A New Quota Approach to Electoral Disproportionality

economies Article A New Quota Approach to Electoral Disproportionality Miguel Martínez-Panero 1,* , Verónica Arredondo 2, Teresa Peña 1and Victoriano Ramírez 3 1PRESAD Research Group, BORDA Research Unit, IMUVa, Departamento de Economía Aplicada, Universidad de Valladolid, 47011 Valladolid, Spain; [email protected] 2PRESAD Research Group, Unidad Académica de Matemáticas, Universidad Autónoma de Zacatecas, Zacatecas 98000, Mexico; veronica.arr[email protected] 3Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain; [email protected] *Correspondence: [email protected]; Tel.: +34-983-186591 Received: 10 January 2019; Accepted: 26 February 2019; Published: 5 March 2019   Abstract: In this paper electoral disproportionality is split into two types: (1) Forced or unavoidable, due to the very nature of the apportionment problem; and (2) non-forced. While disproportionality indexes proposed in the literature do not distinguish between such components, we design an index, called “quota index”, just measuring avoidable disproportionality. Unlike the previous indexes, the new one can be zero in real situations. Furthermore, this index presents an interesting interpretation concerning transfers of seats. Properties of the quota index and relationships with some usual disproportionality indexes are analyzed. Finally, an empirical approach is undertaken for different countries and elections. Keywords: electoral systems; proportionality; electoral quota; disproportionality indexes; measurement; Spain; Sweden; Germany 1. Introduction Electoral systems are mechanisms by which votes become seats in a parliament. In order to reflect the overall distribution of voters’ preferences, some of these systems advocate for proportional representation, so that political parties will receive percentages of seats corresponding to their respective percentages of votes. Since a seat cannot be divided, it is impossible to assign exactly the obtained vote shares in seat terms. This apportionment problem generates something known as electoral disproportionality. Consequently, some parties are overrepresented while others become underrepresented. Even more, disproportionality may increase, due to the existence of many districts and electoral thresholds. There is not an agreement about an instrument to determine such distortions generated during the process of translating votes into seats and many efforts have been made to measure them. Disproportionality indexes are usually employed to this aim and there exists a wide literature on this approach. A survey compilation of indexes resulting from the application of different techniques is presented by Taagepera and Grofman (2003) (see also Taagepera 2007;Karpov 2008;Chessa and Fragnelli 2012; Goldenberg and Fisher 2017). These authors also develop an interesting analysis of the properties that they fulfill. From a computational point of view, Ocaña and Oñate (2011) presents a software for calculating nine disproportionality indexes. On the other hand, Koppel and Diskin (2009) and Boyssou et al. (2016) propose axiomatizations for some indexes measuring disproportionality. Finally, relationships among some disproportionality indexes appear in Borisyuk et al. (2004) and Bolun (2012). Economies 2019,7, 17; doi:10.3390/economies7010017 www.mdpi.com/journal/economies Economies 2019,7, 17 2 of 17 All the proposed indexes measure deviations (in some way) from exact proportionality, which is not affordable in practice. Balinski and Young (2001, pp. 79–83) deals with a more realistic requirement concerning the apportionment problem: No party’s representation should deviate from its quota (number of seats that should be received by the parties in exact proportionality) by more than one unit. In other words, no party should get less than its quota rounded down, nor more than its quota rounded up. This property is called “staying within the quota” or “verification of the quota rule”. Taking into account that usually the quota is not an integer number, votes-seats disproportionality could be non-forced (if the quota rule is not satisfied), or forced, otherwise. This paper presents a new index that just measures non-forced disproportionality, avoiding that inherent to the fact that exact proportionality is unfeasible, as pointed out. Remarkably, this index is zero if and only if the quota condition is satisfied. Even more, from this index, it is possible to obtain the minimum number of seats that would be necessary to transfer from some parties to others, so that the distribution of parliament seats will satisfy the quota condition. The paper has the following structure: Section 2introduces the notation and basic concepts, paying particular attention to the quota. Section 3presents some of the most used disproportionality indexes, namely: The maximum deviation, Loosemore-Hanby and Gallagher indexes. Section 4 introduces a new index, which will be called “quota index”. Section 5shows the properties that the last index verifies and some relationships with the previous disproportionality indexes. In Section 6 the aforementioned indexes are computed for different elections in Spain, Sweden and Germany, and comparisons among them are established. In Section 7, some conclusions are presented. Finally, technical proofs, electoral results and data resources are left in Appendices A–C, respectively. 