Attempting to measure the intensity of opposing feelings in elections: A polarization approach to Catalonia’s independence case

This paper addresses the Catalonian political process for independence. Based on the outcome of the 2017 Catalonian Regional Election, it firstly innovates by building an independence-feeling indicator for each municipality. Subsequently, we resort to the concept of polarization to assess the level of inherent conflict. Besides, we evaluate to what extent polarization can be explained by different variables. Then, in the second part of the paper, we redo the analysis but, to handle the potential aggregation problem that arises with geographically reference data (MAUP problem), we compute for each municipality two (antiindependence-feeling and proindependence-feeling) indicators rather than one. In doing so, we avoid merging votes that offset each other and, by applying the polarization index, we not only test for (inter-) polarization but also (intra-) polarization (within municipalities). The results show important differences. More specifically, although polarization across municipalities is relatively small, there is a high level of polarization within them. Moreover, while population density, Catalan proficiency and place of birth are instrumental when explaining polarization if a single indicator is computed, in the case of two indicators unemployment rate, age and wealth also emerge as remarkable variables, while among the three previous ones the importance of population density decreases.


Introduction
Independence movements are becoming more frequent in different parts of the world, especially in Europe (Conversi, 2014), with the economic recession of 2008 serving as a kind of breeding ground for them. Among these independence demands, the case of Catalonia and Spain is one of the most prominent for several reasons (see, for example, Colomer, 2017, andQuiroga &Molina, 2020, as good references focused on the economic crisis and Catalonia). On the one hand, because it can arguably be considered as an example of how the lack of flexibility of the State to meet the demands of regional autonomy, along with some other factors, might trigger these claims of independence (Lecours & Dupré, 2020). On the other hand, since it is a rather peculiar case from which, therefore, some particular lessons can be learned. We refer to the fact that Catalonia is one of the richest regions in the country, which differentiates the Catalan case from others such as Scotland and Quebec, regions that are arguably poorer than their respective countries and therefore have other motivations for either independence or self-determination (Stiglitz, 2015). Because of that, in addition to the well-known reasons linked to national identity and social cohesion, which are common to practically all independence processes in the world, another factor alluded to as an important reason to support Catalonian independence is to avoid redistribution (see, for example, Serrano, 2013). Accordingly, its peculiarities make the case of Catalonia and Spain especially attractive to scholars.
There is also a third, completely different reason that, although not linked to the idiosyncrasies of our case study, should not be overlooked in any way. The Catalonia-Spain conflict is seen, in some spheres, as another test, not as important as the Brexit and the crisis of the Eurozone but also relevant, for the governance and ultimately the survival of the EU, since there are some doubts about its ability to cope with this kind of difficulties (Barber, 2017).
The facts speak for themselves: many papers have been published recently, dealing with different but connected facets, focusing on the Catalonian dilemma. It is, in fact, nearly impossible to acknowledge all of them. As a short reference, we here want to mention some interesting papers trying to explain the determinants of the pro-independence vote in recent elections, such as Rico and Liñera (2014), Orriols and Rodon (2016), Lepič (2017), Maza et al., (2019), and Guntermann et al., (2020). The reason we pick these works is that they deal with an issue closely related to ours, drawing important conclusions about the role played by some economic and social factors (such as language, place of birth, income …) in the process of political independence. As seen below, we will take advantage of these findings later.
Against this backdrop, the paper, employing data coming from the outcome of the 27 December 2017 Catalonian Regional Election at the municipal level, aims to deal with a related but distinct topic that has been rather overlooked so far: it tries to assess the intensity of the independence conflict. As will be remembered, the December election was called by the National Government to put an end to the suspension of Home Rule sanctioned by the Spanish Parliament two months earlier. Before this ruling, two illegal self-determination consultations had been held and the "Declaration of Independence" proclaimed on October 27, 2017; for this reason, we think the exceptional election held in Catalonia in December 2017 is arguably the best choice to test for independence feeling and to address the degree of discrepancy in this regard. 1 However, the electoral outcome says very little about the degree of conflict among voters. Consequently, to accomplish this aim, our initial step is to construct an indicator to proxy what we call the "independence feeling" of each municipality. This is the first novelty of this piece of work since, usually, the percentage of the proindependence vote is taken as the variable of interest. As we will explain below, the error of that approximation is to assume the same position on the issue of independence by political parties (and by extension, by their voters) that, actually, show clear differences on it. Our approach overcomes this problem.
