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Constructing, evaluating and visualizing value and utility functions for decision support

https://doi.org/10.1016/j.envsoft.2013.01.017Get rights and content

Abstract

Formal methods of decision analysis can help to structure a decision making process and to communicate reasons for decisions transparently. Objectives hierarchies and associated value and utility functions are useful instruments for supporting such decision making processes by structuring and quantifying the preferences of decision makers or stakeholders. Common multi-attribute decision analysis software products support such decision making processes but they can often not represent complex preference structures and visualize uncertainty induced by uncertain predictions of the consequences of decision alternatives. To stimulate strengthening these aspects in decision support processes, we propose a set of visualization tools and provide a software package for constructing, evaluating and visualizing value and utility functions. In these tools we emphasize flexibility in value aggregation schemes and consideration and communication of prediction uncertainty. The use of these tools is demonstrated with an illustrative example of river management decision support.

Introduction

Formal methods of decision analysis are useful for structuring a decision making process and increasing the transparency about objectives and their expected fulfillment by different decision alternatives. This is of particular importance in environmental management, where decision making is often affected by one or several of the following difficulties:

  • Stakeholders with different perspectives are involved;

  • Difficult trade-offs between competing objectives have to be agreed upon;

  • Experts from different fields are required to predict outcomes of decision alternatives;

  • Predictions and/or valuations are affected by significant uncertainty;

  • Decisions need to be justified publicly.

To help addressing these problems, the use of formal decision support techniques has gained attention in environmental management (Beinat, 1997; Lahdelma et al., 2000; Mendoza and Martins, 2006; Reichert et al., 2007; Schwenk et al., 2012; Schuwirth et al., 2012).

The use of value and utility functions for quantifying preferences in decision support (Keeney and Raiffa, 1993; Clemen, 1996; Eisenführ et al., 2010) has significant conceptual advantages compared to alternative approaches, such as outranking procedures (Brans et al., 1986; Vincke, 1999) or the Analytical Hierarchy Process, AHP (Saaty, 1980, Saaty, 1994). In particular, they support goal- or value-focused rather than alternative-oriented thinking (Keeney, 1992), they make it possible to add alternatives without the need for re-eliciting preferences, and they avoid rank reversals when changing the set of alternatives (Belton and Gear, 1983; Dyer, 1990; Wang and Triantaphyllou, 2008).

However, implementation of these concepts in practical decision support is still a challenging task. For this reason, software products have been developed to help applying these concepts in practical decision support (French and Xu, 2005; Patchak, 2012). These products are designed to support problem structuring, value elicitation and evaluation of results. However, so far, not much effort has been devoted to identifying complex, non-additive preference models and to addressing the effect of model prediction uncertainty on decision support.

The first objective of this paper is to discuss visualizations that support the use of multi-criteria decision analysis (MCDA) techniques in environmental management with a focus on communicating uncertainty. The second objective is to present a small software package that complements the software cited above by (i) making the use of non-additive preference models possible, (ii) offering the option of switching from values to utilities at the appropriate level of the objectives hierarchy to consider risk attitudes, and (iii) producing the visualizations discussed in the first part. The paper starts with a short review of the underlying theory (Section 2), it then introduces the visualizations (Section 3), describes the software package (Section 4), illustrates the use of these tools for river management (Section 5), and ends by drawing conclusions (Section 6).

Section snippets

Construction of value and utility functions based on objectives hierarchies

One of the core principles of decision analysis is the hierarchical decomposition of an overall objective into sub-objectives. This helps decision makers to find a comprehensive set of complementary aspects that characterize the overall objective (Keeney and Raiffa, 1993; Clemen, 1996; Eisenführ et al., 2010). Fig. 1 shows an example of an objectives hierarchy.

A measurable or cardinal value function quantifies the degree of fulfillment of an objective as a function of attributes (Dyer and

Visualization of structure and results

In this section, we introduce visualizations of the structured objectives, the value or utility functions and the results of the application of such a function. The final goal is to find a visualization that allows us to compare alternatives while also representing uncertainty.

R package “utility”

Testing aggregation schemes (as shown in Fig. 3) and new visualization techniques as described in Section 3 can be extremely facilitated by a flexible software tool. Many software products exist that support various steps of the decision making process and also offer visualizations, such as objectives hierarchies as shown in Fig. 1, visualization of weights of additive value functions, or visualizations of the sensitivity of results to weights and attributes (French and Xu, 2005; Patchak, 2012

Illustrative example of river management decision support

The visualization concepts and tools described in this paper are applicable to any decision problem. In this section, we illustrate such an application by showing some aspects of their use in river management decision support (Reichert et al., 2007, Reichert et al., 2011).

The translation of river assessment procedures into value functions leads to much larger objectives hierarchies than those shown so far. Fig. 9 illustrates the objectives hierarchy for a good ecological state of a river

Conclusions

We designed a set of visualizations of hierarchically structured value and utility functions that support the user in gaining an overview of the degree of fulfillment of all (sub-)objectives in the objectives hierarchy, to compare the results for two management alternatives or expected states under different development scenarios, and to represent and communicate uncertainty. We tested these tools in a workshop on river assessment with representatives of authorities and consulting companies.

Acknowledgments

We thank Carlo Albert, Anne Dietzel, Judith Ellens, Barbara Känel, Judit Lienert, Pius Niederhauser, Lisa Scholten, the editor, three reviewers, and the participants of a practice-oriented course on structuring and visualizing river assessment procedures for constructive comments to the manuscript or earlier versions of our tools. This project was partially supported by the Swiss National Science Foundation as part of the National Research Program 61 on Sustainable Water Management. Application

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    Present address: Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Müggelseedamm 301 and 310, 12587 Berlin, Germany.

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