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Preference
View on WikipediaIn psychology, economics and philosophy, preference is a technical term usually used in relation to choosing between alternatives. For example, someone prefers A over B if they would rather choose A than B. Preferences are central to decision theory because of this relation to behavior. Some methods such as Ordinal Priority Approach use preference relation for decision-making. As connative states, they are closely related to desires. The difference between the two is that desires are directed at one object while preferences concern a comparison between two alternatives, of which one is preferred to the other.
In insolvency, the term is used to determine which outstanding obligation the insolvent party has to settle first.
Psychology
[edit]In psychology, preferences refer to an individual's attitude towards a set of objects, typically reflected in an explicit decision-making process.[1] The term is also used to mean evaluative judgment in the sense of liking or disliking an object, as in Scherer (2005),[2] which is the most typical definition employed in psychology. It does not mean that a preference is necessarily stable over time. Preference can be notably modified by decision-making processes, such as choices,[3][4] even unconsciously.[5] Consequently, preference can be affected by a person's surroundings and upbringing in terms of geographical location, cultural background, religious beliefs, and education. These factors are found to affect preference as repeated exposure to a certain idea or concept correlates with a positive preference.[6]
Economics
[edit]In economics and other social sciences, preference refers to the set of assumptions related to ordering some alternatives, based on the degree of happiness, satisfaction, gratification, morality, enjoyment, or utility they provide. The concept of preferences is used in post-World War II neoclassical economics to provide observable evidence in relation to people's actions.[7] These actions can be described by Rational Choice Theory, where individuals make decisions based on rational preferences which are aligned with their self-interests in order to achieve an optimal outcome.[8]
Consumer preference, or consumers' preference for particular brands over identical products and services, is an important notion in the psychological influence of consumption. Consumer preferences have three properties: completeness, transitivity and non-satiation. For a preference to be rational, it must satisfy the axioms of transitivity and Completeness (statistics). The first axiom of transitivity refers to consistency between preferences, such that if x is preferred to y and y is preferred to z, then x has to be preferred to z.[9][10] The second axiom of completeness describes that a relationship must exist between two options, such that x must be preferred to y or y must be preferred to x, or is indifferent between them.[9][10] For example, if I prefer sugar to honey and honey to sweetener then I must prefer sugar to sweetener to satisfy transitivity and I must have a preference between the items to satisfy completeness. Under the axiom of completeness, an individual cannot lack a preference between any two options.[11]

If preferences are both transitive and complete, the relationship between preference can be described by a utility function.[12] This is because the axioms allow for preferences to be ordered into one equivalent ordering with no preference cycles.[13] Maximising utility does not imply maximise happiness, rather it is an optimisation of the available options based on an individual's preferences.[14] The so-called Expected Utility Theory (EUT), which was introduced by John von Neumann and Oskar Morgenstern in 1944, explains that so long as an agent's preferences over risky options follow a set of axioms, then he is maximizing the expected value of a utility function.[15] In utility theory, preference relates to decision makers' attitudes towards rewards and hazards. The specific varieties are classified into three categories: 1) risk-averse, that is, equal gains and losses, with investors participating when the loss probability is less than 50%; 2) the risk-taking kind, which is the polar opposite of type 1); 3) Relatively risk-neutral, in the sense that the introduction of risk has no clear association with the decision maker's choice.[16]
The mathematical foundations of most common types of preferences — that are representable by quadratic or additive functions — laid down by Gérard Debreu[17][18] enabled Andranik Tangian to develop methods for their elicitation. In particular, additive and quadratic preference functions in variables can be constructed from interviews, where questions are aimed at tracing totally 2D-indifference curves in coordinate planes without referring to cardinal utility estimates.[19][20]
Empirical evidence has shown that the usage of rational preferences (and Rational Choice Theory) does not always accurately predict human behaviour because it makes unrealistic assumptions.[21][22][23] In response to this, neoclassical economists argue that it provides a normative model for people to adjust and optimise their actions.[24] Behavioural economics describes an alternative approach to predicting human behaviour by using psychological theory which explores deviations from rational preferences and the standard economic model.[25] It also recognises that rational preferences and choices are limited by heuristics and biases. Heuristics are rules of thumb such as elimination by aspects which are used to make decisions rather than maximising the utility function.[26] Economic biases such as reference points and loss aversion also violate the assumption of rational preferences by causing individuals to act irrationally.[27]
Individual preferences can be represented as an indifference curve given the underlying assumptions. Indifference curves graphically depict all product combinations that yield the same amount of usefulness. Indifference curves allow us to graphically define and rank all possible combinations of two commodities.[28]
The graph's three main points are:
- If more is better, the indifference curve dips downward.