Once the indicator is built, an important decision lies in choosing the best measure to compute the discrepancy in independence sentiments between municipalities. The first thought that comes to mind probably refers to any inequality measure. However, as proven by Esteban and Ray (1994), this is by no means the best option. Polarization is a better measure of discrepancy or, in other words, of conflict. Let us set an example in line with that given by Ezcurra et al., (2005) for, in that case, income polarization. Imagine we have data on the independence feeling in Catalonia and it is quite clear the region is undergoing a double process of municipal convergence. That is to say, the gaps between pro-independence (at one end of the range) and antiindependence municipalities (at the other one) are closing. If this process continues over time, there will eventually be two large homogeneous groups. Here, any measure of inequality will give a message of low inequality, despite the obvious fact that the rift is extraordinarily strong. The corollary is quite straightforward: as indicated by Esteban and Ray (1994), the traditional notion of inequality is inadequate in this kind of setting. Consequently, we will use a polarization measure to evaluate discrepancies/conflict between municipalities. When it comes to adopting joint policies, for instance, this piece of information can be very important. 2 Indeed, our aim is not only to provide an accurate assessment of conflict based on a standard polarization measure (the well-known EGR index as we will see shortly) but also, in an attempt to gain additional knowledge, to uncover some of the factors/variables explaining that polarization. In doing so, to some extent and bearing in mind data availability problems at the municipal level, we go in line with the papers mentioned above on the determinants of the election outcome when it comes to selecting potential explanatory variables.
Finally, and this is likely the main contribution of the paper, we delve into what is called the ecological fallacy-namely, erroneous conclusions inferred from aggregated data on individual phenomena-and one of its main forms, the so-called Modifiable Areal Unit Problem (MAUP) effect. 3 This problem is usually present in any polarization analysis regardless of the variable at hand, whether it is income, welfare or, as in this occasion, independence sentiment. In that respect, we agree with Lepič 1 In any case, our approach could be adapted to any case study other than the Catalan one and to any electoral process. 2 There are several recent examples of political struggle featured by the existence of polarization, as the UK decision on the issue of leaving or remaining the EU (Zmigrod et al., 2018) and how the ever-closer fusion between self-and group identities spurred polarization between U.S. Democrats and Republicans (Mason, 2018). Focusing on our case study, a paper by Oller et al., (2019) has to be highlighted. 3 For a nice explanation, see Díaz-Dapena et al., (2016). (2017, p. 194) when, in a nice paper analysing the results of elections in Catalonia, he states that, "although the municipal spatial resolution minimizes the risk of MAUP, the risk of ecological fallacy, i.e., to infer from aggregated data about the explanation of individual-level phenomena, remains". The reason is that, for each municipality, data are taken for the "average person", which implies, in our case, that data are merged and, consequently, pro-and anti-independence feelings are offset each other. 4 .
The point is that, due precisely to our specific case study, the proposal presented in this paper will be able to show the relevance of this problem. Unlike, for instance, when referring to variables such as income, we have here more information than a single value for the "average person" living in each municipality. Specifically, as there is information on the number of voters supporting each party, we can divide the independence-feeling indicator into two (antiindependence-feeling and proindependence-feeling indicators) to partially avoid the aggregation problem and, consequently, to include in the analysis the existence of polarization within each municipality. Our strategy is then to test if, as expected, a relatively low polarization index between municipalities (when a single indicator is used) is masking the existence of a strong conflict between the citizens of each territory (two indicators per municipality). There may exist, in line with a study by Kinsella et al., (2021) for the U.S. case, a micro-scalar geographic political polarization. As it is obvious, from a social point of view this is an important point to clear up. If this were so, it would alert us, especially whether the problem becomes entrenched-namely, in case the independence issue is not finally solved in an adequate manner -, to the potential emergence of problems of coexistence among individuals, of social division and even, although not very likely in our view, of public order problems (such as street fights and rowdyism). As indicated by Oller et al., (2020, p. 2), "neighbours, colleagues and even friends and families who had shared feelings of belonging to both Catalonia and Spain (in different degrees) as a part of their attachments and values, are now divided on the issue of secession and must endure living together amid unsolved tension".
In summary, in this paper we want to test two main hypotheses. The first one has two different parts: H1a: Due to aggregation problems, the traditional use of the polarization index, with the independence-feeling indicator in this case, underrates the real conflict that exists in Catalonia since it does not pay any attention to intra-group polarization (within municipalities in our case).
H1b: Accordingly, the index of polarization when pro-independence and antiindependence feelings are differentiated within each municipality (i.e., considering two separate indicators to somehow sort out the aggregation problem) is much higher than when a single indicator is used.
