it has larger district magnitudes or a more proportional electoral rule. Negative signs indicate that the lower house should feature a lower percentage of women. A question mark indicates no clear prediction.12 The results begin with the average difference between the lower and upper house across all elections. The “Fitting Elections” column indicates how many elections fulfilled the directional prediction. The final column, “Strength of Fit,” provides a rough summary measure of how well electoral
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Roberts et al. Table 4. Strength of Fit.
Strength of fit All Without fused votes Without subordinate Strong contrasts Strong Good Weak Poor
3 7 7 4
2 6 6 3
3 4 6 3
3 3 3 0
Entries represent number of country cases in a given category.
results fit the predictions. “Strong” fitting countries are ones where virtually all elections fit the prediction and the average difference is greater than 5% in the correct direction. “Good” fitting means that most elections fit and the average difference is between 2% and 5% in the correct direction. “Weak” fitting means that around half of elections fit and the average difference is between 0% and 2% in the correct direction. “Poor” fitting means that a majority of elections are contrary to predictions and the average difference is in the opposite direction of the prediction. Table 4 summarizes the results. Three countries—Australia, Dominican Republic, and Japan1—are strong fits. Seven countries—Belgium2, Colombia1, Czech Republic, Italy1, Romania, Spain, and Switzerland—are good fits. Seven countries—Bolivia1, Brazil, Mexico, Paraguay, Philippines, Poland, and Venezuela2—are weak fits. And four countries—Argentina, Belgium1, Colombia2, and Uruguay—are poor fits. In short, the cases are about split between good and bad fits, though slightly more than 70% (88 of 122) of elections fit the directional prediction.13 These results in fact show a curious pattern. The advanced industrialized countries appear to fit expectations very well: Of the 10, 8 are in the strong or good category. Conversely, the Latin American countries plus the Philippines tend not to fit expectations: Of the 11, 9 are in the weak or poor category. This supports the idea mentioned above that causal heterogeneity may characterize the effect of electoral laws (Matland, 1998). In fact, the mechanisms we suggested earlier do provide a rough fit to stereotypical views of the regions: an even distribution of nonsexist attitudes across elites and masses in the industrialized countries and a more nonsexist elite in Latin America. Some difficulties crop up in these comparisons. One difficulty is fused votes. In these systems, voters can choose only one party for both houses. Fused votes applied to Bolivia1, Dominican Republic, Uruguay (to 1997), and Venezuela1. Eliminating these cases removes one case from each category and thus does not alter the overall results. Another problem is that some
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upper houses are subordinate to the lower houses—they can be overruled by majorities of the lower house—and may be taken less seriously by voters. The clear cases of subordination are Belgium1, Belgium2, Czech Republic, Poland, and Spain, which represent three good fits, one weak fit, and one poor fit. Again, relative power does not significantly affect the results. What if we look at different distinctions between electoral rules? The strongest contrasts are a plurality rule with very small district magnitudes in one house and a PR system with reasonably high district magnitudes in the other. The clearest cases of these contrasts are Australia, Brazil, Czech Republic, Dominican Republic, Japan1, Philippines, Poland, Switzerland, and Venezuela. Three of these cases fit strongly (Australia, Dominican Republic, and Japan1), another three are good fits (Czech Republic, Switzerland, and Venezuela1), and three are weak fits (Brazil, Philippines, and Poland).14 These results provide the strongest support for existing theory, but are still less than overwhelming. The short summary of the results is that although most of the differences occur in the predicted direction, some do not and the effects are not large.15 About half of the countries have average differences of less than 2% with less than half of the elections producing directional fits. The effects were strongest for countries with large differences in electoral rules. Smaller differences in electoral rules were more ambiguous. Moreover, the pattern of results supports our ideas about the heterogeneity of causal effects. The impact of electoral rules may depend on the nature of the society.
