Abstract
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 in some extent to embed human attitude in the decision process.
TopBackground
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.
Key Terms in this Chapter
Majority Voting: A coordination mechanism in collective choice where each decision maker must pronounce himself over a single alternative and the alternative that obtains the maximum voices win.
BOCR Analysis: A framework of decision analysis where potential actions, options, decisions, or alternatives are evaluated through four indicators: benefit (B), their certain or immediate positive contribution to decision goal; their opportunity (O), the positive uncertain or long term contribution; cost (C) that summarizes their immediate or certain aspects that work against the achievement of decision goal; and risk (R), an indicator that aggregates uncertain or long term potential threats.
Coordination mechanism: Process by which the views points of many decision makers are aggregated to address collective choice problems.
Bipolarity: A notion that consists, for an actor, in viewing or evaluating anything in two directions: a direction positively seen by the actor and a direction considered to impede his aspirations.
Collective Choice: A decision making problem where a certain numbers of actors, decision makers, stakeholders or players must choose a subset (possibly reduced to a singleton) of alternatives or actions among a large number of potential actions or alternatives in order to achieve some collective as well as individual objectives.
Satisficing Game: A decision analysis framework where each action or alternatives is evaluated over two measures or degrees: a selectability measure that works towards the achievement of decision maker goal and the rejectability measure that constitutes the cost, in a broad sense, to pay to achieve the goal.
Aggregation: A process that permit to go from data represented in a high dimension set to a representation in a set of low and compact dimension.
Rejecting: A notion to express the fact that behavior of something (attribute for instance) is negatively correlated with that of another thing (objective for instance).
Supporting: A notion to express the fact that behavior of something (attribute for instance) is positively correlated with that of another thing (objective for instance).