As a result, because of the notable differences between the two approaches, which will be explained in detail below, the factors that explain polarization are expected to differ. Therefore, our second hypothesis reads as follows: H2: Factors that explain polarization depend largely on how the indicator of independence feeling is calculated, i.e., whether an aggregate indicator or two indicators measuring pro-and anti-dependence feelings are considered.
With all these considerations in mind, the remainder of this article is organised as follows. The next section presents data to compute the aforementioned independence-feeling indicators as well as our approach to measuring conflict. Subsequently, the paper deals with the results. Firstly, it assesses polarization in the single independence-feeling indicator between municipalities, and try to figure out some factors explaining it. Subsequently, it addresses the aggregation problem by computing two independence indicators (anti vs. pro) per municipality and the corresponding polarization measure; it then again attempts to weigh the importance of some potential explanatory factors. The last section summarises the main findings and opens future avenues of research.

Data and methodology
In this section, we are presenting, on the one hand, the independence-feeling indicators that are the basis of our study and, on the other hand, the polarization index we use to approximate the intensity of the conflict.

Independence-feeling indicators
As indicated in the Introduction, the paper uses, as a source of data, the outcome of the 27 December 2017 Catalonian Regional Election, at the municipal level. If we briefly look back over the previous events, it seems quite clear that this election can be considered, more than just another simple election, like the one in which, back stage, the key issue at stake was the independence of Catalonia. As everybody will recall, just a few months earlier, on October 1, the so-called Catalan Independence Referendum took place, also known by the numeronym 1-O (for '1 October') in Spanish media. Although that election was in theory legitimised by the Law on the Referendum on Self-determination of Catalonia, passed by the Catalonian Government ('Generalitat de Catalunya'), it was later declared illegal. Not only that, and in the face of fear of a secessionist movement, the Senate (Low Chamber) approved the use of Article 155 of the 1978 Constitution for the first time in Spain's history. As a result, the Catalan Parliament was dissolved, the Central Government took control of the regional institutions and new elections were immediately called on December 27. In short, we believe that this new Regional Election was mostly taken as a legal version of the previous one, that is, as a referendum on independence. A simple glance at the Spanish and world press at the time supports this idea. 5 An important question comes to mind here: Why election data rather than survey data? In our modest opinion, there are at least two main advantages of the former. On the one side, data are extracted for all municipalities in the region, regardless of their population, thereby preventing any bias problem since survey data are taken mainly from the inhabitants of the most populated areas. On the other, when employing electoral data the sample is complete, i.e., the electoral roll. An additional reason is that, lately, the accuracy of pre-election surveys has proven to be quite limited. 6 With that in mind and as we also mentioned, here we want to define, and then compute an independence-feeling indicator. To do so, the first impulse is to follow the flow. We refer to the fact that, as you can read in the media and scholarly journals, the most prominent feature of the election was the tight result between the group of proindependence parties (47.50% of the votes) and the one of non-independence parties (43.45%). Likely because of this, it has been recurrent in the literature when addressing this issue to simply distinguish two major groups of political parties in terms of independence, even though it is technically problematic since it puts all the political parties belonging to each group in the same basket. That is to say, it is not the same to vote for Esquerra Republicana de Catalunya-Cataluya Sí (ERC), Junts Per Catalunya (JxCat) or Candidatura d'Unitat Popular (CUP) within the pro-independence block, let alone to vote for Partido de los Socialistas de Cataluña (PSC), Ciudadanos (Cs) or Partido Popular de Cataluña (PPC) within the anti-independence one.
Consequently, our idea in defining the indicator is to weigh the feeling of independence of the voters of the seven main political parties (the previous six together with CatComú-Podem party (CatComú)) in the aforementioned election. Thus, to set the ranking score of parties, we pay attention to some remarkable questions (namely, which ask the respondents directly or indirectly to place parties in the pro-antiindependence scale) included in several surveys published by the Centre d'Estudis d'Opinió (CEO)-reference body in the field of public opinion studies of the 'Generalitat de Catalunya' -, as well as to Regional Parties Manifestos. Hence, accepting for simplicity the validity of the equal interval assumption, we have a range that goes from 'not at all pro-independence', with a value of 1, to 'extremely pro-independence', with a value of 7 ( Fig. 1). Within this range, it is generally accepted that the two extreme positions are PPC (complete opposed to independence, a value of 1 in our scale) and CUP (value of 7), while the middle, most neutral position is for CatComú, hence with a value of 4. In addition, it seems clear that among the nonindependence parties the Cs voters are more against autonomy than the PSC voters are, so these parties have a value of 2 and 3, respectively. The most debatable decision is regarding the pro-independence feeling of JxCat electorate in comparison with ERC one, but according to the CEO Barometers we believe it is a little higher in the first case (since the exclusively Catalonian identity is stronger), so JxCat is scaled inclusive movement, but from the call for a referendum centered on the slogan "the right to vote", everything changed. Not only from the point of view of independentism, but also the Catalan unionists became much more activist (Barrio & Field, 2018). The result was clear: many low-intensity clashes at the streets. Society began to clearly divide (that is, polarize) around a political issue. 6 At any event, we must admit that surveys can be a useful source of additional information on issues that could help explain polarization, such as elitism and partisanship. with 6 while ERC with 5. 7 Our independence-feeling indicator is then obtained by averaging scaled independence feelings of voters in each municipality.
