Electoral systems exhibit macroscopic regularities that can be analyzed using macroecology. We propose a direct analogy between elections and ecology: political parties act as species, votes as their abundances, and polling stations as communities. In microbial ecosystems several macroecological laws have been described. These include the abundance fluctuation distribution (AFD) following a gamma distribution, Taylor's law relating variance and mean abundance with a scaling exponent of 2, and the mean abundance distribution (MAD) following a log-normal distribution. These laws are captured by the stochastic logistic model, while the inclusion of interactions in the stochastic generalized Lotka-Volterra model has been shown to reproduce those laws and also capture the pairwise correlations of abundances.
This master thesis investigates the macroecological laws governing the Spanish congressional elections (1982--2023) through the framework of statistical mechanics and population dynamics. By analyzing empirical electoral data, we evaluate the AFD, Taylor's law, and the MAD, finding similarities and deviations compared to microbial ecosystems. The AFD depends on the mean abundance of the parties with shapes similar to gamma or log-normal distributions, and the Taylor scaling exponent fluctuates around 1.33, and the MAD is well represented by a logit-normal distribution. We also observe that the distribution of party-party Pearson correlation coefficients is symmetric and heavy-tailed.
Traditional unconstrained ecological models fail to capture the finite-size restrictions of electoral environments. To address this, we formulate a series of models. First, we introduce the constrained stochastic logistic model (CSLM) by establishing the abstention variable as a compositional sink, ensuring the conservation of the electoral simplex. The CSLM captures the AFD of large parties, but produces a Taylor exponent of 2. Next, we implement a discrete multinomial sampling phase to account for the demographic noise inherent to finite polling stations. This approach reduces the Taylor exponent to empirical ranges ($b \approx 1.6$), reproduces the AFD for all parties, and predicts the emergence of a logit-normal distribution for the MAD. Finally, to reconstruct the symmetric, heavy-tailed empirical correlation distributions, we expand the framework to a constrained stochastic Lotka-Volterra model (CSLVM) by adding sparse stochastic party-party interactions. This work lays the groundwork for an ecological theory of voting.