The problem of choice is one of the fundamental aspects of economic studies: as emancipated from the definition that Lionel Robbins writes, "Economics is the study of human relationship between end and means which have alternative uses". This definition is one that is based goal based assessment of social analysis with reference to environment of human wants. However at this stage Robbins persuaded that non-comparisons among the persons concerned and epistomological neutrality of interpersonal comparisons of utility. Refuting a prior value judgment on alternatives related Kenneth Arrow put forth that choice functions be defined for set of environment where weak orderings are defined. Arrow's analysis is based on theory of lattice and it numerical representation when choices can be described by preference-indifferent varieties. The problem of preference-indifferent varieties as seen by Geogersceu-Roegen has two way relation one seen by choice as primary and optimal as secondary in a sense and also by rationalization of optimal by choice based on indifference and offer curves (the revealed preference analysis). Relatedly Lancaster emphasized the need to analyse the notion of characteristic functions defined such that some meaning can be related to choice functions rather than collapse into arbitrary thinking.
Having based on foundations, I see the definition of choice may be referred to as: 1) Associated Relations 2)Decision Procedure and 3)Aggregation of Information. For each I base it on the following explanations. The question of associated relations is clear pointer to the fact that unless a relation is defined over variables under consideration, choices are not alternatives from preference-indifference possibilities are read off. Secondly, procedures are meant to general acceptance of rules and decision procedure is what is expected from an alternative that exist. Thirdly information may not have what is referred to 'alternative uses' if it cannot be aggregated.