As previously indicated, in the second part of this study the independence-feeling indicator is split into two indicators: the antiindependence-feeling and the proindependence-feeling indicators. It is done by using the same scale of values as shown in Fig. 1 but, obviously, only considering the political parties belonging to each group, plus 50% of the votes obtained by the CatComú-Podem party given its somewhat ambiguous position on independence. This being so, the first indicator goes from 1 to 4, while the second goes from 4 to 7.
With these considerations in mind, data for municipalities, extracted from the Catalonian Institute of Statistics (IDESCAT), allowed us to compute the three independence-feeling indicators, a summary of which is presented in Table 1 and, graphically, in Figs. 2, 3 and 4. Briefly, as these indicators are simply the base data we will use to assess the level of conflict, Fig. 2 shows that the coastal area of the region is, in general, less prone to independence than the other ones. Having said that, Figs. 3 and 4 provide additional information about pro-and anti-independence feelings, respectively. More specifically, these figures convey the idea that there are some municipalities located in the Centre and West of the region whose citizens keep quite extreme positions with respect to independence; these, of course, are compensated in the overall indicator.

EGR Polarization Index and Explained Polarization (EP) Index
As indicated, now we examine discrepancies in independence feelings by using a standard polarization measure. 8 Following Esteban et al., (2007), the so-called EGR index can be expressed, for our specific case study, as: where α is a parameter denoting the degree of sensibility of the index to polarization-by construction it takes on values between 1 and 1.6; v i and v j are the relative population sizes of groups i and j , in this case the relative number of voters; 9 IF I i and IF I j are the mean of the independence-feeling indicator of both groups; µ is the mean of this indicator in Catalonia; β is a parameter reflecting the sensitivity of the index to the groups' level of cohesion; G and G S are the Gini coefficients of the original and grouped distributions, respectively; and n is the number of poles considered.
7 In any case, it is arguable, being the results quite similar when changing it.
8 This kind of polarization measurement has been used for a range of topics as disparate as income (Ezcurra et al., 2005;Gorning & Goebel, 2018;Ricci & Scicchitano, 2021), migration (Hierro et al., 2012), pollution (Duro & Padilla, 2013), and so on. Two studies closer to the topic at hand are Oosterwaal and Torenvlied (2010) and Muller (2015). 9 Obviously, the importance of each group depends on its share of voters. To compute the EGR index you have to provide the value of the independence-feeling indicator of each municipality along with its number of voters. Several points have to be taken into account when computing this index. First, it is an extension of the polarization measure proposed by Esteban and Ray (1994). Specifically, EGR = ER − β , being ERriptivestatisticsf orindependen the original Esteban and Ray polarization measure, and the so-called specification error. In other words, as the computation of the polarization index always entails the split of the distribution in a set of exhaustive and mutually exclusive groups, involving some loss of information (some intra-group dispersion is to be expected), the EGR index corrects it with a measure of the grouping error .
Second, the approach requires setting the number of groups or poles beforehand; here, we only consider the bi-polarization index. The reason is twofold. On the one hand, and more importantly, because we are trying to assess the conflict between anti-and pro-independence groups; bi-polarization is hence the only relevant case in this context. On the other hand, since if following Duro and Padilla (2008), you pay attention to the share of cross-municipalities differences that is explained by the measure when it comes to making a decision, you see here that the increase when considering 3 or 4 groups is not quite remarkable. Accordingly, we are only dealing with the special case of bi-polarization, in which it is important to note, for the sake of clarity, that the benchmark between the two groups coincides with the mean value of the distribution. 10 Third, we have also to agree on the values of α and β . Regarding α , the lack of consensus on this issue inclines us to choose several, namely 0.5, 1.0 and 1.5; as we will see, although by definition the value of the index decreases when α increases, the interpretation regarding the degree of polarization is roughly the same in all cases. As for β , the situation is different since there is a general agreement indicating that this parameter has to be close to 1, so we go with the flow and pick this value. Fourth, the EGR polarization index is not bounded, which is probably its biggest drawback. For this reason, in line with what has been done by Maza et al., (2010) for a different topic (a new mobility measure for transition matrices to be precise), we perform some simulations to be able to properly interpret the values obtained. Specifically, to get a reference value representing a high degree of bi-polarization, we divide municipalities so that approximately half of the voters are located in municipalities in which the mean independence-feeling indicator is set at 2, and half is in those with a value of 6. 11 We carry out several simulations-i.e. changing the municipalities belonging to each group-and values are always around 0.35 (when α = 0.5 ), 0.25 (α = 1) and 0.18 (α = 1.5). Therefore, these values are our benchmarks to assess the degree of polarization.