Matching Methods The various estimates discussed up to this point do not focus directly on the problem of selection based on observables. It is possible that countries selfselect into electoral systems based on factors that are likely to affect levels of women’s representation. Estimates that do not take this possibility into account will tend to misestimate the effect of electoral laws. An additional problem is that the results presented so far are easiest to interpret if the assumption is maintained that there is a single, uniform, and universal effect of electoral institutions on the proportion of elected legislators that are female. This assumption involves a counterfactual, so that it is neither fully nor directly empirically testable. But if it is not met, then the results of the estimates are problematic. Some techniques do allow us to both correct for selection on observables and to assess whether the effect in question varies across categories of cases. For this purpose, the analysis below takes advantage of propensity-score
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matching methods (see Morgan & Winship, 2007, pp. 87-121; Rosenbaum, 2002; Rubin, 2006), which allow a comparison of countries whose background conditions suggest they would choose similar electoral laws and allow estimation of a variety of different averages of case-specific effects.16 Our aim is to compare the level of women’s representation across countries that, based on observed covariates, are expected to have the same electoral institutions but in some cases actually have different institutions. This requires us to condition our comparisons on factors that tend to produce specific electoral laws. Although it is not clear that the literature has fully identified the root causes of electoral laws, we build on the work of Persson and Tabellini (2003, pp. 142-148), who have used a similar technique to estimate the economic effects of electoral laws.17 They condition on a country’s income level, proportion of the population older than 65, Freedom House democracy score, federal or centralized state structure, status as a former British colony, and location in Latin America. Because we are not sure whether these conditioning variables capture the factors involved in electoral system choice, we developed an alternative set of conditioning variables. In addition to a country’s income level, Freedom House democracy score, status as a former British colony, and location in Latin America, we add the date of female suffrage and Catholic religious status while dropping the proportion of the population older than 65 and the presence of federalism. We also condition the second set of estimates on the long-term percentage of left-wing governments as coded by the World Bank Database of Political Institutions (Beck, Clarke, Groff, Keefer, & Walsh, 2001).18 We borrow Persson and Tabellini’s data set, which includes 85 democratic states from around the world during the mid-1990s. We add to their data the percentage of women elected to the lower house of parliament at the same point in time, again using data from IPU (2011) and Paxton, Hughes, and Green (2006). We estimate two different averages of case-specific effects: the average treatment effect for the treated cases (ATET) and the average treatment effect for the control cases (ATEC). The ATET is the average of Effecti, or each case’s potentially idiosyncratic causal effect of electoral institutions on women’s representation, across all cases i in which the observed value on the independent variable is the treatment, whereas the ATEC is the average of Effecti across all cases i in which the observed value on the independent variable is the control. We stipulate that the treatment is majoritarian institutions whereas the control is PR electoral rules.19 The ATET is thus the average case-specific effect of having majoritarian as opposed to PR electoral rules among countries that actually do have majoritarian rules; the ATEC is the
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Table 5. Matching Estimates of the Effect of Electoral Institutions on Women’s Legislative Representation. Conditioning variables Sample ATET ATEC ATE Treatment cases Control cases
Persson and Tabellini
New
All
Quota cases excluded
All
Quota cases excluded
–0.08 (2.66) –7.27* (3.75) –4.84 (3.04) 23 45
2.00 (2.34) –7.02* (3.82) –3.88 (3.17) 16 30
–1.46 (4.77) –8.62* (4.35) –6.50 (4.19) 13 31
0.83 (4.45) –6.72 (4.89) –4.42 (4.36) 11 25
ATE = average treatment effect; ATET = average treatment effect for the treated cases; ATEC = average treatment effect for the control cases. Standard error of effect estimate in parentheses. *Significant at p < .10.