2. Notation and Basic Concepts Let V be the number of voters, n the number of parties and S the number of seats to be distributed; (V1,V2, . . . , Vn) is the vector whose components are the votes obtained by each party, so that V= n ∑ i=1 Vi ; on the other hand, (S1,S2, . . . , Sn) is the vector whose components are the seats assigned to each party, where S=n ∑ i=1 Si ; finally, we denote by vi and si the proportion of votes and seats that party ireceives. Thus, vi=Vi/Vand si=Si/Sare the vote and seat shares, respectively, for each party i. A party i is overrepresented when si>vi , and underrepresented when si<vi . Any of these inequalities represents a distortion with respect to the voters’ real preferences. The quota (or “fair share”) is the number of seats that the party i should receive in exact proportionality after obtaining Vivotes. That is, the quota for party iresults qi=Vi VS. In terms of the quota, a party is underrepresented if Si<qi and overrepresented if Si>qi . Since n ∑ i=1 Si=n ∑ i=1 qi, if a party is underrepresented, at least another one will be overrepresented. The lower quota is the closest integer number that does not exceed qi ; it will be denoted by bqic . Likewise, the upper quota is the smallest integer number bigger than or equal to qi ; it will be denoted by dqie . In other terms, the lower quota is obtained by rounding down qi , and the upper quota by rounding up qi. Usually, for each party, quotas are fractional numbers and hence dqie=bqic+ 1. Otherwise, if qi is an integer number, then bqic=dqie . The interval whose extremes are lower and upper quotas will be called quota interval. An apportionment satisfies the quota rule if the number of seats Si assigned to each party differs from its quota less than one, this is: |qi−Si|< 1, or equivalently, bqic≤Si≤dqie for each i=1, 2, . . . , n. On the other hand we will say that a party is overrepresented with respect to the upper quota if Si>dqie ; and is underrepresented with respect to the lower quota if Si<bqic . Obviously, these are more restrictive requirements for parties than being merely overrepresented or underrepresented. Economies 2019,7, 17 3 of 17 3. Some Indexes of Electoral Disproportionality and Their Relationship The literature on indexes is devoted to measuring the quality of an electoral system, in some way. One of the most important issues in this context is electoral disproportionality, which could be defined as the deviation level of vote and seat shares of the participating parties in an election. In order to determine electoral disproportionality various indexes have been proposed. As aforementioned, compilations of these indexes have been made by different authors ( Taagepera and Grofman 2003 ;Karpov 2008). Among them, the maximum deviation index, the Loosemore-Hanby index proposed by Loosemore and Hanby (1971) and the least squares index, presented by Gallagher (1991), are some of the most frequently used ones. 3.1. Maximum Deviation Index This index measures the maximum difference between vote and seat shares in absolute terms. The mathematical expression for this index is: IMD =max i=1,...,n|si−vi|. As it can be observed, the maximum deviation index only provides information of one party that can be either the most underrepresented or overrepresented one, regardless of the deviation sizes of the other parties. 3.2. Loosemore-Hanby Index This index adds all the deviations generated during the allocation, meaning the sum of absolute values of the differences between the vote and seat shares. Mathematically the index is defined as ILH =1 2 n ∑ i=1 |si−vi|. The sum of absolute values of the differences between the vote and seat shares for overrepresented parties coincides with the same sum for underrepresented ones. Hence, the total sum appearing in ILH is divided by two in order to obtain the seat share that has not been distributed in a completely proportional way. 3.3. Gallagher Index The least squares index is also known as Gallagher index, and it is defined as the square root of the sum of the squared differences between vote and seat shares of every party divided by two. Formally: IG=s1 2 n ∑ i=1 (si−vi)2. This index takes into account both big and small deviations in the proportion of assigned seats and obtained votes. However, small differences have less influence than big differences. Consequently, this index is less sensitive than the previous one to the appearance of small parties. 