Finally, intending to study this question in more detail, our aim now is to try to explain polarization. Following the proposal presented by Gradín (2000), we are interested in assessing to what extent some variables can explain the already computed degree of bi-polarization. Specifically, the analysis is based on different partitions of the Catalonian municipalities, according to criteria other than the independence feeling. Once these groups are made up, the EGR polarization index is once again calculated. The idea is, then, quite simple: by comparing the two polarization indexes, you can proxy the explanatory power of the variable you used for the alternative partition of the distribution. For the sake of simplicity, due to the robustness of previous results, it is only done when α = 1. As indicated by Gradín (2000), in this case you simply have to compute the ratio between the Gini coefficient for each new partition (G E ) and the one for the original distribution (G ). Consequently, the explained polarization (EP ) measure reads as: 3 Results

A single independence-feeling indicator
Moving on to the results, Table 2 (EGR index and its components) and 3 (shares of voters and mean values) display the calculations obtained when the global independence-feeling indicator is taken. As can be seen, the polarization index is, compared to our benchmark values, quite low regardless of the value of α . That is to say, the degree of conflict between municipalities seems to be very small. This is a conclusion that fits with the hypothesis that the polarization index underestimates the real conflicting existing in Catalonia (H1a); in any case, we will qualify it in the next sub-11 This decision is, of course, debatable. We did not choose extreme values (1 and 7) as this situation turns out to be impossible in practice, so it is not a good reference to compare with. section. As for the share of voters and mean value of each group, we can see the first group comprises 64% of total votes, with 92% of the average independence feeling in Catalonia, while the remaining 36% of voters are included in the second group, with 113% of the mean independence sentiment. Now it is time to try to explain polarization by applying Eq. (2). In particular, according to the results obtained in previous papers mentioned in the Introduction and, mainly, to data constraints at the municipal level (data coming in all cases from IDESCAT), 12 we consider six potential explanatory variables. (1) Knowledge of the Catalan language, since "language became the core value for Catalan nationalism" (Serrano & Bonillo, 2017, p. 374). As also indicated by Aramburu (2020), from 2017 it seems that the discourse on the irrelevance of an ethnic divide between Catalan and Spanish speakers began to change. In the same vein, Oller et al. (2019, p. 3) state that "This is mandatory since previous findings either from survey data or from electoral results had established the priority of this ethnolinguistic cleavage rooted on ascendancy origins". Concerning the definition of the variable, we use the level of spoken language ability. (2) Place of birth. Specifically, we employ a variable capturing the share of the population that was born in Catalonia; alternatively, we could have employed the share of population born in the rest of Spain (Serrano & Bonillo, 2017), but the explanatory power of the former was greater than that of the latter. 13 (3) Age. Explicitly, a youth ratio, defined as the share of people between 15 and 29 years old. (4) Average pension (euros per month). Used as a proxy for wealth or per capita income disparities, due to the unavailability of these variables at the municipal level. 14 There is no doubt that this decision is questionable, since pension systems have a redistributive component that leads to territorial redistribution in the presence of territorial inequalities, which undeniably skews disparities downwards. In any case, to check the appropriateness of our choice, and given that average income data are available by county (the 947 municipalities that make up Catalonia are grouped into 12 Data for the place of birth, population density and unemployment rate refer to 2017. For age and pension, data correspond to 2016. Finally, for the knowledge of the Catalan language, data refer to 2011, as there are no more recent data since they come from the population census. All data come from IDESCAT's municipal files. 13 In any case, as indicated by Serrano (2013), the gap between Catalans and immigrants is becoming narrower over time. A very interesting article published on this topic, which lists and details several of the reasons behind this phenomenon, is Conversi and Jeram (2017). 14 It is commonly accepted the link between economic inequality and polarization (see e.g. Ippolito & Cicatiello, 2019). 42 counties), we approximated the average pension data by county from the municipal data and calculated the correlation coefficient between the two series. This correlation was very high (0.82), which makes it clear that the use of pension data achieves the objective set. (5) Unemployment rate. The variable we employ is, actually, a proxy of the unemployment rate computed as the ratio between unemployed people and working-age population (there is no data on active population for municipalities).
