Malapportionment in Mongolian elections: Does institutional structure matter?

Abstract This article examines malapportionment in Mongolia from the introduction of a unicameral parliament in 1992 to the parliamentary elections in 2016. We especially address the question whether the level of malapportionment was significantly influenced by various types of electoral systems at both national and district levels. Due to its frequent electoral engineering, Mongolia can serve as a very useful case for testing the relationship between levels of malapportionment and different types of electoral systems. The results show that almost irrespective of the type of electoral system applied, the level of malapportionment grew constantly at both national and district levels until the election of 2016, when the growth ended. The importance of this finding lies in the fact that while most existing cross-national analyses of malapportionment presented rather contrary arguments, the Mongolian case demonstrates that plurality systems, or single-member district systems, are not unambiguous factor distorting fair apportionment.


Introduction
The 2016 Mongolian parliamentary elections were historical as their results dealt a complete defeat to the party that had, shortly before the elections, driven a transformation of the electoral system from a mixed-member majoritarian (MMM) system used in the elections of 2012 to a firstpast-the-post (FPTP) system.The distribution of the forces supporting FPTP was the most surprising aspect.Historically, the former ruling party, the Mongolian People's Party (Mongol ardyn nam, MPP), which had governed the country since 1921, was the main champion of FPTP, especially with regard to its power in rural districts and its more developed organizational structure inherited from the era of the non-democratic regime, in which it had been the only existing party (Barkmann, 2005, p. 45;Fritz, 2008, p. 773;Ginsburg, 1995, p. 464). 1 In contrast, the Democratic Party ABOUT THE AUTHOR Pavel Maškarinec is an associate professor at the Department of Political Science, Faculty of Arts, Jan Evangelista Purkyně University in Ústí nad Labem.He specializes on electoral geography, spatial analysis of elections, quantitative research of electoral behaviour, political participation, women's political representation and quality of democracy.His research has appeared in Politics, Post-Soviet Affairs, Electoral Studies, Communist and Post-Communist Studies, Eurasian Geography and Economics, Europe-Asia Studies, Swiss Political Science Review, Cities, Urban Affairs Review, and Journal of Asian and African Studies, among other outlets.
However, in 2016, the roles reversed and it was a part of the DP's top leadership that started advocating FPTP (in spite of opposition by another part of the party leadership), while the MPP's position on FPTP was not entirely positive.One of the reasons behind the reluctance of MAN (then an opposition party) was the concern that the ruling DP along with its coalition partners would, given their majority in the parliament, control the delimitation of single-member districts (SMDs) in a way to advantage their own candidates (Radchenko & Jargalsaikhan, 2017).
However, as there are missing the detailed analysis of development of malapportionment in Mongolia, 2 this article tests the level of malapportionment in the Mongolian elections since 1992 (the first elections to the unicameral parliament after the Mongolian transition to democracy) to the parliamentary elections in 2016 by analysing national and district-level data.Especially, we address the questions whether the level of malapportionment was significantly influenced by various types of electoral systems, both at national as well as district-level, whether is it possible to confirm that malapportionment results from overrepresentation of sparsely populated rural areas, and there are signs that one of the intentions behind malapportionment is to strengthen the parties that enjoy stronger support in overrepresented areas.
Malapportionment, i.e. inadequate (disproportionate) sizing of electoral districts that fails to respect (or respects disproportionately) local population or the number of voters living in these geographical units, may result in overrepresentation of some districts in terms of the number of members of parliament representing them.As for the quality of democracy and political representation, malapportionment affects the proportionality of electoral results at district level (Horowitz, 2006, p. 5;Taagepera, 2007, p. 65); both malapportionment and disproportionality represent two important examples of distributional deviation (Monroe, 1994, p. 138).
Our perspective on the study of malapportionment is thus based on the relationship between the fair representation of constituencies (in terms of the number of seats allocated here) and the number of residents living there.We therefore do not deal (considering the length of the paper and the availability of the data) with the second of the important electoral abuses-gerrymandering, which, although it may lead to similar electoral results, differs from malapportionment in that it involves drawing districts to shape the electoral outcome, within the constraint of having roughly equal populations between those districts. 3  More specifically, we measure malapportionment as a sum of differences between the percentage of all seats allocated to specific district and the percentage of the overall population of this district (see Samuels & Snyder, 2001).The resulting values then indicate the percentage margin of difference between the distribution of seats among the country's electoral districts and the ideal of fair representation.However, as our goal is not only to determine aggregate level of malapportionment at national level (which is primarily suitable for cross-national comparison), but especially to compare of malapportionment levels across Mongolia's electoral districts, in order to identify any violations to fair representation between regions (or electoral districts), we will use also two indicators of district-level malapportionment.First, the so-called advantage ratio (Taagepera & Shugart, 1989), which indicates the level of over-or underrepresentation of the district's local population in terms of the seats held, and second, the deviation of a district's voter population from average district size.