average case-specific effect among countries that, in fact, have PR elections. For more discussion of these estimands, see Sekhon (2008).20 It is worth noting that if there is a constant and universal effect of electoral institutions on women’s representation, then the ATET and the ATEC should be identical; sample estimates should differ only by estimation error. After all, if every single case has the same effect, then it is obviously true that the effect for the collection of all treatment cases should be identical to that constant effect; the same is true for the control cases.21 Table 5 reports a range of matching estimates, using genetic matching (Diamond & Sekhon, 2005), that can help resolve these questions. The table reports 12 different matching estimates of conditional differences related to the effect of electoral institutions on the female share of the legislature. For each of the two sets of conditioning variables there are estimates of the ATET, the ATEC, and the sample average treatment effect. We also report results for the sample without countries that had a binding national-level quota on women’s representation because, as described earlier, these quotas may obscure the effect of electoral rules. All of the estimates use a version of the sample in which cases are trimmed to ensure that all treatment cases fall within the range of propensity scores observed for the control cases.22 The first set of parameter estimates are for the ATET, that is, the effect of having majoritarian as opposed to PR electoral rules on women’s legislative representation among cases that, in fact, have majoritarian electoral rules. The effects vary substantially, but the two estimates excluding quotas are positive, and one
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negative estimate is quite close to zero. This means that for countries that currently have majoritarian electoral rules, the effect of switching to PR rules would be to reduce women’s representation in the legislature by between 0% and 2%. The standard errors for these estimates are sometimes larger than the estimates themselves, a result that suggests a note of caution in concluding that the relevant conditional difference for currently majoritarian countries is in fact positive. Even so, it is worth reiterating that, for these countries, there is no evidence that PR electoral rules would enhance women’s legislative representation, and, indeed, such rules might in fact slightly undermine such representation. Turning to the ATEC, the estimates suggest that, using both sets of conditioning variables, the conditional difference between majoritarian and PR countries in the proportion of legislators who are female, when weighted to correspond with the real-world distribution of PR countries, is negative and quite possibly substantively meaningful. The estimate is large enough relative to the standard error that, if these data were a random sample from a population, we would be statistically able to reject the hypothesis of a zero effect. For countries that currently have PR electoral rules, the data suggest that the average conditional difference between their current level of women’s legislative representation and the level in the most comparable currently majoritarian countries shows proportional representation as favorable for women by about 7%. This is prima facie evidence that the effect in question, given this particular specification of conditioning variables, is not constant across countries. Because the effect in question seems to vary from country to country, there can be no universal policy recommendation or causal conclusion on this topic. PR rules may enhance women’s representation in some contexts, but they may be totally irrelevant in others. When causal effects are heterogeneous, what meaning can be assigned to estimates from regression-type models, like those that have dominated the literature on this topic to date? Such estimates are not meaningless, but they are difficult to interpret and may not be of direct substantive interest. Generally speaking, regression-type models estimate a conditional-variance-weighted average of case-level effects; effects associated with categories of cases for which the conditional variance in a given variable is large, given all the other variables in the model, are given higher weight than effects associated with categories of cases for which this conditional variance is low (Angrist, 1998; Angrist & Krueger, 1999; Morgan & Winship, 2007, pp. 142-151). To show this more clearly, Online Appendix 2 presents regression estimates of the effect of electoral rules on women’s representation using the same set of countries as our matching estimates and a variety of standard
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controls drawn from Kenworthy and Malami (1999). Majoritarian electoral rules appear to have a strongly negative effect on women’s representation—in the most fully specified model they more than halve the level of women’s representation—though with substantial variation depending on the controls. This is consequential in the current context because the evidence suggests that the effects of interest are heterogeneous, and indeed vary from near zero or even slightly more favorable on the majoritarian side to substantially more favorable on the PR side. Different weighting and averaging schemes can thus produce results that vary between these two bounds. A simple matching-based average that weights only according to the proportion of sample cases that have PR electoral rules is given as the third estimate in Table 5. This estimate more closely approximates the ATEC than the ATET for the simple reason that the sample is composed of one third majoritarian countries and two thirds PR countries. Therefore, the overall average treatment effect is equal to one third of the ATET plus two thirds of the ATEC. If the sample were instead two thirds majoritarian countries and only one third PR countries and the ATET and ATEC were the same, the overall average treatment effect would instead be far smaller than the sample average treatment effect, and that would probably lead to far different conclusions in the overall debate.
