Preferences

The preferences of a decision-maker (DM) represent a judgment, expressed in some way, about whether one option has an advantage over another or over all others. This is a fundamental component of the choice process, providing guidelines for evaluating alternatives and making a decision. Preferences can be expressed explicitly (in the form of rankings, judgments, or criteria) or implicitly—through actions, reactions, or a preferred choice made without formal justification.

Subjectivity and Rationality of Preferences

In decision theory, preferences are treated as subjective, yet it is assumed that the DM acts rationally. This means the choice should follow an internally consistent logic that reflects the individual's goals, interests, and value system. In this context, there is no single "objectively" best solution, as different DMs may interpret the same options differently, each making a subjectively optimal decision.

Preferences are manifested in:

• the evaluation and comparison of options,
• the identification of significant features,
• the assessment of the acceptability or dominance of alternatives.

Explicit and Implicit Preferences

• Explicit preferences are formalized and can be represented as decision rules or choice models.
• Implicit preferences are identified through behavior, observation, or an iterative dialogue with the DM. Documenting them is difficult, especially with a large number of alternatives or in group decision-making scenarios with differing value systems.

Frame

Decision theory acknowledges the influence of problem formulation and the context of information presentation on a DM's behavior. This means that the same decision can be perceived differently depending on:

• the order in which options are presented;
• the highlighted features and characteristics;
• the contextual interpretation of the problem.

Thus, the problem formulation, language of presentation, and evaluation structure become tools capable of altering the structure of preferences. This corresponds to what is described in cognitive psychology as the framing effect—where preferences change depending on how information is presented.

Contradictions and Inconsistency of Preferences

Even when preferences are explicitly stated, a DM may:

• exhibit logical contradictions,
• be inconsistent,
• erroneously evaluate alternatives.

These characteristics are taken into account when designing decision support systems that involve clarifying preferences in an interactive mode.

Modeling Preferences

Approaches to formalizing preferences include:

• Relational models — describe preferences as binary relations (preference, equivalence, incomparability).
• Verbal analysis methods — based on a qualitative description of criteria and subjective ordinal scales, similar to natural language.
• Aggregation models — preferences are expressed through weighting coefficients and evaluation functions, which allow criteria to be aggregated into a composite score.

Each model has limitations and can distort actual preferences, especially when attempting their numerical interpretation, a point highlighted in critiques of the universal scaling of qualitative characteristics.