A toolbox for the choice of indicator classes for ranking of watersheds

There has been considerable work on determining a suitable method to accomplish a satisfactory ordering of a group of objects, when there are multiple evaluation criteria. A weighted index can be used to combine the opinion of all stakeholders to obtain a criterion for ranking the objects. Data from 21 watersheds of the Atlantic Slope Consortium (ASC) has been examined with the goal of determining an accurate ranking by overall watershed condition. In particular, there are three groups of indicators that range from Level I to Level III, increasing in the quality and accuracy of the data as well as the cost and effort needed to obtain the data. Due to the high cost, Level III data is available only for six watersheds; however the interest is in ranking all 21 watersheds. The investigators using their expertise have developed indices for the Level I and Level II indicators, and we would like to determine if those indices are effective in ranking the watershed condition. In addition, we introduce a method of selecting effective weights using POSAC (Partial Order Scalogram Analysis), which gives us insight for improving the weights already selected by the stakeholders. We also use elements of poset (Partial order set) theory as a foundation for our analysis. The Poset linear extension method can be used to find rankings without using an index, relying only on pairwise comparisons of the objects.