Conclusion At the end of their comprehensive text on women and politics, Paxton and Hughes (2007) ask how we can get to a world where women are more equally represented in politics. They suggest three pathways: “furthering women’s position in the social structure” through education and training, “influencing culture” through international pressure and challenging stereotypes, and “disrupting politics as usual” by altering electoral laws, introducing quotas, and making legislatures more women friendly. Although this article has not evaluated all of these possibilities, it does suggest that electoral laws may not be the magic bullet for increasing women’s representation. Countries that have changed their electoral systems have not typically experienced large changes in women’s representation. Similarly, bicameral systems with different electoral laws in the two chambers show the expected differences in women’s representation only some of the time. Finally, matching methods produce inconsistent results for hypothesized changes in electoral laws. The evidence we have presented is more consistent with explanations that see social and cultural changes driving expansions in female representatives. Though we have not tested these explanations and do not have evidence on the effectiveness of specific social interventions, we suggest that scholars
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focus more on the sources of changes in these areas perhaps by looking for exogenous changes in social structure or cultural attitudes. One telling work in this area is Hughes’s (2009) finding that armed conflicts are often a prelude to large jumps in women’s representation because such conflicts lead to rapid changes in society and culture. We would not dismiss, however, all attempts at institutional engineering. Recent works have demonstrated that quota laws, when properly designed, can have significant effects on women’s representation (Caul, 2001). It is not yet clear whether these laws are a consequence of the factors we identified above or are introduced for other reasons. What we do believe is driving our relatively weak results is causal heterogeneity. Both the bicameral and the matching results gave clear indications that electoral laws have different effects in different places. Although there is a plausible case that PR laws may help women, this may occur only if certain background conditions are met. This conclusion is supported by existing studies showing that electoral laws interact with social structure (Amorim Neto & Cox, 1997; Ordeshook & Shvetsova, 1994). Our findings push this line of reasoning further by showing that the existence and even the causal direction of an institutional effect may depend on broader social structures We would recommend two paths in future research on the effects of electoral laws on women’s representation. First, the heterogeneity of causal effects identified in the fifth section suggests that research should be more alert to the precise mechanisms through which electoral institutions act. In doing this, it may be possible to uncover steps in the causal sequence where contextual variables of one kind or another may reasonably be thought to alter the relationship in question. Second, given the difficulty of causal inference in this area, we believe that experimental methods may yield considerable gains. By having participants vote for hypothetical alternatives under different rules in a laboratory setting, it may be possible to isolate the effect of these rules and even the mechanisms driving them. Given the effects of culture and familiarity with existing rules, conducting these studies in diverse contexts will be particularly important. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.
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Notes 1. A related finding is that quotas for women—the legal requirement that a certain percentage of candidates or elected officials be women—increase women’s representation. However, it is not clear whether quotas are an exogenous cause or an intermediary variable. Since quotas mandate that women must be placed in electable positions, it is almost inevitable that they will increase women’s representation if designed correctly. The question is why countries or parties adopt these quotas, and the answer may be in the factors cited above (Caul, 2001). Because of these results, we take care in the analyses below to control for the presence of quotas. 2. In fact, recent research shows that women are equally successful as men in both primaries and general elections, at least in the United States (Lawless & Pearson, 2008). 3. A parallel would be poor, racist voters choosing Barack Obama because he better represents their socioeconomic interests. 4. Exceptions are Paxton, Hughes, and Green (2006), who use hazard models, and Salmond (2006) and Rosenbluth, Salmond, and Thies (2006), who use panel data. 5. Lijphart (1994) uses a similar method to assess the effects of electoral systems, but he does not assess women’s representation. 6. Data on women’s representation are drawn from the International Parliamentary Union’s (IPU, 2011) Women in National Parliaments database and Paxton et al. (2006). 7. We wished to add controls for the change in the percentage of seats held by left-wing parties—some previous studies have found that this affects women’s representation—but we could not find any cross-national measures that covered these countries. We expect, however, that the inclusion of these variables would reduce the effect of electoral laws even further. Since PR appears to favor leftwing parties and left-wing parties elect more women, including a variable for these parties would capture part of the effect of electoral systems (Iversen, 2005). We did include a left-wing government variable in our matching estimates below. 8. Quotas are, however, more likely to be introduced in proportional systems. 9. This result suggests that the candidate centeredness of elections matters more than the district magnitude. 10. These comparisons assume that the two elections do not influence each other. This assumption may not be warranted, and we discuss it in more detail below. We would note here that the linkage is probably weaker for women’s representation than for other party-system variables that are more commonly studied. 11. Data on women’s representation are taken from the IPU Parline database and Paxton et al. (2006). Electoral system data come from Golder (2005), Johnson and Wallack (2007), and Nohlen (2005).