3.4. Relationship among Disproportionality Indexes Obviously, ILH =IMD =IG= 0 if and only if there exists exact proportionality, i.e., the percentage of votes equals that of seats for each party. Some further relations among these indexes can be established. It is straightforward that ILH =IMD if and only if there exists either just one overrepresented or just one underrepresented party. On the other hand, if there are at least two overrepresented parties jointly with another two underrepresented ones, it is straightforward that ILH >IMD. Economies 2019,7, 17 4 of 17 On the other hand, Borisyuk et al. (2004) proved that IG≤ILH . Besides, it is easy to check that IG=ILH if and only if there is exactly one overrepresented party jointly with just one underrepresented party. In both cases, also IMD reaches the same value. Finally, taking into account the aforementioned relationships concerning the considered indexes we can assert that, if there are at least two overrepresented parties jointly with another two underrepresented ones, then ILH >max{IMD,IG}. 4. The Quota Index All the aforementioned indexes measure deviations between vote and seat shares, and hence, in an implicit way, they take into account the quota as a point of reference. For example, the Loosemore-Hanby index can be expressed in quota terms as ILH =1 2 n ∑ i=1 |si−vi|=1 2S n ∑ i=1 Si SS−Vi VS =1 2S n ∑ i=1 |Si−qi|. Note that ILH = 0 if and only if Si=qi for all the parties (this is also true for the previously considered indexes). However, as the seats are indivisible, this situation requires all qi to be integer numbers, and this is extremely unlikely. Therefore, exact proportionality becomes almost impossible in real elections. On the other hand, in terms of seat transference ILH can be understood as the proportion of seats that we need to transfer from overrepresented parties to underrepresented ones in order to achieve exact proportionality. However, this is merely a theoretical value because, again, such exact proportionality would require the seats to be divided. This is the reason why we have focused our attention not in exact apportionments, but in those staying within the quota, which is a more plausible condition. These considerations do not mean that we advocate for apportionment methods verifying the quota rule, as the largest remainders (a.k.a. Hamilton) rule. That is, regardless of the used method, our aim is measuring post hoc deviations from the quota interval. If the quota qi is not an integer number for some party, depending on the value of Si , two kinds of disproportionality can be considered. We will say that in an allocation of seats, there exists non-forced disproportionality if some party does not verify the quota condition (i.e., it is overrepresented with respect to the upper quota or underrepresented with respect to the lower quota). Otherwise, the quota rule is satisfied for all the parties and we will talk about forced disproportionality, unavoidable due to the nature of the apportionment problem. Such considerations are illustrated in Figure 1. These ideas have been taken into account in our proposal, in which we only measure non-forced disproportionality (i.e., beyond de quota interval): That is, only distances of overrepresented parties from their upper quotas or underrepresented parties from their lower quotas are considered. In this way, we have defined an index, called quota index, as Iq=1 Smax                n ∑ i=1 Si>qi (Si−dqie), n ∑ i=1 Si<qi (bqic−Si)                . The value of Iq is between zero and one. The zero value corresponds to any distribution that verifies the quota rule, while the maximum disproportionality will be reached when all the seats are assigned to parties with no votes. It is worth noting that, while Loosemore-Hanby and the other aforementioned indexes are zero if and only if the apportionment is exact, Iq can be zero without this requirement. But, obviously, Iqis also zero if there exists exact proportionality. Economies 2019,7, 17 5 of 17 Economies 2019, 7, x FOR PEER REVIEW 5 of 17 rule to be verified. And 𝑆∙𝐼 will be exactly the minimum number of seats that would have to be transferred from some parties to others for the distribution to verify the quota condition at a global level. This fact will be illustrated in Section 6 concerning 2016 Spanish elections. Figure 1. Types of disproportionality taking into account the quota rule. 5. Quota Index Analysis and Relationships with Other Indexes Karpov (2008), Taagepera and Grofman (2003) and Taagepera (2007) propose some reasonable properties and analyze their fulfillment for several disproportionality indexes, the maximum deviation, the Loosemore-Hanby index and the Gallagher indexes among them. In this section, after showing the difference of perspectives between the above-mentioned indexes and the new one, we will test for 𝐼 the most relevant properties appearing in the literature. In what follows, we will formulate the above-mentioned disproportionality indexes in terms of the quota. In Section 4 we have shown that: 𝐼=1 2𝑆|𝑆−𝑞|.   