(6) Population density. Defined as population divided by land area, it is a commonly used indicator to characterize a municipality as mainly urban or mainly rural. Before dealing with the results, Table 4 shows some descriptive statistics-mean, maximum, minimum, and coefficient of variation-of the variables employed to explain polarization through Eq. (2). As can be observed, disparities (last column) are salient in population density, as was to be expected due to the existence of markedly urban areas alongside essentially rural ones. With regard to the rest of variables, the situation of the labour market (captured by the unemployment rate) also differs notably according to the municipality while, although to a lesser extent, something similar occurs with age. As for the Knowledge of the Catalan language and the birthplace (Catalonia or outside Catalonia), municipal differences, although still very significant, are not so apparent.
Subsequently, Table 5 reports the results. Population density, the knowledge of the Catalan language and the place of birth emerge as the main factors explaining municipal bi-polarization (80%, 74%, and 67% of it, respectively). Although to a lesser extent, wealth and the unemployment rate seem also to play a significant role, while age appears to have very limited influence when explaining the origin of bipolarization. In addition, paying attention to the relative mean values of each group (last columns of the table), it is quite clear that the level of Catalan proficiency and having been born in Catalonia are factors that promote the independence sentiment, while population density, wealth and the unemployment rate are hindering it. As for age, it is quite balanced, although marginally against independence.

Dealing with the aggregation problem: Two independence-feeling indicators
As mentioned above, now we want to test our hypothesis H1b. In other words, we believe the low value of the EGR polarization index when using single data at the municipal level is due to an aggregation problem. As it is obvious, and we provided some information on this issue above, there are people for and against independence within each municipality, and they partially compensate each other when computing the independence-feeling indicator. To make this absolutely clear, let us imagine that within each territory the portion of people pro-and anti-independence is 50%, and not only that but with the same composition by political parties (remember the construction of the indicator and its advantages over considering only the share of pro-independence votes); in an extreme situation, for the sake of understanding, 50% of people voting for PPC and 50% voting for CUP. If this were the situation, the value of the independence-feeling indicator would be the same in all municipalities and, thus, the degree of polarization would be 0. Needless to say, this result would be masking the existence of a huge degree of polarization within each municipality. This is indeed a common problem when computing polarization, regardless of the issue at hand. The good point here is that, as has been indicated, in our case study we can solve the problem, at least partially. What, then, is the difference between assessing polarization in voting behaviour or, shall we say, income polarization? The difference is that, when computing income polarization, you only have information on the average per capita income of people living in each territory. When studying elections, however, we take advantage of the greater availability of election data compared to other types of data (Charney & Malkinson, 2015); more specifically, we have the number of votes each party got. In other words, we have additional information that can be used, as shown above, to compute the proindependence-feeling and antiindependence-feeling indicators. By doing this, we believe we are going to get a much better proxy of polarization in Catalonia, as we are including both intra-e inter-polarization (inside and between municipalities). 15 Obviously, for each group within a municipality, we use, as its share in the computation of the polarization index, the number of people voting accordingly.
Hence, we now re-calculate the EGR index but with two indicators per municipality. The results are shown in Table 6, being now the index much higher than before, which confirms our hypothesis H1b. In fact, according to the simulations we explained above, we can state that the degree of polarization, of conflict, is quite remarkable. More specifically, the index is, regardless of the value of α , around 80% of the polarization that would exist in the hypothetical case where half of the voters had an independence-feeling indicator of 2 and the other half had an indepen-dence-feeling indicator of 6. The conclusion is clear: the ecological fallacy problem is instrumental when measuring polarization. In fact, due to aggregation, most of it vanishes, is not observed. That is to say, polarization within the municipalities is quite large.
As regards the shares and group means, Table 7 reports notable differences from Table 3. As can be seen, 48% of voters belong to the first group, with a rather weak sentiment of independence, since it only accounts for 59% of the Catalonian mean, while 52% of voters belong to the second one, with rather strong support for independence (138% of the mean).
