A Modern Approach to Electoral Delimitation using the Quadtree Data Structure

Abstract: The boundaries of electoral constituencies for assembly and parliamentary seats are drafted using a process referred to as delimitation, which ensures fair and equal representation of all citizens. The current delimitation exercise suffers from a number of drawbacks viz. inefficiency, gerrymandering and an uneven seat-to-population ratio, owing to existing legal and constitutional dictates. The existing methods allocate seats to every state but remain silent about their actual shape and location within the state. The main purpose of this research is to study and analyse the performance of existing delimitation algorithms and further propose a potential solution, along with its merits, that involves using a computational model based on the quadtree data structure to automate the districting process by optimizing objective population criteria. The paper presents an approach to electoral delimitation using the quadtree data structure, which is used to partition a two-dimensional geographical space by recursively subdividing it into four quadrants or regions on the basis of population as a parameter value associated with the node. The quadtree makes use of a quadrant schema of the geographical space for representing constituencies, which not only keeps count of the allocated constituencies but also holds their location-specific information. The performance of the proposed algorithm is analysed and evaluated against existing techniques and proves to be an efficient solution in terms of algorithmic complexity and boundary visualisation to the process of political districting.