Mongolia could serve as a very useful case for testing this relationship between levels of malapportionment and different types of electoral systems for at least two reasons.First, Mongolia is the case of emerging and transforming party system and one of a few successful democratizations in the region of Central, East and Southeast Asia (Aagaard Seeberg, 2018;Fish, 1998Fish, , 2001;;Fish & Seeberg, 2017;Fritz, 2002Fritz, , 2008;;Jacob & Schenke, 2020;Soni, 2013), and second, especially due to the frequent electoral engineering, as Mongolian voters can opportunity to choose their representatives by many types of electoral systems, although most of them were plurality-majority or semiproportional electoral systems, which tended to exaggerate disproportionality and favour the largest parties (see below).For these reasons, Mongolian case can be illustrative also for wider comparative research of malapportionment.
The format of this analysis is as follows.First, we briefly review the existing formal literature on malapportionment.In the second part, we briefly introduce the evolution and transformation of the Mongolian electoral and party systems.In the third part, the methods of analysis are introduced.In the fourth part a detailed analysis of development of malapportionment in Mongolia is presented.The concluding section formulates some implications of the results for further research.

Malapportionment from theoretical perspective
Based on most people's perception of being adequately represented by the ruling elite, fair representation is one of the basic conditions of satisfaction with democracy (Dalton, 1999;Norris, 1999).In this respect, Snyder and Samuels (2001, p. 149) emphasize that precisely formal institutions (and the electoral system, above all), as well as informal rules, may decrease the quality of democracy because "responsive democracies require that all citizens' preferences are adequately represented in the political decision making process" (Bühlmann et al., 2012, p. 526).Importantly in this context, Snyder and Samuels (2001, p. 652) concluded that comparative research of electoral system effects tends to neglect precisely malapportionment as one of the basic system characteristics-and malapportionment issues tend to be ignored even by quality of democracy scholars in spite of the phenomenon's numerous consequences for the representation of political parties as voter representatives in geographically defined districts.
Other authors even consider malapportionment to be a "pathology" of electoral systems (Taagepera & Shugart, 1989, pp. 17−18;Taagepera, 2007, pp. 42-43) or the main source of unfairness (Horowitz, 2006, p. 13).According to Samuels and Snyder, malapportionment has both practical and normative consequences.At the practical level, malapportionment affects: (1) coalitional dynamics and the resulting policy choices (in terms of the decision-making contexts of executives and legislators); (2) executive-legislative relations; (3) intra-legislative bargaining; (4) performance of the democratic systems; and as for the normative requirements posed by democratic theory, "the discrepancy between the shares of legislative seats and the shares of population held by geographical units violates the 'one person, one vote' principle" (Samuels & Snyder, 2001, pp. 652-653), i.e. one of Dahl's (1989) criteria of the democratic process (vote equality) and, at the same time, one of the necessary conditions (key characteristics) of democracy.This is because under high levels of malapportionment, one cannot guarantee that all voters' preferences (however freely articulated) will be treated as equal to other citizens' preferences, resulting in unequal consideration of different voters' preferences (in terms of different social groups, identities, political opinions and interests).
At the same time, Snyder and Samuels consider malapportionment to be a serious, however neglected, challenge jeopardizing the quality and fairness of democracy in many countries of Latin America, where malapportionment levels are considerably above the rest of the world (cf.Snyder & Samuels, 2006, pp. 169-170).Latin American experience also tells us that malapportionment tends to strengthen politically conservative rural districts at the expense of politically progressive urban districts (Samuels & Snyder, 2001, p. 668).Similarly, Gallagher and Mitchell (2005) emphasize that malapportionment usually results from overrepresentation of sparsely populated rural areas or it is intended to strengthen parties that enjoy stronger electoral support in overrepresented areas.
In one of a handful of comparative studies of malapportionment, Samuels and Snyder (2001) demonstrated the highest malapportionment levels (for lower legislative chambers) especially in less developed (mostly freshly consolidated, non-consolidated or developing) countries of Latin America, the Caribbean and Africa (in the latter continent, this was especially in former British colonies), whereas the opposite side of the spectrum was populated by traditional Western democracies (with the exception of Iceland) as well as most countries from the third wave of democratization in the regions of post-communist Central and Eastern Europe and Asia (with the exception of South Korea).
As for the role of individual factors, Samuels and Snyder found strong effects of district size on malapportionment level: the latter grew by an average margin of 4 percentage points in countries with SMDs or in the Latin American region (cf.Samuels & Snyder, 2001, pp. 664-665).Similarly, Horiuchi (2004) and Ardanaz and Scartascini (2013) also identified higher malapportionment levels in countries with SMDs plurality systems and in countries with higher levels of socio-economic inequality (Ardanaz & Scartascini, 2013;Horiuchi, 2004) and change in the urban population ratio (Horiuchi, 2004).
However, although Samuels and Snyder (2001) analysis did not find association between degree of democracy and levels of malapportionment, Ong et al. (2017) in their cross-national analysis (including 160 countries compared to Samuels and Snyderʼs 112 countries) found a curvilinear relationship between them, with the lowest presence of malapportionment in established democracies and electoral authoritarian regimes, compared to new democracies and authoritarian regimes. 4Degree of malapportionment in full democracies (including Mongolia, according to the authors) reached 0.045, in democracies 0.076, in autocracies 0.059, in open anocracies 0.121 and in closed anocracies 0.130 (cf.Ong et al., 2017, pp. 120-121).
