Democracy and political polarization in the National Assembly of Republic of Korea
DDemocracy and political polarization in the NationalAssembly of Republic of Korea
Jonghoon Kim, Seung Ki Baek
Department of Physics, Pukyong National University, Busan 48513, Korea
Abstract
The median-voter hypothesis predicts convergence of party platforms across aone-dimensional political spectrum during majoritarian elections. Assumingthat the convergence is reflected in legislative activity, we study the timeevolution of political polarization in the National Assembly of Republic ofKorea for the past 70 years. By projecting the correlation of lawmakersonto the first principal axis, we observe a high degree of polarization fromthe early 1960’s to the late 1980’s before democratization. As predictedby the hypothesis, it showed a sharp decrease when party politics revivedin 1987. Since then, the political landscape has become more and moremulti-dimensional under the action of party politics, which invalidates theassumption behind the hypothesis. Our finding thus suggests the power andlimitation of the median-voter hypothesis as an explanation of real politics.
Keywords:
Legislation, Political polarization, Median-voter hypothesis,Co-sponsorship, Principal-component analysis, Bimodality coefficient
1. Introduction
Democracy is noisy. Through party politics, it invites the public intoconflict which was once private, so that the conflict is socialized as a pub-lic affair [1]. Conflict of great social importance becomes a cleavage aroundwhich parties are positioned, and the parties compete for votes by repre-senting different views on the cleavage. Therefore, polarization of parties isan inherent and inevitable feature of democracy, despite a growing concern
Email address: [email protected] (Seung Ki Baek)
Preprint submitted to Elsevier January 12, 2021 a r X i v : . [ phy s i c s . s o c - ph ] J a n bout its negative consequences [2]. At the same time, the median-voter hy-pothesis (MVH) argues that two parties will converge to the same positionacross a one-dimensional political spectrum, as long as voters always votewith single-peaked preferences [3, 4]: To be more specific, let us imagine anumber of voters, each of whom has his or her own political position as a realnumber and votes for a party whose position is the closest to his or her own.A party has to obtain more votes than the other parties to win the election,and if two parties play this zero-sum game, the Nash equilibrium is reachedwhen both converge to the median voter’s position. A rough sketch of partypolitics would be an interplay between these two forces of polarization andconvergence.The empirical evidence of the MVH is mixed, and the main reason isthat the political privacy in the secret-ballot system poses an obstacle to itsdirect verification. One way to get around the difficulty is to assume that themedian voter is effectively equal to a voter with the median income (or themedian tax price) [5, 6, 7, 8]. If this is the case, the MVH provides testablepredictions: For example, a more unequal society is predicted to choosegreater redistribution because the median voter will be relatively poorer ina more unequal society when compared with the mean income [8]. As analternative indirect measure, one can compare the dispersion in expendituresof local governments: An early finding was that local governments with asingle party showed a greater coefficient of variation than those with twoparties, suggesting that moderate policies tend to be adopted as a resultof political competition [9, 10]. Still, it remains in doubt whether the MVHoutperforms the existing models mostly based on mean incomes, and it is alsotrue that a number of studies present statistical results against the MVH [11,12, 13].In this work, we wish to use the MVH as a working hypothesis to un-derstand the political polarization in the National Assembly of Republic ofKorea for the past 70 years. The period can be divided into three parts:The first corresponds to the First Republic, which was ended in 1960 by theApril Revolution against autocracy. Shortly after the revolution, Korea ex-perienced military dictatorships from 1961 to 1987. Opposition parties didexist, but they were always minorities by the rules of the game. The lastperiod started in 1987 with the establishment of the Sixth Republic, afterwhich Korea has been on the road to democracy. We will mainly contrastthe last period with the second under military governments because they aresimilar in length but substantially different in the political ideas.2ur question is how the different political structures have affected the de-gree of polarization, measured by lawmakers’ correlation in their co-sponsorshipof bills [14, 15, 16, 17, 18, 19, 20, 21, 22]: According to the MVH, it is likely todecrease after democratization, whereas we would have no reason to expectsuch an effect under dictatorship. Our analysis indeed shows that the lackof democracy induced a high level of polarization, which in turn shrank thepolitical landscape to nearly one dimension. The accumulated tension wasfirst released in the late 1980s when democracy began to work in the SixthRepublic. Since then, the political landscape has constantly become moreand more multi-dimensional while the level of polarization fluctuates up anddown.
