Hoag, D  
Ascough, James  
Englerpalma, A 
Submitted to: Ecological Indicators
Publication Type: Peer Reviewed Journal Publication Acceptance Date: 3/15/2002 Publication Date: 7/25/2002 Citation: HOAG, D.L., ASCOUGH II, J.C., ENGLERPALMA, A. THE IMPACT MATRIX APPROACH AND DECISION RULES TO ENHANCE INDEX DIMENSIONALITY, FLEXIBILITY AND REPRESENTATION. JOURNAL OF ECOLOGICAL INDICATORS. 2(2002):161168. Interpretive Summary: Many people desire 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. 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 b its 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. The payoff matrix utilizes the probability function for management alternatives to represent multiple pieces of information at one time (e.g. mean, mode, variance, standard deviation). A Matrix of these vectors allows for the development of many types of decision rules that can represent alternative value systems. For example, the maximum criterion represents extremely risk averse people by finding the system that has the best of the worst possible outcomes. Our proposal is to create an "impact matrix" that uses the same concepts as a payoff matrix. We have already developed the concept and will demonstrate it by creating indices for agricultural systems. We will create a vector of possible environmental outcomes for several agricultural systems (e.g. ground water contamination, surface water contamination, and soil erosion). Then we will develop criterions that utilize this information to represent the different ways that people think about environmental impacts. The result of this research will be a tool that allows indicators to be included in an index that can be used in a variety of ways so that it can be adapted to different situations, while remaining simple to understand. Technical Abstract: Many people desire 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. 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 b its 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. The payoff matrix utilizes the probability function for management alternatives to represent multiple pieces of information at one time (e.g. mean, mode, variance, standard deviation). A Matrix of these vectors allows for the development of many types of decision rules that can represent alternative value systems. For example, the maximum criterion represents extremely risk averse people by finding the system that has the best of the worst possible outcomes. Our proposal is to create an "impact matrix" that uses the same concepts as a payoff matrix. We have already developed the concept and will demonstrate it by creating indices for agricultural systems. We will create a vector of possible environmental outcomes for several agricultural systems (e.g. ground water contamination, surface water contamination, and soil erosion). Then we will develop criterions that utilize this information to represent the different ways that people think about environmental impacts. The result of this research will be a tool that allows indicators to be included in an index that can be used in a variety of ways so that it can be adapted to different situations, while remaining simple to understand.
