Geographic expected utility model and application to risk assessment

In the field of land management, it is usual to have a geographic map, representing a region under study, and divided into geographic units. Each unit is assessed on an ordinal scale describing its degree of suitability for some usage, for instance housing, or its state of degradation with respect to sustainable development criteria. We call such a map a decisional map. After a while, and for example, after the application of some policies aiming at improving the situation, the state of the units has evolved. For some units, the state has improved, and for some others, it has deteriorated. What we want to know is whether the global state of the map has improved or not. So, we have developed several formal models to help a decision maker to express his preference over maps. One of them is based on an expected utility function and is able to take into account some geographic aspects such as the proximity to habitations, roads or watercourses. We provide axioms under which the decision maker's preference can be represented by this model. We also illustrate an elicitation process used to determine the model's parameters on a real-world example, which is the risk assessment of an industrial project.