Preference (economics)


In economics, and in other social sciences, preference refers to an order by which an agent, while in search of an "optimal choice", ranks alternatives based on their respective utility. Preferences are evaluations that concern matters of value, in relation to practical reasoning. Individual preferences are determined by taste, need,..., as opposed to price, availability or personal income. Classical economics assumes that people act in their best interest. In this context, rationality would dictate that, when given a choice, an individual will select an option that maximizes their self-interest. But preferences are not always transitive, both because real humans are far from always being rational and because in some situations preferences can form cycles, in which case there exists no well-defined optimal choice. An example of this is Efron dice.
The concept of preference plays a key role in many disciplines, including moral philosophy and decision theory. The logical properties that preferences possess also have major effects on rational choice theory, which in turn affects all modern economic topics.
Using the scientific method, social scientists aim to model how people make practical decisions in order to explain the causal underpinnings of human behaviour or to predict future behaviours. Although economists are not typically interested in the specific causes of a person's preferences, they are interested in the theory of choice because it gives a background to empirical demand analysis.
Stability of preference is a deep assumption behind most economic models. Gary Becker drew attention to this with his remark that "the combined assumptions of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach as it is." More complex conditions of adaptive preference were explored by Carl Christian von Weizsäcker in his paper "The Welfare Economics of Adaptive Preferences", while remarking that. Traditional neoclassical economics has worked with the assumption that the preferences of agents in the economy are fixed. This assumption has always been disputed outside neoclassical economics.

History

In 1926, Ragnar Frisch was the first to develop a mathematical model of preferences in the context of economic demand and utility functions. Up to then, economists had used an elaborate theory of demand that omitted primitive characteristics of people. This omission ceased when, at the end of the 19th and the beginning of the 20th century, logical positivism predicated the need to relate theoretical concepts to observables. Whereas economists in the 18th and 19th centuries felt comfortable theorizing about utility, with the advent of logical positivism in the 20th century, they felt they needed a more empirical structure. Because binary choices are directly observable, they instantly appeal to economists. The search for observables in microeconomics is taken even further by the revealed preference theory, which holds consumers' preferences can be revealed by what they purchase under different circumstances, particularly under different income and price circumstances.
Despite utilitarianism and decision theory, many economists have differing definitions of what a rational agent is. In the 18th century, utilitarianism gave insight into the utility-maximizing versions of rationality; however, economists still have no consistent definition or understanding of what preferences and rational actors should be analyzed.
Since the pioneer efforts of Frisch in the 1920s, the representability of a preference structure with a real-valued function is one of the major issues pervading the theory of preferences. This has been achieved by mapping it to the mathematical index called utility. Von Neumann and Morgenstern's 1944 book "Games and Economic Behavior" treated preferences as a formal relation whose properties can be stated axiomatically. These types of axiomatic handling of preferences soon began to influence other economists: Marschak adopted it by 1950, Houthakker employed it in a 1950 paper, and Kenneth Arrow perfected it in his 1951 book "Social Choice and Individual Values".
Gérard Debreu, influenced by the ideas of the Bourbaki group, championed the axiomatization of consumer theory in the 1950s, and the tools he borrowed from the mathematical field of binary relations have become mainstream since then. Even though the economics of choice can be examined either at the level of utility functions or at the level of preferences, moving from one to the other can be useful. For example, shifting the conceptual basis from an abstract preference relation to an abstract utility scale results in a new mathematical framework, allowing new conditions on the preference structure to be formulated and investigated.
Another historical turning point can be traced back to 1895, when Georg Cantor proved in a theorem that if a binary relation is linearly ordered, then it is also isomorphic in the ordered real numbers. This notion would become very influential for the theory of preferences in economics: by the 1940s, prominent authors such as Paul Samuelson would theorize about people having weakly ordered preferences.
Historically, preference in economics as a form of utility can be categorized as ordinal or cardinal data. Both introduced in the 20th century, cardinal and ordinal utility take opposing theories and mindsets in applying and analyzing preference in utility. Vilfredo Pareto introduced the concept of ordinal utility, while Carl Menger led the idea of cardinal utility. Ordinal utility, in summation, is the direct following of preference, where an optimal choice is taken over a set of parameters. A person is expected to act in their best interests and dedicate their preference to the outcome with the greatest utility. Ordinal utility assumes that an individual will not have the same utility from a preference as any other individual because they likely will not experience the same parameters which cause them to decide a given outcome. Cardinal utility is a function of utility where a person makes a decision based on a preference, and the preference decision is weighted based on a quantitative value of utility. This utility unit is assumed to be universally applicable and constant across all individuals. Cardinal utility also assumes consistency across individuals' decision-making processes, assuming all individuals will have the same preference, with all variables held constant. Marshall found that "a good deal of the analysis of consumer behavior could be greatly simplified by assuming that the marginal utility of income is constant", however, this cannot be held to the utility of resources and decision-making applied to income. Ordinal and cardinal utility theories provide unique viewpoints on utility, can be used differently to model decision-making preferences and utilization development, and can be used across many applications for economic analysis.

