Design of a consensus seeking allocation method

Abstract

An objective method for assisting decisions regarding allocation of resources, particularly public sector resources, was developed based on systems engineering principles. Systems engineering documents from the first phase of the systems process were prepared. Random allocation simulations were completed to establish a baseline for comparison with empirical information. Simulated allocations showed that the number of decision makers was a much more important factor affecting the amount of resource allocated than was the number of potential allocation categories. Simulation also showed that allowing decision makers to establish a range of acceptable allocations speeded a consensus allocation process. Decision maker's preferred allocation ranges were used as a fuzzy number preference functions, and a method for combining opinions to get consensus based on fuzzy set methods was proposed. Indices describing amounts of consensus based on fuzzy preferences were developed. A field experiment was designed based on principles of human decision making processes. Subjects answered three different questions using three different methods of assessing acceptable allocation ranges. Assessment methods included direct assessment, assessment using decision trees, and assessment using linguistic equivalents of fuzzy numbers. Decision makers rated each of the assessment methods regarding honesty, comprehensibility, and ease. Analysis of results evaluated which of the three methods tested resulted in the largest amount of consensus allocation and which method was the most highly rated by decision makers. The method based on linguistic equivalents of fuzzy numbers gave the largest amount of consensus allocation, with the decision tree method as a close second. The method preferred by the decision makers was the decision tree by a large margin. The fuzzy consensus indices worked well to give information on amounts of consensus and to identify decision makers whose opinions did not contribute to consensus. The paper concludes that the concept of developing group consensus allocations for public sector resources is a valid one, and that refined fuzzy linguistic methods or decision trees may be an appropriate tool in developing those allocations.