Limitations of spatial models of voting: Difference between revisions

[[Spatial model of voting|Spatial models]] are ubiquitous in theoretical study and simulations of voting methods. In this model of agent behavior, agents (e.g. voters, candidates) are placed in an abstract geometric space, usually Euclidean, in which each dimension denotes some ideological alignment or opinion on an issue. The behavior of agents is modeled by how "close" (under some appropriate metric) they are to other agents in this space. In the context of voting, voters are modelled as ranking candidates depending on their proximity to each candidate within this space.

However, the number of dimensions chosen for this geometric embedding imposes fundamental restrictions on the allowed number of candidates which may be effectively distinguished by the voters using ballots, as there is only a finite number of regions possible for each possible ranking assignment of candidates.

The following article discusses this limitation and some implications. The specific numerical results below assume an Euclidean space and Euclidean distances, but similar qualitative arguments apply to any spatial model and chosen metric.