In a similar way, it is easy to check that: 𝐼=1𝑆max ,…,|𝑆−𝑞|, and Figure 1. Types of disproportionality taking into account the quota rule. Moreover, our index has an interesting interpretation in transference terms: The quota index Iq is the minimum proportion of seats in a parliament of S seats that we would need to transfer from overrepresented parties with respect to the upper quota to others underrepresented (or from overrepresented parties to others underrepresented with respect to the lower quota), for the quota rule to be verified. And S·Iq will be exactly the minimum number of seats that would have to be transferred from some parties to others for the distribution to verify the quota condition at a global level. This fact will be illustrated in Section 6concerning 2016 Spanish elections. 5. Quota Index Analysis and Relationships with Other Indexes Karpov (2008), Taagepera and Grofman (2003) and Taagepera (2007) propose some reasonable properties and analyze their fulfillment for several disproportionality indexes, the maximum deviation, the Loosemore-Hanby index and the Gallagher indexes among them. In this section, after showing the difference of perspectives between the above-mentioned indexes and the new one, we will test for Iq the most relevant properties appearing in the literature. In what follows, we will formulate the above-mentioned disproportionality indexes in terms of the quota. In Section 4we have shown that: ILH =1 2S n ∑ i=1 |Si−qi|. Economies 2019,7, 17 6 of 17 In a similar way, it is easy to check that: IMD =1 Smax i=1,...,n|Si−qi|, and IG=1 Ss1 2 n ∑ i=1 (Si−qi)2. These expressions are intended to establish in an easy way their relationships with the quota index. It will be also used in further computations. 5.1. Quota Index and Disproportionality Indexes: Difference of Scopes In Section 4, disproportionality has been split into two types. As shown in the previous expressions, traditional approaches to this issue measure the distances from quotas, and hence they take into account both forced and non-forced disproportionality. On the other hand, the quota index just measures distances to the quota interval, and therefore just consider non-forced disproportionality. In other words, usual disproportionality indexes contemplate underrepresented on overrepresented parties, while the quota index just considers those over the upper quota or below the lower quota. The following example illustrates these aspects. Example 1. Consider parties A and B, and let the number of seats to allocate S= 10. Suppose that SA= 8 and qA= 7.6 are the number of seats and the respective quota of the party A. Also consider that SB= 2and qB=2.4 are the number of seats and the quota of the party B, respectively. Then, we obtain: IMD =ILH =IG=0.04. However, as the quota rule is verified, Iq= 0. Notice that with these data all the appearing disproportionality is forced (unavoidable). 5.2. Disproportionality Indexes Properties and Quota Index Following Karpov (2008), some compelling properties are taken into account: 1. Anonymity: Any permutation of party labels does not change the value of the index. 2. Principle of transfers: If we transfer a seat from an overrepresented party to an underrepresented one, then the value of the index should not increase. 3. Independence from split: Suppose there are many parties with equal vote and seat shares, and these parties are grouped into one. Then, the value of the index calculated for all the parties in the group should be equal to the value of the index for the group considered as a whole. 4. Scale invariance (homogeneity): The index should not depend on any proportional change in the number of votes or seats 5. Zero normalization: This property is satisfied if, when vi=si for all i= 1, . . . , n , then the value of the index is 0. Next, we will check the fulfillment of the previous properties by Iq. Proposition 1. The indexIqsatisfies anonymity, principle of transfers and zero normalization. (The proof can be found in Appendix A). Now, Example 2 shows that Iqdoes not satisfy the property of independence from split. Example 2. Suppose nine parties whose quotas and assigned seats appear in Table 1, where S =6. Economies 2019,7, 17 7 of 17 Table 1. Electoral data for testing independence from split (before grouping). Parties Results A B C D E F G H I qi1.4 1.