Alternative (decision-making)
An alternative in the context of Decision theory is one of the possible courses of action available to a decision-maker to achieve a goal or solve a problem. In other words, an alternative represents a distinct choice that can be selected from a given set. The existence of at least two alternatives is a necessary condition for a meaningful choice.
Alternatives in Classical Decision Theory
Classical Decision theory is based on the assumption of fully rational choice. In this framework, a decision problem is formalized through a set of alternatives, from which a rational agent must choose the best one. Each alternative represents a specific action that the decision-maker can implement. Classical theory typically assumes that the set of alternatives is predefined and known to the decision-maker (DM), and that the DM is capable of identifying all alternatives and evaluating the consequences of each option.
Under conditions of certainty, each alternative leads to a single, known outcome; under conditions of uncertainty, the result depends on external factors (states of nature). A rational strategy is based on optimality criteria: according to the maximum expected value criterion, the alternative with the highest expected value is chosen; a more sophisticated approach is the maximization of expected utility.
Alternatives in Multi-Criteria Decision Analysis
Multi-criteria decision analysis (MCDA) evaluates alternatives based on a set of criteria. Given a set of alternatives and criteria, the task is to rank the alternatives or select the best one.
The foundation of MCDA is the alternatives evaluation matrix, where rows represent alternatives, columns represent criteria, and the cells contain the values Kj(ai).
A key concept is Pareto dominance: alternative X dominates Y if it is no worse in all criteria and better in at least one. Dominated alternatives are eliminated from consideration. When criteria are in conflict (i.e., when an option is better on some metrics but worse on others), a set of Pareto-optimal solutions is formed.
Methods for comparing multi-criteria alternatives include:
- Constructing a single utility function (e.g., a weighted sum of scores)
- Pairwise comparisons (Saaty's AHP method)
- Outranking methods (ELECTRE, PROMETHEE)
MCDA is often integrated with handling uncertainty, where criteria are probabilistic or evaluations are fuzzy, combining elements of decision-making under risk.
Classification of Alternatives
- Discrete and continuous alternatives. The set of alternatives can be finite and discrete or infinite (continuous). With continuous parameters, the problem becomes one of mathematical optimization.
- Mutually exclusive and compatible alternatives. Typically, alternatives are mutually exclusive (only one can be chosen). Sometimes, selecting multiple options or their combinations is allowed, forming a higher-level alternative as a set of simpler ones.
- Dominant and dominated alternatives. According to the principle of dominance, alternative A dominates B if A is no worse than B on all criteria and is strictly better on at least one. Dominated alternatives are excluded from consideration. Non-dominated alternatives are considered efficient and form the Pareto-optimal set.
- Static and dynamic alternatives. In simple models, a one-time choice is made. In complex, multi-stage problems, alternatives are considered at each stage, often using a decision tree model.
Methods for Representing and Comparing Alternatives
The following tools are used for decision analysis:
Decision matrix – a table where rows represent alternatives and columns represent evaluation factors. The main types are:
- An 'alternatives × outcomes' matrix (payoff matrix) for problems under uncertainty
- An 'alternatives × criteria' matrix for multi-criteria problems
Decision tree – a graphical diagram of a sequence of decisions and events. It contains: decision nodes (squares) representing choices among alternatives, chance nodes (circles) representing random outcomes, and branches leading to final outcomes with their results. A decision tree allows for the calculation of the value of each strategy using the 'rollback' method, and is particularly useful for sequential decisions.
Preference and utility functions assign a numerical value to each option, reflecting the degree of preference. They are used to:
- Transform criteria with different units into a common scale
- Mathematically optimize the choice
- Rank alternatives and perform 'what-if' analysis
Other tools include influence diagrams, efficiency frontiers, and interactive decision support systems.
Bounded Rationality and Behavioral Aspects of Choice
Bounded rationality (a concept by Herbert Simon) describes situations where there is a lack of resources to find the optimal solution. Instead of maximization, the satisficing strategy is employed—the search for a "good enough" solution, where an individual chooses the first satisfactory alternative they encounter without analyzing all possible options.
Heuristic choice strategies show that people use simplified rules:
- Elimination by aspects: sequentially eliminating alternatives based on important criteria
- Lexicographic choice: preference is given to the alternative that is best on the most important criterion
The influence of context and the presentation of alternatives is demonstrated by effects such as:
- The decoy effect: adding a dominated alternative changes preferences between the main options
- The paradox of choice: an excess of options makes decision-making more difficult
- The framing effect: different presentations of the same alternative influence the choice