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12. Countries that have PR with low district magnitudes in one house and a mix of single member districts and large magnitude PR districts in the other produce ambiguous predictions. 13. One reason for the high percentage is the larger number of democratic elections in the good fitting countries. 14. The Philippines might be excused here because its upper house allows voters to cast 12 votes for 12 candidates to be elected in a nationwide district. The identities of the candidates may thus be more important than in a country where voters choose a party list. 15. Several scholars have conducted similar examinations of mixed electoral systems and have found significant differences between the majoritarian and PR components (Kostadinova, 2007; Moser, 2001). We suspect that these results may derive from stronger contamination effects than in bicameral systems (Ferrara, Herron, & Nishikawa, 2005). Our reasoning is as follows. In a mixed system, parties nominate candidates in the plurality tier based on the strength of their personal vote, and their personal vote in turn depends on seniority. If there is an increasing trend in women’s representation, then men will be overly represented in the plurality half of the system. Only as women gain more experience and older men exit politics will women begin to emerge as strong candidates in the plurality half of the system. One piece of evidence in favor of this explanation is the absence of a strong difference between the two parts of the system in new democracies (Moser, 2001). If it is seniority within the party that produces the differences, then we should expect smaller differences in younger democracies where personal votes have not yet emerged. More investigation of the relation between seniority and gender in mixed systems may shed light on this explanation. 16. The effects estimated by the application of matching methods to observational data are perhaps more accurately described as conditional differences, rather than as causal effects; matching methods estimate causal effects only if the variance on the treatment conditional on the matched variables is random with respect to causal processes surrounding the outcome of interest. Even when a correct collection of conditioning variables can be identified, matching methods may still fail to produce causal estimates if the cases in some categories are sparse or if other technical problems arise. The discussion in the text suppresses these issues because it is not evident how scholars could, at present, definitively resolve the central problem of identifying an appropriate set of conditioning variables, and because that problem is itself sufficient to guarantee that the estimates presented in the text are descriptive conditional differences rather than causal effects. Different sets of conditioning variables can always produce variation in resulting estimates; this is a universal issue in observational studies and will not be pursued further here. However, even if we set aside the issue of selecting an appropriate
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set of conditioning variables and assume that we have found the correct set, heterogeneity in causal effects may arise across categories of cases. 17. For a helpful discussion of the criteria that would need to be met to make valid causal inferences by conditioning, see Morgan and Winship (2007, pp. 61-86). 18. There is still considerable controversy over the causes of election laws. Geographical patterns are strong partially because of colonialism. Most British colonies use plurality systems—justifying our British colony variable—and most Latin American countries have proportional laws—justifying the Latin American dummy. Plurality rules are also relatively more common in poor countries and less democratic countries, which explains these variables. Left-wing government is associated with proportional rules for reasons explained by Iversen (2005). 19. The choice of which set of rules to call the treatment is substantively empty; reversing the selection would only reverse terminology and the signs of the estimates reported below. 20. In this discussion, each case’s effect is treated as a constant, so the ATET and ATEC are also technically constants. It is important to bear in mind that although each case-level effect is constant, the effects are not assumed to be constant across cases. Estimates of the ATET and ATEC may be random variables even though each individual effect is a constant if the sample used to generate the estimate is itself a random sample from some larger population. That is not the case for the data used here, and so standard errors are difficult to interpret. They are nonetheless reported to comply with social-science tradition. 21. The inverse is, of course, not quite true; it is possible to imagine situations in which effects differ from case to case but in which the average for all treatment cases is nonetheless the same as the average for all control cases. Hence, when ATET and ATEC are essentially identical, it can be the case either that there is a single, constant causal effect or that there is not. When ATET and ATEC differ, though, we may much less ambiguously conclude that there is not a single, constant effect—at least for the sample at hand and given a particular set of conditioning variables. 22. Untrimmed estimates were also calculated but were not substantially different.
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Author Biographies Andrew Roberts is associate professor of political science at Northwestern University. His research interests are in the quality of democracy, political institutions, and postcommunist Europe. He is the author of The Quality of Democracy in Eastern Europe: Public Preferences and Policy Reforms (Cambridge University Press, 2009) and articles in such journals as the British Journal of Political Science, Comparative Politics, Legislative Studies Quarterly, and Party Politics. Jason Seawright is assistant professor of political science at Northwestern University. His research interests are in methods of causal inference, multimethod research, and political decision making in Latin America. He is the author of PartySystem Collapse: The Roots of Crisis in Peru and Venezuela (Stanford University Press, 2012), articles in such journals as Political Analysis, Political Research Quarterly, and Studies in Comparative International Development, as well as chapters in a range of edited volumes. Jennifer Cyr is assistant professor of political science at the University of Arizona. Her research interests include the study of political parties and political institutions more generally in Latin America. Her dissertation examines the different fates of political parties in the aftermath of party system collapse in Peru, Venezuela, and Bolivia. She has coauthored articles in the International Social Science Journal and the Handbook of Latin American Politics.
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