Size: b.; Раиса Александровна познакомить с аббревиатурами английского языка, через. и права зарубежных стран ; как как делать сравнительную. Мобільні та зв'язок. Офіс та канцелярія. Спорт та активний відпочинок. Как выбрать мандарины, чтобы они были безопасными для вашего здоровья и при этом вкусными. Інтегрований курс «Література (російська та світова)» Надозірна Т. В., Полулях Н. С.
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We study in details the turnout rate statistics for 77 elections in 11 different countries. We show that the empirical results established in a previous paper for French elections appear to hold much more generally. We find in particular that the spatial correlation of turnout rates decay logarithmically with distance in all cases. This result is quantitatively reproduced by a decision model that assumes that each voter makes his mind as a result of three influence terms: one totally idiosyncratic component, one city-specific term with short-ranged fluctuations in space, and one long-ranged correlated field which propagates diffusively in space.
A detailed analysis reveals several interesting features: for example, different countries have different degrees of local heterogeneities and seem to be characterized by a different propensity for individuals to conform to the cultural norm. We furthermore find clear signs of herding i.
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Empirical studies and models of election statistics is a classical field of Political Economy  — . This subject has attracted considerable attention in the recent physics literature, see e. In  , the present authors have studied the statistical regularities of the electoral turnout rates, based on spatially resolved data from 13 French elections since Two striking features emerged from our analysis: first, the distribution of the logarithmic turnout rate defined precisely below was found to be remarkably stable over all elections, up to an election dependent shift.
Second, the spatial correlations of was found to be well approximated by an affine function of the logarithm of the distance between two cities. The cultural field itself can be decomposed into an idiosyncratic part, with short range correlations, and a slow, long-range part that results from the diffusion of opinions and habits from one city to its close-by neighbours. We showed in particular that this local propagation of cultural biases generates, at equilibrium, the logarithmic decay of spatial correlations that is observed empirically .
The aim of the present note is to provide additional support to these rather strong statements, using a much larger set of elections from different countries in the world.
We discuss in more depth the approximate universality of the distribution of turnout rates, and show that some systematic effects in fact exist, related in particular, to the size of the cities. We also confirm that the logarithmic decay of the spatial correlations approximately holds for all countries and all elections, with parameters compatible with our diffusive field model.
The relative importance of the idiosyncratic, city dependent contribution and of the slow diffusive part is however found to be strongly dependent on countries. We also confirm the universality of the logarithmic turnout rate for different elections, for different regions or for different cities, provided the mean and the width of the distribution is allowed to depend on the city size.
Overall, our empirical analysis provides further support to the binary logit model of decision making, with a space dependent mean the cultural field mentioned above. We have analysed the turnout rate at the scale of municipalities for 77 elections, from 11 different countries.
For some countries, the number of different elections is substantial: 22 from France Fr, municipalities in mainland France , 13 from Austria At, municipalities , 11 from Poland Pl, municipalities , 7 from Germany Ge, municipalities , while for others we have less samples: 5 from Canada Ca, municipalities , 4 from Spain Sp, municipalities in mainland Spain , 4 from Italy It, municipalities in mainland Italy , 4 from Romania Ro, municipalities , 3 from Mexico Mx, municipalities , 3 from Switzerland CH, municipalities and 1 from Czech Republic Cz, municipalities.
More details on the nature of these elections and some specific issues are given in Appendix S1. For each municipality and each election, the data files give the total number of registered voters and the number of actual voters , from which one obtains the usual turnout rate.
For reasons that will become clear, we will instead consider in the following the logarithmic turnout rate LTR , defined as: 1 Because we know the geographical location of each city, the knowledge of for each city enables us to create a map of the field and study its spatial correlations. Whereas the average turnout rate is quite strongly dependent on the election both on time and on the type of election — local, presidential, referendum, etc.
The notation means a flat average over all cities, i. The LTR standard-deviation, skewness and kurtosis were found to be very similar between different elections. We have extended this analysis to the 9 new election data in France, and to all new countries mentioned above.
For France, the Elections Municipales election of the city mayor , not considered in  , have a distinctly larger standard deviation than national elections.
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These happen to be coupled with other local elections in half municipalities, which clearly introduces a bias. The distributions for all elections in France are shown in Fig. The distribution is clearly non Gaussian, with a positive skewness equal to and a kurtosis equal. A more precise analysis consists in computing the KS distances between each pair of elections.
We recall here that a KS distance of corresponds to a probability that the two tested distribution coincide, while corresponds to a probability.
These numbers are slightly too large to ascertain that the distributions are exactly the same since in that case the average should be equal to. On the other hand, these distances are not large either as visually clear from Fig.
We will explain below a possible origin for these differences. A standardized Gaussian is also shown.
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The inset similarly shows the probability distribution of the usual turnout rate. We use the same symbols and color codes for the French elections throughout this paper. The same analysis can be done for all countries separately; as for France, we find that for different elections are all similar, except for Germany for which — see Table 1 , where we show the mean and the standard-deviation of KS distances between elections of a given country, and of the skewness and kurtosis of the distributions in a given country.
