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Stylized facts appear in electoral processes worldwide, from Brazil to India. Here, we update a statistics carried on in Mexican elections but considering the inhomogeneities in electoral districts through the Nominal List (NL) (the list of valid electors in a given decision process) for the last three presidential elections. We find that the NL distribution at polling station detail is composed of, at least, three windows with a step function structure. Next, we study the consequences of the windows structure for the statistical properties of the processes. We obtain that the asymmetric vote distribution by polling station recovers a Gaussian shape for two of the windows; meanwhile, the standardized distribution of votes follows a distorted Gaussian, near to a skew normal. The distribution of the turnout at each polling station or voters’ participation ratio is close to a skew normal one in the bulk and failing at the wings. The average of voters increases in a linear way with the Nominal List and depends on the window considered. The results do not depend on the municipality, political district or urban versus nonurban distinction, and the electoral process considered.

frontiers in applied mathematics and statistics

Geopolitical Inhomogeneities in the Registered Voters’ Distribution and Their Influence in the Voters’ Participation Ratio Distribution: The Mexican Case