Preference regions and their probabilities based on a rectangular grid

In this article we consider a town in which the thoroughfares are laid out in a rectangular grid. Using the l₁ metric, we determine the Dirichlet regions for competitive convenience stores. Under the assumption of normality, we exemplify a technique for calculating the probability of the Dirichlet region associated with each convenience store. This method is generalized to the case where intersecting thoroughfares are oblique. Finally the example is used to illustrate the calculation of posterior Pitman's measure of closeness for various Bayesian estimators.