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 Si330000000 Calculating separately Iqfor all the appearing parties, we obtain: Iq=max3−d1.4e+3−d1.4e 6, 0=2 6=0.33. Now, in Table 2, Iq is calculated for parties with equal percentage of seats and quotas as unique coalitions: Table 2. Electoral data for testing independence from split (after grouping). Parties Coalitions Results A + B C + D + E F + G + H + I qi2.8 1.2 2 Si6 0 0 And hence Iq=max6−d2.8e 6,b1.2c−0+(2−0) 6=3 6=0.5. Table 3shows the properties that IMD , ILH , IG and Iq satisfy or do not (Karpov (2008) and Taagepera and Grofman (2003) for the three first indexes). A “+” sign means that the index satisfies the property and “ − ” means that it does not. Occasionally, these signs may appear enclosed into parentheses to point out that the corresponding property is or not satisfied under specific circumstances. Table 3. Summary of indexes and properties. Index Anonymity Transfer Principle Independence from Split Scale Invariance Zero Normalizing IMD + (+) −+ + ILH + (+) + + + IG+ (+) −+ + Iq+ + −(−) + Parentheses appearing in the column relative to the Principle of Transfers in Table 3mean that IMD,ILH and IGmay violate the principle of transfers in some situations, as shown in Example 3. Example 3. Consider parties A and B , and S= 10. Suppose that qA= 7.6, SA= 8, qB= 2.4 and SB= 2. That is, A is overrepresented and B is underrepresented. In this situation: IMD =ILH =IG=0.04. Now, if we transfer a seat from A to B : IMD =ILH =IG=0.06. Note that, in this example, after the seat transference the overrepresented party becomes underrepresented, and vice versa. Economies 2019,7, 17 8 of 17 However, it is easy to check that IMD , ILH and IG satisfy a weaker Principle of Transfers establishing that, if a seat is transferred from an overrepresented party verifying Si−qi> 0.5 to an underrepresented one that satisfies qi−Si> 0.5, then the value of these indexes should not increase. In particular, this situation happens when a seat is transferred from an overrepresented party with respect to the upper quota to an underrepresented one with respect to the lower quota. Concerning different versions of the Principle of Transfers in electoral disproportionality and their connection with the original Dalton’s Principle in more general inequality contexts, see Taagepera and Grofman (2003), Van Puyenbroeck (2008) and Goldenberg and Fisher (2017). On the other hand, the parentheses appearing in the column relative to Scale Invariance in Table 3 means that Iq violates this property just with proportional changes in the number of seats, but not in the number of votes, as shown in Example 4. Example 4. Consider again parties A and B , and S= 10. Suppose that qA= 7.6, SA= 8, qB= 2.4 and SB= 2. Note that in this situation the quota rule is satisfied and hence Iq= 0. If we multiply by 10 the number of seats, that is, S= 100, we obtain qA= 76, SA= 80, qB= 24 and SB= 20. Now, the quota rule is not verified and Iq=0.04. However, this fact should not be considered as a drawback of the index because the first situation cannot be improved by transferring seats in any way, while in the second situation if we transfer S∗Iq= 4seats from party A to B, the quota rule is verified. Even more, in this case the apportionment becomes exact. Concerning this issue, Boyssou et al. (2016) assert that although the homogeneity with respect the number of seats “seems rather reasonable for large parliaments, a good disproportionality index should perhaps be sensitive to the size of the parliament, at least for small parliaments”. Obviously, proportional changes in the number of votes (maintaining the number of seats to allocate) do not affect the quota and consequently neither the value of Iq. Some other properties can be considered for a disproportionality index (Taagepera and Grofman 2003;Taagepera 2007), among them: •Informationally complete (makes use of all siand vi) •Uses data for all parties uniformly •Does not depend on the number of parties •Varies between 0 and 1 (or 100%) As shown by the previous authors, these properties are satisfied by the disproportionality indexes considered along this paper, except the first one by IMD . On the other hand, it is straightforward that Iqalso verifies all of them. 5.3. Relationships among Iqand Disproportionality Indexes The relationships existing among different disproportionality indexes have been shown in various ways (Borisyuk et al. 2004;Bolun 2012). In the present paper some relationships that the quota index has with the disproportionality indexes appearing above will be analyzed. Proposition 2. The value of the quota index is always minor than or equal to the Loosemore-Hanby index: Iq≤ILH. (The proof can be found in Appendix A). Proposition 3. The values of the quota and the maximum deviation indexes verify the following inequality: Iq≥IMD −1 S. Economies 2019,7, 17 9 of 17 (The proof can be found in Appendix A). Obviously, Iq=ILH =IMD =IG= 0 if there exists exact proportionality. If not, other relations can be established. It is obvious that Iq=ILH if and only if qi are integer numbers for all the overrepresented parties and the