Furthermore, and more importantly, while most previous studies (Ardanaz & Scartascini, 2013;Christensen, 2004;Horiuchi, 2004;Samuels & Snyder, 2001) confirmed strong effect of SMD on increasing degree of malapportionment, Ong et al. did not confirm this finding as well as they rejected expected effect of socio-economic inequality and on the contrary to Samuels and Snyder, found decreasing level of malapportionment in electoral systems with upper tiers (cf.Ong et al., 2017, pp. 122-123).

Development of Mongolian electoral and party politics
Since Mongolia's democratic transition in 1990, frequent changes have been characteristic of its electoral system. 5When Mongolia's new constitution was adopted in 1992, the 76-member new unicameral parliament-the Great State Khural (Ulsyn ikh khural)-was elected by plurality vote in 26 electoral districts, with district magnitudes ranging from two to four seats (so-called unlimited, multiple, or bloc vote). 6In the election of 1992, the ruling post-communist MPP captured 70 out of the 76 seats (92.11%) with 56.90% of the vote, while its two main rivals-the Alliance (Kholboo) 7 and the Mongolian Social Democratic Party (Mongolyn sotsial demokrat nam, MSDP) gained only four and one seats, respectively (see Agwaandorjiin, 1999, pp. 212−231;Barkmann, 2005 , pp. 49 −50;Fritz, 2008, pp. 776-777).The election results thus confirmed some expectations attributed to this system: (1) a tendency to strengthen political parties with the highest levels of coherence and organisational ability; and (2) a tendency to highly disproportional election results, as most voters tended to cast all their votes to candidates of one preferred party instead of splitting them between parties (Taagepera, 2007).
Contrarily, in three following elections, all 76 members of parliament were elected using a specific modification of the two-round system (TRS), plurality-majority, in SMDs (see Agwaandorjiin, 1999 , pp. 191−203;Ginsburg, 1997, pp. 61-62), with a required plurality of at least 25% of the vote for first-round victory.Otherwise, a second round was to be held between the two most successful candidates from the first round.However, the second round was not held in any SMD during the three elections under the nominally two-round system between 1996 and 2004.Before the 1996 election, the Democratic Alliance (Ardchilsan kholboo) coalition was formed by both major opposition parties, the Mongolian National Democratic Party (Mongolyn ündesnii ardchilsan nam, MNDP) 8 and the MSDP, together with some smaller parties, and as a result, the MPP was voted out of power for the first time since 1921.The Democratic Alliance captured 50 out of 76 seats (65.79%) with 47.05% of the vote, while the incumbent MPP won only 25 seats (32.89%) with 40.49% of the vote (see Barkmann, 2005, pp. 53-55).
However, due to a complete fragmentation of the Democratic Alliance before the 2000 election, the MPP enjoyed a landslide victory with 51.64% of the vote, taking 72 of the total of 76 seats (94.74%) (see Barkmann, 2005, pp. 58−61;Maškarinec, 2017, pp. 150-151).In response to the situation, a new wave of concentration occurred in the party system, similarly as before the election of 1996.In December 2000, the Democratic Party (Ardchilsan nam, DP) was established by a merger of the MNDP, the MSDP and some smaller parties and finally, at the end of 2003, the DP joined the Motherland-Mongolian Democratic New Socialist Party (Ekh-oron-Mongolyn ardchilsan shine sotsialist nam, M-MDNSP) and the Civil Courage-Republican Party (Irgenii zorigbügd nairamdakh nam, CC-RP) to form an election coalition entitled, Motherland-Democracy Coalition (Ekh oron-Ardchilal evsel, MDC).As a result, before the election of 2004, the main opposition parties ran against the MPP as a single coalition, unlike in 2000, and although the ruling MPP successfully defended its top position with 48.83% of the vote, it obtained only 36 seats, half its number from 2000; the MDC coalition fell behind the MPP by a margin of less than 4 percentage points (44.85%) and won 34 seats (see Schafferer, 2005, pp. 745-746).
For the election of 2008, unlimited vote was reinstated, but it did not result in any major transformation of the Mongolian party system.The MPP achieved a clear victory, despite surpassing the DP by less than 4 percentage points.The MPP received 43.06% of the vote and 45 seats (59.21%), while the DP obtained 39.21% of the vote and only 28 seats (36.84%) (see Bulag, 2009, pp. 129-131).More importantly, the most profound change in Mongolian electoral legislation laws accompanied the parliamentary election of 2012, as a new mixed-member majoritarian (MMM) system was implemented.The outcome of the 2012 election then demonstrated a tentative disruption of the bipolarization of electoral politics in Mongolia due to introduction of MMM.The DP won 31 seats (43.06%), the MPP 25 seats (34.72%), and the MPRP (the Justice Coalition, respectively) ranked third with 11 seats (15.28%), 9 which amounted to a historic success because no other third party in Mongolia had won more than one seat since 1992 (see Maškarinec, 2019, pp. 240-243).