2. Materials and Methods
We have collected the bill data from 1950 to 2019 through Open DataPortal ( ). For each bill, we have its date of motion,title, chief author, and co-sponsors. The first National Assembly (May 311948 — May 30 1950) has been excluded from our analysis because it wasthe constituent assembly with no co-sponsored bills. We also exclude theyears 1962, 1971, 1979, and 1992 when no or few bills were sponsored. SeeTable 1 for details of the data.
To examine the data from the viewpoint of the MVH, we have used prin-cipal component analysis (PCA). Let us consider N data points, each ofwhich is M -dimensional. For the co-sponsorship data, N and M are thenumber of lawmakers and the number of bills, respectively, for a given pe-riod. The whole data can then be represented by an M × N matrix R , anda column vector [ R n , . . . , R Mn ] (cid:124) denotes the n th data point, where (cid:124) meanstranspose. We set R mn = 1 if the n th lawmaker sponsored the m th bill, and R mn = 0 otherwise. After removing all-zero rows and columns, we work witha standardized matrix: X = R − µ s . . . R N − µ N s N ... . . . ... R M − µ s . . . R MN − µ N s N , (1)3 able 1: Summary of data used in this work. The first column means the session numberof the Assembly, and the second and third columns show the dates of establishment anddisbandment, respectively. The fourth column shows the number of seats, and the figuresin the parentheses mean the numbers of lawmakers awarded through proportional rep-resentation, or through recommendation of the president (marked by ∗ ). Single-memberconstituencies comprise the other seats in most cases, but we have a few exceptions ofthe medium constituency system as noted in the last column. The fifth column shows thenumber of collected bills. For the 20th Assembly, we use the bill data in [22], which wascollected up to June 3, 2019 ( † ). The Assembly has been unicameral except for the 5thsession. session ∗ ) 221 medium10 3/12/1979 10/27/1980 231(77 ∗ ) 127 medium11 4/11/1981 4/10/1985 276(92) 266 medium12 4/11/1985 5/29/1988 276(92) 304 medium13 5/30/1988 5/29/1992 299(75) 68314 5/30/1992 5/29/1996 299(62) 42715 5/30/1996 5/29/2000 299(46) 102116 5/30/2000 5/29/2004 273(46) 189017 5/30/2004 5/29/2008 299(56) 610618 5/30/2008 5/29/2012 299(54) 1156419 5/30/2012 5/29/2016 300(54) 1580620 5/30/2016 5/29/2020 300(47) 20967 † µ n ≡ M − (cid:80) m R mn and s n = (cid:112)(cid:80) m ( R mn − µ n ) / ( M −
1) are thesample mean and standard deviation of the n th column vector, respectively.The next step is to construct a correlation matrix: Q = 1 M − X (cid:124) X = 1 M − X . . . X M ... . . . ... X N ... X MN X . . . X N ... . . . ... X M ... X MN , (2)whose element Q ij means correlation between the i th and j th data points: Q ij = 1 M − M (cid:88) m =1 X mi X mj = 1 M − M (cid:88) m =1 (cid:18) R mi − µ i s i (cid:19) (cid:18) R mj − µ j s j (cid:19) . (3)Note that Q ij takes a value from [ − Q ii = 1. If Q ij is close toone, it means two lawmakers i and j have highly correlated co-sponsorshipbehavior. If Q ij is negative, on the other hand, the lawmakers are anti-correlated, meaning that they usually do not work together. We diagonalizethe correlation matrix Q , e.g., by using the singular-value decomposition,and take the principal eigenvector corresponding to the largest eigenvalue. Itis a one-dimensional representation of co-sponsorship among lawmakers, andthe validity of this dimensionality reduction is measured by the proportionof variance explained by the principal component. If the Assembly is highlypolarized, we will find two clusters of lawmakers on the opposite sides of theaxis, and the distance between the clusters will explain most of the variancein the data. To quantify political polarization, we compute the bimodality coefficient [23,24]: β = γ + 1 κ , (4)where γ is the skewness and κ is the kurtosis of the distribution. The rationalebehind this quantity is that a bimodal distribution often has asymmetricpeaks and light tails, both of which increase the value of β . For the normaldistribution, we get β = 1 /
3, whereas the maximum value of β = 1 isobtained for the bi-delta distribution. The uniform distribution with β = 5 / nd(1950.05.31)3 4 5 6 7 8 9 1011 12th(1985.04.11)13 14 15 16 17 18 19 20th(2016.05.30)Year & Assembly0.2 B i m o d a li t y C o e ff i c i e n t P r o p o r t i o n o f V a r i a n c e (a)(b) Figure 1: Time evolution of political polarization in the Assembly. (a) Each year’s dis-tribution of lawmakers along the first principal axis. When two sessions coexist in thesame year because of an election, they are treated separately. (b) Sample bimodality co-efficients [Eq. (5)] depicted as the line graph. The dashed horizontal line means β = 5 / can be regarded as a borderline between unimodal and bimodal ones. For N samples on the principal axis, the formula should be rewritten as b = g + 1 k + N − ( N − N − , (5)where g is the sample skewness and k is the sample excess kurtosis.