Note that the values of are close to for Italy and Poland.
On the other hand, these distributions is clearly found not to be identical across different countries. Compatible elections have roughly the same distribution , i. They are chosen as follows: for Canada and Poland all elections; for France all pure national elections nor combined with local elections, i.
In order to understand better these results, one should first realize that the statistics of the LTR does in fact strongly depend on the size of the cities. This was already pointed out in  , .
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For example, the average LTR for all cities of size within a certain interval , that we denote as , is distinctly dependent, see Fig.
S1 in Appendix S1. In most cases, the average turnout rate is large in small cities and declines in larger cities, with notable exceptions: for example, the trend is completely reversed in Poland, with more complicated patterns for parliament elections in Italy or Germany. Similarly, the standard-deviation of , , also depends quite strongly on see below Figs. S2 in Appendix S1. These quantities are obtained as averages over bins with for France municipalities of size.
See Fig. Each point comes from around communes of size. Dashed line: as extracted from the spatial correlations of cf. The exponent in is here equal to for all countries in order to take into account each country in the same way. These quantities are obtained as averages over bins with municipalities of size. The dashed line corresponds to as extracted from the spatial correlations of cf. For election labels, see Figs. However, the distribution of the rescaled variable over all cities of size for each election can be considered to be identical from a KS point of view, both within the same country for different but now also across different countries, at least when is large enough arguments will be provided below to understand why this should be expected.
For example, the average KS distance between distributions corresponding to different ranges of in France is equal to , with standard-deviation. These numbers are respectively , and for Italy, Spain and Germany. We have excluded the smallest cities, , that have a distinctly larger KS distance with other cities — see below.
Bins, ranked according to the municipality size contain each around municipalities.
In Table 3 , we show for different bins of values the mean and standard-deviation KS distance between countries, illustrating that all distributions are statistically compatible, at least when is large enough. Now, even if was really universal and equal to , would still reflect the country-specific and possibly election-specific shapes of and , and the country-specific distribution of city sizes,.
Indeed, one has: 3 which has no reason whatsoever to be country independent. But since for a given country the dependence on of and tends to change only weakly in time, the approximate universality of for a given country follows from that of.
In fact, French national elections can be grouped into two families, such that the dependence of on is the same within each family but markedly different for the two families see next section and Fig.
Restricting the KS tests to pairs within each families now leads to an average KS distance for of with a standard deviation identical for the two families , substantially smaller than from Table 1. This goes to show that the election specific shape of is indeed partly responsible for the weak non-universality of within a given country. Three families of elections clearly appear. Each point comes from the average over around communes of size.
Zooming in now on details, we give in Table 4 the KS distance between aggregated over all elections of a country and a normalized Gaussian, for different ranges of and different countries. The skewness and kurtosis of the distribution and the KS distance to a Gaussian, aggregated over all , are given in Table 5 for different countries, and aggregated over countries for fixed in Table 6.
Two features emerge from these Tables:. In order to delve deeper into the meaning of the above results, we need a theoretical framework.
In  , we proposed to extend the classical theory of choice to account for spatial heterogeneities.
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A registered voter makes the decision to vote or not on a given election. We can view this binary decision as resulting from a continuous and unbounded variable that we called intention or propensity to vote.
The final decision depends on the comparison between and a threshold value : when , and otherwise. In  , the intention of an agent at time who lives in a city , located in the vicinity of , was decomposed as: 4 where is the instantaneous and idiosyncratic contribution to the intention that is specific to voter , and and are fields that locally bias the decision of agents living in the same area.
The first field is assumed to be smooth i. The second field , on the other hand, is city- and election-specific, and by assumption has small inter-city correlations. It reflects all the elements in the intention that depend on the city: its size, the personality of its mayor, the specific importance of the election that might depend on the socio-economic background of its inhabitants, as well as the fraction of them who recently settled in the city, etc.
See  for a more thorough discussion of Eq. Consider now agents living in the same city, i. The turnout rate is by definition: 5 For sufficiently large, and if the agents make independent decisions , the Central Limit Theorem tells us that: 6 where is the probability that the conviction of the voter is strong enough, and is a standardized Gaussian noise. Therefore we will write more generally:.
Therefore, in this model, the statistics of directly reflects that of the cultural and idiosyncratic fields. Let us work out some consequences of the above decomposition, and how they relate to the above empirical findings.
Since the cultural field is by definition not attached to a particular city, it is reasonable to assume that and are uncorrelated. Without loss of generality, one can furthermore set. Therefore: 10 Two extreme scenarios can explain the dependence of : one is that the dispersion term is strongly dependent while the statistics of is independent, the other is that is essentially constant and reflects an intrinsic dispersion common to all voters in a population, while the average of the city-dependent field depends strongly on the size of the city.
Of course, all intermediate scenarios are in principle possible too, but the data is not precise enough to hone in the precise relative contribution of the two effects. Here, we want to argue that the dependence of on is likely to be dominant.