However, the mixed system, too, was short-lived, as a first-past-the-post (FPTP) system was implemented instead of MMM before the election of 2016.In 2016, the governing DP suffered a disastrous defeat with 33.12% of the vote but only 9 seats (11.84%), compared to 45.09% of the vote and 65 seats (85.53%) obtained by the MPP.Furthermore, the MPRP received only one seat (for 8.02% of the vote), compared to 11 seats of the Justice Coalition in the previous term, and its result confirmed the complete disruption of the tendency to multiparty competition observed in the election of 2012 (see Radchenko & Jargalsaikhan, 2017, pp. 1032−1033;Maškarinec, 2018, pp. 517-518).
More generally, Mongolian political competition was characterized by contestation between the former ruling party, the MPP, which had governed the country since 1921, and political parties established after 1990 (the so-called "democratic camp").However, while the post-communist MPP had inherited an extensive organizational structure from the communist period and also preserved a high degree of electoral support within the country's (especially rural) population, the opposition was characterized by frequent establishing and merging of parties, especially around parliamentary elections.Nevertheless, these changes in the political landscape were largely enacted by the same political leaders, who were merely switching from existing groups to new ones.The permanent fragmentation of the party spectrum was also facilitated by the absence of any substantial ideological or programmatic differences between Mongolia's main parties (see Prohl & Sumati, 2008, pp. 372−382;Sumati, 2009, pp. 99-106).
Overall, as electoral systems generally favoured larger parties, the fragmentation of the "democratic camp" was decisive for the shape of the party system.Furthermore, although Mongolia used largely plurality-majority or semiproportional electoral systems, these failed to give rise to classical bipartism or Duverger (1954) competition.The shape of the party system and competition thus alternated between relative symmetry and extreme asymmetry (Barkmann, 2005, pp. 47−62;Croissant & Völkel, 2012, pp. 241-252).Especially the low degree of party system institutionalization acted, according to some authors (Maškarinec, 2017), against bipolarization of Mongolian electoral politics.Thus, for instance, Croissant and Völkel (2012) classified Mongolia between 1990 and 2008 as having a two-party system with one dominant party, Reilly (2007) considered Mongolia to have a two-party system between 1992 and 2004 (especially in 2004), and Maškarinec (2022) showed that after a short period of multipartism due to the use of MMM in the election of 2012, the introduction of FPTP in 2016 shifted the party system to one-party dominance; these findings were also confirmed by the values of effective number of parliamentary parties as a measure of parliamentary fragmentation (see Appendix 1).
Finally, in Mongolia, as well as in many other East Asian democracies, social cleavages, in the sense of the Lipset and Rokkan (1967) paradigm, are only loosely related to party support. 10 Especially, the influence of a class cleavage is not statistically significant in Mongolia, although there is a slight preference of left-wing voters for the MPP (see Huang, 2013, pp. 156-157), and on the contrary, there is high importance of the urban-rural cleavage which affects both party vote and electoral participation (Maškarinec, 2018;Tamir, 2004). 11

Methods and research design
We constructed an original dataset of malapportionment for Mongolia, which consist of districtlevel election data of the Mongolian elections between 1992 and 2016, i.e. seven elections to the unicameral parliament, as collected by the General Election Commission of Mongolia.Furthermore, for comparison of malapportionment in Mongolia with another countries, we used Samuels and Snyder (2001) dataset.
We take different approaches to studying the levels of malapportionment in Mongolian elections.First, we use the classical measure of malapportionment (MAL) introduced by Samuels and Snyder (2001) as a modification of the Loosemore and Hanby (1971) index of electoral disproportionality (D). 12Since MAL is constructed similarly as the D index, the resulting values of MAL also range between 0 (perfectly even distribution of seats among districts according to local population or number of voters living in them) and 100 (perfect disproportionality of distribution of seats among districts to local population or number of voters living in them).Therefore, the resulting values indicate the percentage margin of difference between the distribution of seats among the country's electoral districts and the ideal of fair representation. 13  However, given its construction as a sum of differences for all electoral districts (i.e. an aggregate-level indicator), MAL is primarily suitable for cross-national comparison.Our goal is not only to determine aggregate level of malapportionment at national level, which would rather be the first step in a comparative analysis of Mongolia with other countries, but especially to compare of malapportionment levels across Mongolia's electoral districts, in order to identify any violations to fair representation between regions (or electoral districts).Therefore, we are going to use a second indicator of district-level malapportionment, namely the so-called Taagepera and Shugart's (1989) advantage ratio or seat-vote ratio (A).This is traditionally used for measurement of over-or underrepresentation of the different political parties. 14A MAL indicates the level of over-or underrepresentation of the district's local population (or, in our case, number of voters) in terms of the seats held. 15Finally, the third indicator of malapportionment consists of the deviation of a district's voter population from average district size (∆), which equals the number of voters in the district as a percentage of the average number of voters per seat.

Results
Let us first briefly focus on cross-national comparison analysing effects of electoral systems on degree of malapportionment.Table 1 shows that countries using FPTP have by far the highest levels of malapportionment (0.113), followed by countries where elections take place in SMDs (albeit not exclusively) under mixed-member systems of the independent and dependent combinations (0.081 and 0.073, respectively), personalized proportional systems (0.073) and two-round systems (0.061).In contrast, the lowest malapportionment levels (under one-half of those found under FPTP) can be found in countries using proportional electoral systems (0.048) 16 ; in the case of alternative voting, the value found is as little as 0.024, albeit this category covers only a single country, Australia.
