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Many democratic countries use district-based elections where there is a"seat" for each district in the governing body. In each district, the partywhose candidate gets the maximum number of votes wins the corresponding seat.The result of the election is decided based on the number of seats won by thedifferent parties. The electors (voters) can cast their votes only in thedistrict of their residence. Thus, locations of the electors and boundaries ofthe districts may severely affect the election result even if the proportion ofpopular support (number of electors) of different parties remains unchanged.This has led to significant amount of research on whether the districts may beredrawn or electors may be moved to maximize seats for a particular party. Inthis paper, we frame the spatial distribution of electors in a probabilisticsetting, and explore different models to capture the intra-districtpolarization of electors in favour of a party, or the spatial concentration ofsupporters of different parties. Our models are inspired by elections in India,where supporters of different parties tend to be concentrated in certaindistricts. We show with extensive simulations that our model can capturedifferent statistical properties of real elections held in India. We frameparameter estimation problems to fit our models to the observed electionresults. Since analytical calculation of the likelihood functions areinfeasible for our complex models, we use Likelihood-free Inference methodsunder the Approximate Bayesian Computation framework. Since this approach ishighly time-consuming, we explore how supervised regression using LogisticRegression or Deep Neural Networks can be used to speed it up. We also explorehow the election results can change by varying the spatial distributions of thevoters, even when the proportions of popular support of the parties remainconstant.

Electoral David vs Goliath: How does the Spatial Concentration of Electors affect District-based Elections?