Notation

There are two fundamental comparative value concepts, namely strict preference and indifference. These two concepts are expressed in terms of an agent's best wishes; however, they also express objective or intersubjective valid superiority that does not coincide with the pattern of wishes of any person.
Suppose the set of all states of the world is and an agent has a preference relation on. It is common to mark the weak preference relation by, so that means "the agent wants y at least as much as x" or "the agent weakly prefers y to x".
The symbol is used as a shorthand to denote an indifference relation:, which reads "the agent is indifferent between y and x", meaning the agent receives the same level of benefit from each.
The symbol is used as a shorthand to the strong preference relation: ), it is redundant inasmuch as the completeness axiom implies it already.
Non-satiation of preferences
Non-satiation refers to the belief any commodity bundle with at least as much of one good and more of the other must provide a higher utility, showing that more is always regarded as "better". This assumption is believed to hold as when consumers are able to discard excess goods at no cost, then consumers can be no worse off with extra goods. This assumption does not preclude diminishing marginal utility.
Example
Option A
  • Apple = 5
  • Orange = 3
  • Banana = 2
Option B
  • Apple = 6
  • Orange = 4
  • Banana = 2
In this situation, utility from Option B > A, as it contains more apples and oranges with bananas being constant.

Transitivity

Transitivity of preferences is a fundamental principle shared by most major rational, prescriptive, and descriptive models of decision-making. In order to have transitive preferences, a person, player, or agent that prefers choice option A to B and B to C must prefer A to C. The most discussed logical property of preferences are the following:
  • A≽B ∧ B≽C → A≽C
  • A~B ∧ B~C → A~C
  • A≻B ∧ B≻C → A≻C
Some authors go so far as to assert that a claim of a decision maker's violating transitivity requires evidence beyond any reasonable doubt. But there are scenarios involving a finite set of alternatives where, for any alternative there exists another that a rational agent would prefer. One class of such scenarios involves intransitive dice. And Schumm gives examples of non-transitivity based on Just-noticeable differences.

Most commonly used axioms

  • Order-theoretic: acyclicity, the semi-order property, completeness
  • Topological: continuity, openness, or closeness of the preference sets
  • Linear-space: convexity, homogeneity

    Normative interpretations of the axioms

Everyday experience suggests that people at least talk about their preferences as if they had personal "standards of judgment" capable of being applied to the particular domain of alternatives that present themselves from time to time. Thus, the axioms attempt to model the decision maker's preferences, not over the actual choice, but over the type of desirable procedure. Behavioral economics investigates human behaviour which violates the above axioms. Believing in axioms in a normative way does not imply that everyone must behave according to them.
Consumers whose preference structures violate transitivity would get exposed to being exploited by some unscrupulous person. For instance, Maria prefers apples to oranges, oranges to bananas, and bananas to apples. Let her be endowed with an apple, which she can trade in a market. Because she prefers bananas to apples, she is willing to pay one cent to trade her apple for a banana. Afterwards, Maria is willing to pay another cent to trade her banana for an orange, the orange for an apple, and so on. There are other examples of this kind of irrational behaviour.
Completeness implies that some choice will be made, an assertion that is more philosophically questionable. In most applications, the set of consumption alternatives is infinite, and the consumer is unaware of all preferences. For example, one does not have to choose between going on holiday by plane or train. Suppose one does not have enough money to go on holiday anyway. In that case, it is unnecessary to attach a preference order to those alternatives. However, preference can be interpreted as a hypothetical choice that could be made rather than a conscious state of mind. In this case, completeness amounts to an assumption that the consumers can always make up their minds whether they are indifferent or prefer one option when presented with any pair of options.
Under some extreme circumstances, there is no "rational" choice available. For instance, if asked to choose which one of one's children will be killed, as in Sophie's Choice, there is no rational way out of it. In that case, preferences would be incomplete since "not being able to choose" is not the same as "being indifferent".
The indifference relation ~ is an equivalence relation. Thus, we have a quotient set S/~ of equivalence classes of S, which forms a partition of S. Each equivalence class is a set of packages that are equally preferred. If there are only two commodities, the equivalence classes can be graphically represented as indifference curves.
Based on the preference relation on S, we have a preference relation on S/~. As opposed to the former, the latter is antisymmetric and a total order.