Moving on to Mongolia, the first step of our analysis is to compare the overall development of MAL in all seven parliamentary elections that took place in the country.This comparison (Table 2) shows that almost irrespective of the type of electoral system applied, malapportionment grew constantly until the election of 2016, when the growth stopped.Whereas the level of malapportionment was under 4% (MAL = 0.039) in the first election to the unicameral parliament in 1992, it almost tripled until 2004 (MAL = 0.106) and further exceeded that level in 2008 (MAL = 0.130) to reach almost four times the level of 1992 in 2012 (MAL = 0.154 in the nominal tier of mixed system).Despite a decrease in 2016, the 10% threshold continued to be exceeded (MAL = 0.108).
At the same time, this growth cannot be exclusively associated with electoral system type because Mongolia practically applied only two electoral systems throughout the 1992-2012 time period (as long as only the nominal tier of MMM is considered for 2012 -because the list tier distributed seats in a single nationwide district).Across the three elections in which Mongolian voters used unlimited vote, the MAL values ranged from 0.039 (1992)  FPTP -first-past-the-post system; MMM -mixed-member majoritarian system; MMP -mixed-member proportional system; PPS -personalized proportional representation; TRS -two-round system; PRproportional representation; AV -alternative vote.
Source: Samuels and Snyder (2001), and author's calculations.the three uses of two-round system, MAL values grew from 0.052 (1996) through 0.068 (2000) to 0.106 (2004).On one hand, the average malapportionment levels approximated those found by Samuels and Snyder (2001), who identified an average MAL of 0.061 for TRS (0.075 in Mongolia) and 0.113 for FPTP (0.098 in Mongolia). 17On the other hand, the trend we identified testifies to a growing level of malapportionment.The trend was somewhat put on hold in the elections of 2016, when the MAL value declined to 0.108 following a transition from mixed system to FPTP.However, although that value is below the average value for FPTP identified by Samuels and Snyder (0.113), it is still relatively large in the context of developed democracies using FPTP such as Canada (0.076), India (0.062), the United Kingdom (0.046), and the USA (0.014). 18  From an overall perspective, Mongolia's malapportionment has been above the 10% threshold since 2004, whereas the so-called Venice Commission (European Commission for Democracy through Law, VC, 2003), for example, argues that malapportionment should not exceed just that level and only under extremely exceptional circumstances should it exceed the 15% threshold, which Mongolia approximated in 2008 and exceeded in 2012.Yet the construction of MAL as mean deviation from the ideal distribution of seats cannot accurately reflect possible inequalities affecting certain groups of voters.This, along with the fact that different parties have different territorial distributions of electoral support, makes it necessary to study in depth any extreme values at district level which may potentially result in uneven distribution of seats.
When comparing the values of A MAL (Table 2), we can once again observe an almost continuous growth of malapportionment.However, whereas the average value for all districts (nationwide) grew only moderately (A MAL = 1.01 to 1.14 in the elections of 1992 to 2012) and in 2016, A MAL decreased like MAL, namely to 1.07 (the average A MAL value for all elections = 1.06), the same does not apply to extreme values.Those reached their minimums in the 1990s and maximums during the most recent elections.The historic maximum was reached in 2016 (A MAL = 1.80, average A MAL value for all elections = 1.59).The minimum malapportionment level, too, was quite extreme in 2016 (A MAL = 0.61), even compared to the historic minimum reached in the elections of 2004 and 2008 (A MAL = 0.51, average A MAL value for all elections = 0.62).
However, nationwide aggregate levels of A MAL may obscure interdistrict differences as well.This can be documented on histograms showing the frequency distribution of A MAL at district level (Figure 1 and 2).Let us first focus on those elections that took place in SMDs.Here, we can confirm the aggregate-level findings (growing level of malapportionment).In 1996, most districts were found in the range of 0.9-1.0(42.11%) or 0.9-1.1 (60.53%), whereas these categories covered only 25.0% or 47.37% of districts, respectively, in the subsequent election of 2000, 11.84% and 32.89% in 2004 and finally as little as 13.16% and 23.68% of all electoral districts in 2016.It is especially since the 2004 election that we can observe a considerable growth of districts with malapportionment levels deviating by more than 20% from ideal representation, often by more than 40%.Those deviations go in both directions in 2004 and mostly in the direction of overrepresentation in 2016 (exclusively so for electoral districts outside the country's capital).
A similar picture emerges when looking at the distribution of district-level A MAL values for elections with unlimited vote.Whereas most districts were found in the range of 0.9-1.0(42.31%) or 0.9-1.1 (30.77%) in 1992, the same categories covered less than one-fifth or onequarter of districts, respectively, in the following elections: 11.54% or 7.69% in 2008 and 3.85% or 19.23% in 2012.An especially well-apparent trend is the growing number of districts at both extremes of the continuum, i.e. ones whose voters are strongly under-or overrepresented in terms of the number of seats held.Here once again, strong underrepresentation of capital city districts has been identified: 17 of the 18 cases of underrepresentation observed were found in Ulaanbaatar.
