In formal models, the individual preferences or the preferences of a group of individuals (family, society, economy, board of directors, committee of experts, government, general staff, etc.) are often represented by a preference relation. Individual or group behavior is represented by a function called a choice function or a decision rule. Naturally, one may think that there exists a firm relationship between preferences and behavior. In other words, it is natural to assume that a chosen alternative is the preferred one. The common attempt to derive the individual's preference relation from his or her behavior is based on the assumption that such a relationship indeed exists. The basic problem dealt with in Chapter 3 is that a strong connection between preferences and choice does not necessarily exist.

In this chapter, the student is first exposed to the basic concepts that relate to individual or social preferences and choice. We then examine two questions. On one hand, what properties does a preference relation have to satisfy in order to guarantee the existence of a well-defined choice function that is consistent with that preference relation? On the other hand, what properties does the choice function have to satisfy in order to ensure that it can be viewed as intrinsically and naturally related to some preference relation?

The demeanor of people, the resources available to them, their background, nature, attitudes, beliefs and wishes are different.