Here, there is a point left: namely, to test the second hypothesis (H2), which deals with the factors that explain polarization and the existence, or not, of significant differences between our two approaches. However, in explaining the degree of polarization, the situation now, with two indicators per municipality, turns out to be more complicated. The hindrance is that, for the six potential explanatory variables we used before, we only have the municipal mean value. That is to say, there is a clear mismatch: two independence-feeling indicators but only one value for each variable. To solve it, our proposal is the following. We again split the municipalities into two groups (below and above the mean) for each one of the explanatory variables, and now we choose for those included in each group the indicator (antiindependence-feeling or proindependence-feeling) that is in line with the aggregate results we obtained in the previous section. As a way of illustration, for the level of Catalan proficiency, we saw there is a direct relationship between this indicator and the independence feeling; accordingly, for the group of municipalities with a knowledge rate below the mean, we take the antiindependence-feeling indicator, while for those above the mean we take the proindependence-feeling one. By doing this, we believe that a relatively good approximation to the explained polarization can be obtained. Table 8 presents the main results. First, it is important to stress that the explanatory power of all variables is quite high. Second, we can see that the unemployment rate and age seem to be the variables that affect polarization largely (more than 80% of polarization is explained), followed not far behind by wealth, knowledge of the Cata- lan language and place of birth (over 75%). Surprisingly, population density, used as a proxy for the urban-rural division, is in the last position of the ranking, although with a non-negligible at all 62%. Finally, when you take jointly and compare the results in Table 5 (a single independence-feeling indicator) and Table 8 (two indicators), some conclusions can be drawn. On the one hand, variables such as Catalan proficiency and place of birth are quite relevant no matter the case; these results are in line with those obtained by Miley and Garvía (2019, p. 24) when stating that "it remains impossible to understand the dynamics of the current secessionist surge, and especially the limits to its appeal, without paying close attention to the long latent, now ever more salient, ethno-linguistic cleavage inside Catalan society". On the other hand, when computing two indicators for municipality variables such as age, the situation in the labour market and wealth become quite important; tentatively, perhaps their effect was to a great extent vanished by the aggregation problem. Furthermore, population density is, on the contrary, more significant when computing a single indicator; this last result is probably largely due to the case of the most populated municipality, Barcelona, which is also the most urban municipality in the region, full of densely populated areas whose residents are not particularly prone to independence. In short, and with respect to our second hypothesis, its validity seems clear: there are significant differences in the explanatory power of the selected variables depending on the approach used.

Discussion and conclusion
This paper aims at analysing the level of discrepancy, of conflict regarding independence in Catalonia. It attempts to provide new insights into this research gap by computing a new indicator of independence feeling that takes into account, at least partially, the differences between political parties in terms of independence. Subsequently, the polarization measure proposed by Esteban et al. (2007) is used, along with the explained polarization suggested by Gradín (2000). Apart from the above, the main contribution of this paper lies in the treatment of the MAUP effect that results from using averaged or aggregated data. It demonstrates that at least when dealing with voting behaviour, this effect notoriously arises, masking a great share of the degree of polarization that effectively exists. Specifically, our findings show that when computing the EGR polarization measure in the standard way, that is, by using an aggregate indicator for each municipality, the level of polarization is quite low. Conversely, when two independence-feeling indicators per municipality are computed-by splitting votes for anti-and pro-independence parties -, the level of polarization turns out to be really high. Therefore, the general conclusion that we come to is that there is an important conflict in Catalonia concerning the sovereignty process, but it is especially prominent between individuals rather than between artificial administrative boundaries such as municipalities.
As for the variables behind polarization, apart from the existence of differences between the two cases analysed, the relevance of the knowledge of the Catalan language and place of birth is unquestionable both in explaining the polarization when one and two independence-feeling indicators are computed. Additionally, population density is especially significant in the first case (single indicator), while unemployment rate and age are particularly important when the problem of aggregation is coped with.
It is important to point out that our results are somewhat linked to those of previous papers. For instance, dealing with polarization, Esteban and Ray (2008) indicate that the existence of unsealed ethnocultural cleavages is to be understood as a prerequisite for the emergence of deep polarization and partisan alignment in neighbouring areas. Concerning this point, we should be mindful of Miley's (2007) warning about the existence in Catalonia of divergent national identifications linked to an ethnolinguistic boundary even before the secessionist wave. Over the last decade, the importance of ethnic identity has undoubtedly increased, as the growing defence of Catalan identity, largely centred on the defence of the Catalan language, has been counterbalanced by a reinforcement of Spanish identity on the part of citizens who are not in favour of independence, in many cases with a family background from the rest of Spain.