Given the urban-rural disproportion found above, it appears important to compare the values of A MAL between the electoral districts in the countryside and in the capital city (Tables 3 and 4).Source: General election Commission of Mongolia, accessed at https://www.gec.gov.mn, and author's calculations.
election of 2016, average voter representation for all capital city districts approximated the previous time period (average value for all elections 0.86).
Interestingly, all of the most overrepresented districts were found outside the capital (average maximum A MAL in rural districts for all elections = 1.59, compared to 1.09 in Ulaanbaatar).In contrast, all of the most underrepresented districts were in Ulaanbaatar (average minimum A MAL in capital city districts for all elections = 0.62, compared to 1.14 in rural districts).The growing advantagement of rural districts can also be documented on a comparison of the proportion of over/underrepresented districts among districts in and outside Ulaanbaatar.As shown in Table 4, a large majority of capital city districts were underrepresented in terms of the seat-vote ratio for the entire time period from 1992 (even all of them in the years 2008 and 2012).At the same time, the situation in rural districts exhibited a completely opposite trend.Whereas almost one-half of rural districts indicated underrepresentation in terms of A MAL in the 1990s (and still almost onethird in 2000), this declined to one-tenth of districts in 2008 and 2012.Despite some growth in the election of 2016, only less than one-fifth of non-Ulaanbaatar districts were underrepresented, compared to more than four-fifths of Ulaanbaatar districts.
Finally, we will focus on district-level disproportions in the seat-vote ratio.Table 5 shows that in the year 1992 (when unlimited vote was applied), the least-populated electoral district (Ömnögovi with 22,027 registered voters) exhibited a negative deviation from average of 47.22%, whereas the largest electoral district (Ulaanbaatar II with 66,667 voters) had a positive deviation of almost 60% (59.74%).Even after accounting for the fact that Ömnögovi had two members and Ulaanbaatar II four members of parliament, a clear advantagement of Ömnögovi voters can be observed.
The transformation to a two-round majoritarian system further exacerbated the disproportion between the smallest and the largest districts.Whereas the negative deviations for the smallest districts ranged from 26.59% in 1996 (one of the two districts in Ömnögovi with 11,082 voters) through 38.80% to 44.19% (in both cases for one of the three districts in Dornod aimag with 10,042 or 9766 voters, respectively) in 2000 and 2004, the maximum deviation for the largest districts grew from 40.38% in 1996 through 67.10% in 2000 to 95.45% in 2004, which also reflects the growing voter population of the largest districts from 21,191 (1996) through 27,418 (2000) to 34,199 (2004). 19  The continuing advantagement of rural voters (which, however, is largely consistent with the strong migration flow from rural aimags to Ulaanbaatar 20 ) can also be demonstrated on a comparison of the number of districts with voter populations below national average (i.e.ones where an individual vote had stronger influence on the composition of the legislature).In 1992, 12 out of 20 rural districts had underaverage voter populations, compared to only one district in the capital city.Similarly, after the transition to two-round system in 1996, a (soon-to-grow) majority of rural districts had underaverage voter populations (29 of the total of 56 rural districts in 1996, 35 in 2000 and 46 in 2004), whereas this was only the case of 3 out of 20 Ulaanbaatar districts in 1996 and 6 in the years of 2000 and 2004.
The return to unlimited vote in the parliamentary election of 2008 further exacerbated the size discrepancy between the largest and smallest districts.Whereas the district of Dundgovi (with 27,506 registered voters) exhibited a negative deviation of 53.65%, two capital city districts (with 129,084 or 158,467 registered voters, respectively) had a positive deviation twice the size of national average (with a maximum of 167.04%).An even higher disproportion was observed in the nominal tier of mixed system in the 2012 election, where the once-again smallest district of Dundgovi (28,824 registered voters) remained at approximately one-half of the national average (59.19%),whereas the positive deviation in the two above-mentioned Ulaanbaatar districts (with 179,194 or 206,836 registered voters, respectively) grew to as much as 192.82%.Even when accounting for the different number of seats held by the smallest and largest districts (2:4 2008, i.e. similarly as in 1992, or 1:3 in the election of 2012), the largest capital city districts only had a double or triple "advantage", respectively, to Dundgovi in terms of the number of seats held, while their voter populations were almost five to six times higher; therefore, the strength of one's vote in the capital city was far lower.
The final important question related to malapportionment is whether certain political parties derive any benefits from malapportionment.The above findings in the case of Mongolia support the assumption that malapportionment results from overrepresentation of sparsely populated rural areas and, as such, may strengthen politically conservative rural districts at the expense of politically progressive urban districts.(Although the migration flow to the Mongolian capital city prevents us from treating Ulaanbaatar's population as a whole as politically progressive.)Previous research demonstrated that one of the intentions behind malapportionment is to strengthen the parties that enjoy stronger support in overrepresented areas (Batto, 2016;Gallagher & Mitchell, 2005).Therefore, the last question remains whether a relationship can be found before malapportionment levels and support for certain parties.
