A collective choice problem is a decision problem where a certain number (possibly reduced to one) of agents, stakeholders, or decision makers must select alternative(s) from a possibly large set or universe of alternatives in order to satisfy some collective as well as individual objectives. The purpose of this chapter is to consider the modeling process of collective choice problem when coping with human attitude in terms of social influence, indecision, uncertainty, etc. Using bipolar analysis that consist in evaluating alternatives by two opposite measures (a measure taking into account positive aspect of the alternative and that resuming its negative aspects) at individual level as well as community level permit to some extent embedding human attitudes in the decision process.
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In political science, methods for realizing a collective choice (mapping individual preferences onto collective preferences) are dominated since the advent of democracy by simple majority voting process (Picavet, 1996). But many theoretical results such as that of Borda, see (Borda, 1781), Arrow impossibility theorem (Arrow, 1951) show that this way of aggregating individuals preferences can lead to inconsistency. In decision analysis, that actually does have many steps such as formulating decision goal or objectives, identifying attributes that characterize potential alternatives that can respond to the decision goal and making recommendation regarding these alternatives given the decision goal, choice is the final step. But to choose, one must evaluate first; the construction of an evaluation procedure, often carried up by an expert known in the literature as the analyst (Bouyssou et al., 2000) is an important step in the decision process; this step is the main purpose of this chapter. This construction consists in aggregating individual preferences, understood in a broad sense to obtain a way that permits to rank, at least partially, different potential alternatives. Classically, two main approaches have dominated evaluation process in modern decision analysis: value or utility type approach (a value function or an utility measure is derived for each alternative to represent its adequacy with decision goal), see for instance Steuer (1986) and Saaty (1980); outranking methods (a pair comparison of alternatives is carried up under each attribute or criteria to derive a pre-order over the alternatives set), see (Bouyssou et al., 2000), (Brans et al., 1986, 1986a). The approach that will be described in this chapter can be considered as an intermediate one compared to those two approaches evoked previously; indeed by using numerical values to evaluate alternatives look like utility type approach, but as two “opposite” measures are used, it permits incomparability as it is the case in outranking approaches.