maximum of the expression of Iq is reached for these ones, or qi are integer numbers for all the underrepresented parties and the maximum is reached for them. As these situations are extremely unlikely, in general Iq<ILH. On the other hand, it is straightforward that Iq=IMD if and only if there exists either just one overrepresented party with respect to the upper quota and, in addition, its quota is an integer number or just one underrepresented party with respect to the lower quota and, in addition, its quota is an integer. Finally, it is easy to check that Iq=IG if there is just one overrepresented party whose quota is an integer number and, in addition, there is exactly one underrepresented party. In both cases, also IMD reaches the same value. Otherwise both inequalities might appear between Iq and IG . For example, in any allocation verifying the quota with no exact proportionality, Iq= 0 <IG . But if the quota condition is not satisfied, the inequality might be reversed and, in fact, Iq<IG is unlikely (see results in Section 6). 5.4. Discussion about Indexes It can be observed that, as appearing in Table 3, none of the indexes considered along the paper is optimal. This situation is somehow analogous (in another context) to those in Social Choice theory, where is well known that there do not exist perfect voting systems nor apportionment methods, as proven by Arrow and Balinski-Young theorems, respectively. In fact, it is possible to find examples where all the considered indexes present some weaknesses, as will be shown in what follows. In an electoral situation where there exist non integer quotas (in fact, this is the most usual case), it is impossible to achieve exact proportionality, but it is always possible to find an apportionment verifying Iq= 0. It is a simple question of adjustment of each Si in its quota interval, so that, at the end of the process n ∑ i=1 Si=S . In such a situation, there are several possibilities of seat distribution staying within the quota, and this fact might be considered as a criticism, as shown in Example 5. Example 5. Consider parties A and B, and let the number of seats to allocate S= 5. Suppose that qA= 2.4 and qB= 2.6. In this situation there are two possibilities of seat distribution staying within the quota: SA= 2, SB=3and S0 A=3, S0 B=2. Hence, Iq=I0 q=0. However, the second allocation is less compelling than the first one, because the most voted party obtains the least representation. In other terms, there exists a lack of vote/seat monotonicity in the last apportionment. Now, notice that for the first allocation, we have IMD =ILH =IG= 0.08, while for the second allocation, I0 MD =I0 LH =I0 G= 0.12. Consequently, these indexes point out the first allotment as better than the second one. Nonetheless, Example 6 illustrates that the lack of monotonicity might not be captured (even more, it can be inversely reflected) when the usual disproportionality indexes are used. Example 6. Suppose eight parties whose quotas and assigned seats (in two different apportionments) appear in Table 4, where S =10. The first seat distribution is intentionally arbitrary (in fact, it cannot be obtained by any divisor or quotient method). However, the second distribution is obtained by any divisor method in the parametric family (Balinski and Ramírez 1999) between Webster (Sainte-Laguë) and Jefferson (D’Hondt). After some computations, the obtained values for quota and maximum deviation indexes in both allotments are Iq=I0 q= 0and IMD =I0 MD = 0.09. The first apportionment presents two pair of parties, (A,B) and (C,D) , where, in each of them, the most voted is the least represented. However, in this example, unlike the Economies 2019,7, 17 16 of 17 Appendix B. Table A1. Spanish Electoral Results (2016). Parties Votes Quotas Seats PP 7906.185 116.48 137 PSOE 5424.709 79.92 85 PODEMOS-IU-EQUO 3201.170 47.16 45 C’s 3123.769 46.02 32 ECP 848.526 12.50 12 PODEMOS-COMPROMÍS-EUPV 655.895 9.66 9 ERC-CATSÍ629.294 9.27 9 CDC 481.839 7.10 8 PODEMOS-EN MAREA-ANOVA-EU 344.143 5.07 5 EAJ-PNV 286.215 4.22 5 EH Bildu 184.092 2.71 2 CCa-PNC 78.080 1.15 1 PACMA 284.848 4.20 RECORTES CERO-GRUPO VERDE 51.742 0.76 UPyD 50.282 0.74 VOX 46.781 0.69 BNG-NÓS44.902 0.66 PCPE 26.553 0.39 GBAI 14.289 0.21 EB 12.024 0.18 FE de las JONS 9.862 0.15 SI 7.413 0.11 SOMVAL 6.612 0.10 CCD 6.264 0.09 PH 3.288 0.05 SAIn 3.221 0.05 P-LIB 3.103 0.05 CENTRO MODERADO 2.986 0.04 CCD-CI 2.668 0.04 UPL 2.307 0.03 PCOE 1.812 0.03 AND 1.695 0.02 JXC 1.184 0.02 IZAR 854 0.01 CILUS 847 0.01 PFyV 838 0.01 PxC 722 0.01 MAS 718 0.01 UNIDAD DEL PUEBLO 684 0.01 PREPAL 640 0.01 Ln 617 0.01 REPO 569 0.01 INDEPENDIENTES-FIA 556 0.01 IMC 351 0.01 FME 338 0.00 PUEDE 330 0.00 ENTABAN 257 0.00 FE 254 0.00 ALCD 210 0.00 HRTS-Ln 82 0.00 UDT 54 0.00 Total 23,756.674 350 350 Source: Ministry of Interior (Spain). 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).