The first finding in this regard (Table 6) is that in the first two parliamentary elections, there was no considerable link between malapportionment level and support for either the MPP (which held the government in 1992) or the main opposition parties.The same applied after 1996 when the parties' roles reversed and a coalition of the former main opposition parties, the Democratic Alliance (Ardchilsan kholboo), took the government.In contrast, the parliamentary election of 2000 was the first one to exhibit not only a negative (however trivial) relationship in the case of the MPP but, more importantly, a substantial (positive) correlation between malapportionment level and support for the incumbent parties, suggesting a possible problem-in anticipation of a defeat, the government majority (i.e. the MNDP and the MSDP) chose to "redraw" the boundaries of some districts to mitigate its electoral loss.
In contrast, the electoral stalemate of 2004 brought the correlation values closer to the election of 1996 when there was only an extremely weak (positive) association between malapportionment levels and support for both main parties-the MPP and the Motherland-Democracy Coalition.However, the question remains to what extent the relationship identified in the case of DP, which ran as part of the Motherland-Democracy Coalition, was influenced by the existence of that coalition and the electorates of the other coalition parties; this question cannot be answered using available data.
Two subsequent elections changed that pattern when electoral support for the post-communist MPP, the main government party before both elections, was very strongly (2008) or substantially (2012) correlated with malapportionment levels for the first time, whereas support for the DP was correlated negatively, albeit with a low to trivial strength.These findings are consistent with the MPP's long-term higher support in rural regions, which are characterized by overrepresentation in terms of the seat-vote ratio, 21 yet since no similar relationship was demonstrated for the previous elections, one can again hypothesize the ruling party's possible effort to change the boundaries of electoral districts.Such a hypothesis is supported by evidence from the parliamentary election of 2016, as support for the opposition MPP continued to be positively associated with more strongly overrepresented districts (at medium strength of correlation), on one hand, but the direction of the relationship for the government DP reversed to a substantial positive association, on the other hand.One final interesting finding is how malapportionment is linked to support for the MPRP (a break-away faction of the MPP), where a substantial (2012) or medium-strength (2016) negative correlation suggests that support for the party, as opposed to the MPP, was rather found in districts underrepresented in terms of the seat-vote ratio, and the territorial distribution of MPRP's electorate is considerably different from MPP's traditionally rural postcommunist backing.

Conclusions
We have used some alternative methods to study degree of malapportionment in Mongolia both at the national and the district level during the period 1992-2016, and have come to several conclusions.First, our analysis found that almost irrespective of the type of electoral system applied, the level of malapportionment grew constantly at both national and district levels until the election of 2016, when the growth ended.This can be partially ascribed to a change in the number of members representing rural districts and Ulaanbaatar, one that was supposed to reflect the growing population of the capital city as opposed to rural aimags.Therefore, the Mongolian example lends overall support to the findings Ong et al. (2017), rather than those of other authors (Ardanaz & Scartascini, 2013;Horiuchi, 2004;Samuels & Snyder, 2001), namely that plurality systems, or single-member districts as a such, are not unambiguous factor distorting fair apportionment, because the biggest degree of malapportionment was found in elections of 2008 and 2012, when electoral districts ranged between 2 and 4, or 1 and 3, respectively.More importantly, as there were 8 two-member, 12 three-member and 6 fourmember districts in 2008 and, similarly, only six single-member districts in 2012 (all outside the capital), compared to 18 two-member and 2 three-member districts (all in Ulaanbaatar), degree of malapportionment was much higher than when Mongols used solely single-member districts, whether under FPTP in 2016 or two-round system in 1996, 2000 and 2004.
Second, the analysis of malapportionment demonstrated a considerable level of malapportionment in terms of the seat-vote ratio, with long-term advantagement of rural regions at the expense of more urbanized ones, and especially at the expense of Ulaanbaatar inhabitants.This disadvantaging can somewhat be justified by Mongolia's settlement structure, as the capital currently accounts for almost one-half of the country's total population (compared to one-fourth in 1990)-should the number of seats be completely proportional, then people living in some (exclusively rural) districts would not have any representatives in the legislature, given the relatively small number of seats in the Mongolian parliament.
On the other hand, the long-term migration flow to Ulaanbaatar causes a continuous growth of the discrepancy between districts whose voters are strongly over-and underrepresented.In the election of 2016, the largest district's voter population almost tripled that of the smallest district, a fact that not only violates the ideal of political equality but also may importantly shape party competition by advantaging parties with a stronger support base in less-populated districts.In the case of Mongolia, this can be demonstrated on aimags in Western and Eastern parts of the country, where the MPP enjoys stronger support in the long term and which are mostly overrepresented in terms of number of seats held; the electoral competition is, however, more balanced in other rural regions as well as in the capital city.