Concerning the factors that explain polarization, and following the suggestion of a reviewer, we completed the analysis by examining which of them are also decisive in explaining the difference in the preferences of the two opposing groups of voters. The results of a regression exercise, admittedly quite simple and taken with caution, tend to confirm that the knowledge of the Catalan language, together with being born in the region, are the main determinants in explaining support for independence. Consequently, we reaffirm what was indicated in the previous paragraph, as the importance of ethnocultural and ethnolinguistic issues is once again confirmed. On the contrary, population density and the unemployment rate seem to emerge as anti-independence factors. Therefore, the results seem to indicate that the higher the level of urbanisation of the municipality in which you live, the lower the support for independence. If this relationship is confirmed, a very tentative explanation could be that the urban working classes in large cities, in many cases with migrant roots, may be more open to political and social influences from outside Catalonia. About the unemployment rate, our findings convey the idea that the municipalities with the highest unemployment levels do not have a markedly pro-independence character. That is to say, it seems that their citizens, rather than blaming the nation for their precarious labour market situation, fear that independence could provoke a fall in economic activity and the consequent layoffs. Linked to this result may also be the fear of the boycott of Catalan products that, even according to reports from the 'Generalitat de Catalunya', could occur, in addition to the flight of companies from the region and the potential reduction of FDI flows. In any case, a more in-depth analysis, beyond the scope of this study, would be required to confirm and/or qualify these insights.
Be that as it may, and focusing once again our attention on the level of polarization rather than on its determining factors, the findings of this study admit at least two different interpretations. The good view is that, although various theories reveal that political polarisation and linguistic fractionalisation can pose a serious threat to good governance and growth (Alesina et al., 2003), the far-reaching/high-scale political conflict in Catalonia about independence is not so notable on a medium scale level, i.e. between municipalities. Our appraisal is that when it comes to adopting common policies between them-regarding, for instance, telecommunications, tourism attraction and so on-these should be implemented without much trouble, since municipal governments, in line with the mean independence-feeling indicator, are not mostly made up of political parties with extreme positions. Hopefully, provided politicians live up to expectations, the German proverb that says, "when one helps another, both are strong" is applied in developing joint strategic plans and allocating resources efficiently. 16 This first positive interpretation has therefore implications from the point of view of territorial governance since, in this way, a strengthening of the horizontal dimension of the so-called multilevel governance approach would be achieved. This is because it focuses on the importance of designing joint policies at the municipal level, that is, on the search for cooperation agreements between municipalities. In other words, it refers to the need for local governments to be somewhat immersed in territorially overarching policy networks. If progress is made in this direction and these agreements are increasingly common, the region would attain, on the one hand, greater trust in public institutions, on the other hand, more efficiency in the provision of local public services and, additionally, a boost to economic activity that would lie in the elaboration of development strategies among municipalities that can exploit synergies and complementarities between them.
However, a negative reading of our findings refers to the existence of important discrepancies on a low-scale level (between individuals); therefore, to social conflict. For example, demonstrations in favour of and against self-determination and independence that happened in the past when a new election was approaching may even become increasingly frequent if the independence issue is not properly solved. A highly divided society across a host of political issues centred on regional sovereignty demands and with no accommodation in sight is the seed of heightened internal conflict, as a number of empirical studies have shown (for references, see e.g. Hegre, 2008).
Between these two interpretations, while conceding the importance of joint policies at the municipal level as signalled above, the second, the negative one undoubtedly prevails. Although the political option of fostering constructive and inclusive dialogue between population groups with different political sentiments might be one possible, if not the only, way to reduce social conflict (Carling, 2008), the chances of success are apparently low. In this respect, it is not only the responsibility of the Government of Catalonia, but also of the Spanish Government, to soften the discourse and, in this way, reduce tensions between pro-independence and non-independence supporters. To achieve it, and this should be the objective, politicians should, at the very least, avoid the continuous, in some cases even forced and almost always harmful, references in their speeches to the conflict over the independence of Catalonia. On the basis of game theory, they should adopt collaborative practices, not only to reduce the conflict but also to achieve an intermediate solution that would surely be more beneficial than continuing the power struggle. 17 Finally, this paper opens future lines of research. On the one side, to use a completely individual data set, which should be representative enough (not focused on residents of a few municipalities) and include reliable information not only on cast ballots but also on the additional variables needed to complete the analysis. Unfortunately, although there are some really good attempts in the literature, these data are usually rather inaccurate. As indicated by Maza et al., (2019), the existence of substantial differences between the expected outcome according to pre-election polls and the real outcome of the election provides a piece of evidence regarding this point. On the other side, to give a geographical component to the polarization measure, as conflict also depends on the location of the corresponding municipalities. When adopting joint policies, for example, this fact becomes, obviously, quite important.
Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.
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