The Group Consensus Problem.
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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In a group consensus problem, there is a group with K greater than or equal to 2 members who are jointly responsible for the aggregation of their opinions. The group may not have a predefined real decision problem. French called the group consensus problem with a predefined real decision problem a group decision problem and the group consensus problem without a real decision problem a text-book problem. Suppose a group with K members are interested in forecasting demands for a commodity for a given time period. Production planning for this commodity depends on demands. Each group member may have his own opinion for demands in the form of probability distribution. In this case the group has a real decision problem in which they should determine the amount of the commodity to be produced. Here the group consensus opinion is a probability distribution for demands obtained from the group members prior opinions for demands. For example a group of meteorologists are required to give a single forecast for weather without having any real decision problem. This is an example of the text-book problem. Savage suggested that the whole of statistical theory is directly or indirectly aimed at the solution of a version of the text-book problem. The objective of this paper is to give a unified approach for these two problems. In this paper all the group members are assumed to be Bayesians. Keywords Bayesian decision analysis Combining expert opinions Utility functions and Pareto Optimal decisions.
- Statistics and Probability