Third, we found an interesting trend emerging since the 2000 election: government parties were rather more successful in districts with higher malapportionment levels, suggesting another potential representation issue resulting from gerrymandering.Therefore, the question remains whether it would more suitable for Mongolia, also with regard to safeguarding higher levels of party representation and a more equal influence of voters on the composition of the legislature, to consider reforming its electoral system towards fairer representation.This, however, would require, given Mongolia's territorial structure, holding elections in a single nationwide district (under proportional representation).Then again, this might result in dominance of candidates (and subsequently members of parliament) from the capital city and in diminishing representation of rural districts.In our opinion, the most suitable alternative, given the homogenous composition of Mongolia's population, could be to at least somewhat "even out" malapportionment by slightly increasing the number of members representing the capital (while increasing the total number of seats).Alternatively, this could be achieved by reforming the electoral system towards more representativity while preserving the connection between voters and their representatives, for example through alternative vote where an elected candidate enjoys majority support in its district (thus reducing the number of "wasted" votes) while preserving personalized voting.
Future research then should provide a more comprehensive answer as to whether (or to what extent) the Mongolian electoral reforms was not only example of increasing malapportionment but also gerrymandering, i.e. an efforts to redraw electoral districts boundaries to achieve partisan or other advantage (Cox & Katz, 2002) as Radchenko and Jargalsaikhan (2017, pp. 1043-1045) briefly identified some examples of gerrymandering before 2016 Mongolian parliamentary elections and one of the few crossnational analysis of the determinants of gerrymandering (I Coma & Lago, 2018) showed that gerrymandering is exacerbated especially in large countries using majoritarian systems.However, such research would require very different methods, especially those using in political (electoral) geography, which could concentrate not only on consistence of electoral districts with existing administrative units but also, for instance, on distribution of partisan strength across the Mongolian territory-or on whether the rather non-extreme malapportionment levels in most elections (which tightly exceeded 15% in only one case on national level) are also caused by the frequent post-electoral change in country leadership, where both the post-communist MPP and its main competitor, the DP, cannot count on sufficient voter support to attempt any more dramatic reform of the electoral system, whether by means of malapportionment or gerrymandering, because any such reform would damage their reputation to such an extent as to entail an electoral loss, as in the case of the DP in 2016.
More importantly, as Mongolia is possible to classify as a democracy since 1992, or even full democracy since 1996 (according to Polity IV Project [Marshall et al., 2018]), we did not confirm Ong et al. (2017) conclusion about association between degree of democracy and levels of malapportionment, with regard to long-term increasing level of malapportionment in Mongolia.In this context, further research could focus not only on relationship between levels of malapportionment and specific type of political regime per se, but also on various subdimensions of democratic governance as some other indicators (for instance CIRI Human Rights Data Project, see Cingranelli et al., 2014) found some problems in various aspects of Mongolian democracy and similarly some authors mention, for example, that the high electoral participation in Mongolia (which averaged 81.45% across the parliamentary elections of 1992-2016) may be caused by a "frustrated desire for influence" (Ganbat et al., 2008, p. 149), or by horizontal (interinstitutional) accountability issues (cf.Chang, 2018, pp. 230-231), which would require a more detailed analysis of malapportionment and the functioning of democracy in different areas at both national and subnational levels.
Finally, the question also remains whether one should consider, in the case of Mongolia, reforming its electoral system to ensure fairer representation in general, and higher level of party representation and voters' more equal influence on the composition of the legislature in particular.Nevertheless, given Mongolia's settlement structure, that would require elections taking place in single nationwide district (under proportional representation).Then again, that might lead to the predominance of capital city candidates, and consequently members of parliament, at the expense of rural districts' representatives.In our opinion, given the homogenous composition of the Mongolian population, the most suitable alternative might be to at least partially "straighten" malapportionment by slightly increasing the number of seats allocated to the capital city (while increasing the overall number of members of parliament) and reforming the electoral system towards more representativity, all the while preserving the connection between voters and their representatives, perhaps in the form of alternative vote, which requires the elected candidate to win the majority of votes in the district (thus reducing the number of wasted votes) while preserving personalised voting.

Funding
The publication of the paper has been supported by the institutional research funding scheme of the Faculty of Arts, Jan Evangelista Purkyně University in Ústí nad Labem, year 2023, Grant No. 63 209 016 2002 01, "Transformation and current problems of politics in the 21 st century".

A
long-term interregional comparison of malapportionment indicates continued increase (with the minor exception of the most recent election) of overrepresentation of rural districts, where the average values of A MAL grew from 1.03 in 1992 to 1.27 in 2012 and then decreased slightly to 1.19 in 2016 (average A MAL value for all elections = 1.14).In contrast, the average values of representation in Ulaanbaatar tended to oscillate more in time.The A MAL values for the first four elections oscillated around the 0.9 threshold (from 0.85 in 2004 to 0.95 in 1992); they declined to as little as 0.7 in the elections 2008 and 2012 (with mean values of 0.72 and 0.69, respectively); and after the

Table 6 . Correlations between district-level malapportionment levels (A MAL ) and support for the MPP, MPRP and DP-Mongolian parliamentary elections, 1992-2016
The DP value for 1992 indicates the combined result of the Alliance coalition and the independently running MSDP; individual values are as follows: Alliance (0,155), MSDP (−0,181).It indicates the result of the Democratic alliance in 1996 and 2000, and of the MDC in 2004.In 2000, the correlation level for the independently running MSDP reached −0,285.