The impact matrix approach and decision rules to enhance index dimensionality, flexibility and representation

Many people use environmental indices to track and understand ecosystems. Indices make it possible to compare two or more complex, multifaceted systems at one time by reducing information about each system into a single number or diagram. Paradoxically, while this reductionism enhances understandability of the index, it works contrary to both the complex nature of the system and potentially disparate values that might be held by system users. A similar dilemma is found in the world of financial risk. We adapt the payoff matrix approach from financial risk to develop a comparable framework for ecosystem risk and call it the Impact Matrix. The payoff matrix utilizes the probability function for management alternatives to represent multiple pieces of information at one time (e.g. mean, variance, standard deviation). A matrix of these vectors allows for the development of many types of decision rules (e.g. minimax regret and maximin strategies) that can represent alternative value systems. In this paper we develop an “impact matrix” that uses similar features as the payoff matrix. The impact matrix concept is demonstrated for agricultural production systems through creation of a vector of possible environmental outcomes (e.g. surface runoff, nitrate in surface runoff, and soil erosion) for several agricultural management practices. We then develop criteria that utilize this information to represent the different ways that people think about environmental impacts. The result of this research is a tool that allows indicators to be incorporated in an index that can be adapted to different situations, and thus used in a variety of contexts while remaining simple to understand. That is, the impact matrix allows flexibility in developing indices of complex, multifaceted systems so that many disparate value systems may be easily represented.