3. Result
Figure 1(a) shows each year’s distribution of lawmakers along the firstprincipal axis. The bimodality coefficient b for each distribution [Eq. (5)]is depicted as a line graph in Fig. 1(b). As predicted above, b remainedhigh under military governments from the early 1960s to the late 1980s.Another notable feature is that the proportion of variance explained by the6rst principal component (the bar graph) had a clearly increasing tendencyand eventually went beyond 50%, which implies that the effective politicaldimension was close to one.The bimodality showed meaningful decrease for the first time in the 13thAssembly (May 30 1988 — May 29 1992), which was a period of transitionfrom the military dictatorship to formal democracy. Thereafter the line graphof b shows wild fluctuations, but the difference from the earlier period is stillstriking. We also see that the bar graph has decreased down to 10%, whichmeans a considerable increase of the effective dimensionality.
4. Discussion and Summary
When parties take over the control over the government through elec-tions, it becomes risky for them to take extreme positions across the politicalspectrum. On the other hand, a dictatorship would hardly feel motivated tocompromise with others’ opinions: To evade such pressure towards the me-dian systematically, military dictatorships abused the medium-constituencysystem in the 1970s and 1980s, and some lawmakers were even awardedthrough recommendation of the president (Table 1). The result was a highlevel of political polarization without any relaxation for decades.The establishment of the Sixth Republic in 1987 was a milestone in thepolitical history of Korea, which allowed party politics to revive after longmilitary dictatorship. When the government party failed to win a majorityin the 1988 legislative election for the 13th Assembly, it was the first timesince 1950, and the government party had to merge with two oppositionparties in 1990 to regain the majority. Interestingly, Fig. 1(b) shows thatpolarization had already dropped in 1988, suggesting that the competitiontowards the median might be the reason that the three parties decided tomerge. Since 1988, the degree of political polarization has fluctuated widely,and it should not be surprising if we consider that parties obtain power bysocializing conflict and representing different views on it. A more notabletrend is that the principal axis occupies less and less of the total variance astime goes by. It implies that party politics in the Assembly can no longerbe described adequately along a one-dimensional axis: It should rather beunderstood as a combination of multiple cleavages that are simultaneouslyin action, and the MVH ceases to be a realistic description at this stage.In this respect, the MVH could be regarded as a negative theory: Itis better supported by non-vanishing polarization in the absence of democ-7acy, where the political spectrum becomes nearly one-dimensional betweendespotism and democracy. On the other hand, if the MVH is viewed as anaffirmative theory, the dynamics of party politics, which the MVH intends todescribe, will eventually undermine its assumption on one-dimensionality be-cause parties are, by nature, apt to introduce new dimensions of conflict intothe public sphere. Admittedly, we are not dealing with the MVH in its rigor-ous sense: For example, the distinction between the median and mean mightbe virtually nonexistent in political terms such as moderates, and it wouldbe difficult to empirically compare the convergence point of lawmakers withthe actual political position of the median voter among the electorate. Ourgoal was rather to capture the nontrivial dynamics of political convergenceand polarization by looking at the co-sponsorship data from the perspectiveof the MVH.In summary, we investigated the time evolution of political polarizationin the National Assembly of Korea from 1950 to 2019 by applying PCAto the co-sponsorship data. The degree of polarization was measured bythe bimodality coefficient of the distribution of lawmakers along the firstprincipal axis, and we checked the proportion of variance explained by thefirst principal component. For the period of dictatorship from the early 1960sto the late 1980s, we observe no relaxation of political polarization, and theproportion of variance in the first principal component had accumulated overtime throughout this period. The political polarization was greatly reducedby the establishment of formal democracy in 1987. Since then, the levelof polarization has fluctuated, but the proportion of variance in the firstprincipal component has constantly decreased. Our observation provides adynamic view on party politics in terms of socialization of conflict, a noisyyet inevitable process of democracy.
Acknowledgments
This work was supported by Basic Science Research Program throughthe National Research Foundation of Korea (NRF) funded by the Ministryof Education (NRF-2020R1I1A2071670).
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