- Greater transitivity indicates that the indifference curves do not overlap.
- A propensity for diversity causes indifference curves to curve inward.
Risk preference
[edit]Risk preference is defined as how much risk a person is prepared to accept based on the expected utility or pleasure of the outcome.
Risk tolerance is a critical component of personal financial planning, that is, risk preference.
In psychology, risk preference is occasionally characterised as the proclivity to engage in a behaviour or activity that is advantageous but may involve some potential loss, such as substance abuse or criminal action that may bring significant bodily and mental harm to the individual.[29]
In economics, risk preference refers to a proclivity to engage in behaviours or activities that entail greater variance returns, regardless of whether they be gains or losses, and are frequently associated with monetary rewards involving lotteries.[30]
There are two different traditions of measuring preference for risk, the revealed and stated preference traditions, which coexist in psychology, and to some extent in economics as well.[31][32][33]
Risk preference evaluated from stated preferences emerges as a concept with significant temporal stability, but revealed preference measures do not.[34]
Relation to desires
[edit]Preferences and desires are two closely related notions: they are both conative states that determine our behavior.[35] The difference between the two is that desires are directed at one object while preferences concern a comparison between two alternatives, of which one is preferred to the other.[36][35] The focus on preferences instead of desires is very common in the field of decision theory. It has been argued that desire is the more fundamental notion and that preferences are to be defined in terms of desires.[37][36][35] For this to work, desire has to be understood as involving a degree or intensity. Given this assumption, a preference can be defined as a comparison of two desires.[37] That Nadia prefers tea over coffee, for example, just means that her desire for tea is stronger than her desire for coffee. One argument for this approach is due to considerations of parsimony: a great number of preferences can be derived from a very small number of desires.[37][35] One objection to this theory is that our introspective access is much more immediate in cases of preferences than in cases of desires. So it is usually much easier for us to know which of two options we prefer than to know the degree with which we desire a particular object. This consideration has been used to suggest that maybe preference, and not desire, is the more fundamental notion.[37]
Insolvency
[edit]In insolvency, the term can be used to describe when a company pays a specific creditor or group of creditors. From doing this, that creditor(s) is made better off, than other creditors. After paying the 'preferred creditor', the company seeks to go into formal insolvency like an administration or liquidation. There must be a desire to make the creditor better off, for them to be a preference. If the preference is proven, legal action can occur. It is a wrongful act of trading. Disqualification is a risk.[38] Preference arises within the context of the principle maintaining that one of the main objectives in the winding up of an insolvent company is to ensure the equal treatment of creditors.[39] The rules on preferences allow paying up their creditors as insolvency looms, but that it must prove that the transaction is a result of ordinary commercial considerations.[39] Also, under the English Insolvency Act 1986, if a creditor was proven to have forced the company to pay, the resulting payment would not be considered a preference since it would not constitute unfairness.[40] It is the decision to give a preference, rather than the giving of the preference pursuant to that decision, which must be influenced by the desire to produce the effect of the preference. For these purposes, therefore, the relevant time is the date of the decision, not the date of giving the preference.[41]
See also
[edit]- Motivation
- Ordinal Priority Approach
- Preference-based planning (in artificial intelligence)
- Preference revelation
- Choice
- Pairwise comparison
References
[edit]- ^ Lichtenstein, S.; & Slovic, P. (2006). The construction of preference. New York: Cambridge University Press.
- ^ Scherer, Klaus R. (December 2005). "What are emotions? And how can they be measured?". Social Science Information. 44 (4): 695–729. doi:10.1177/0539018405058216.
- ^ Sharot, T.; De Martino, B.; & Dolan, R. J. (2009). "How choice reveals and shapes expected hedonic outcome". Journal of Neuroscience, 29, 3760–3765.
- ^ Brehm, J. W. (1956). "Post-decision changes in desirability of choice alternatives". Journal of Abnormal and Social Psychology, 52, 384–389.
- ^ Coppin, G., Delplanque, S., Cayeux, I., Porcherot, C., & Sander, D. (2010). "I'm no longer torn after choice: How explicit choices can implicitly shape preferences for odors". Psychological Science, 21, 489–493.
- ^ Zajonc, Robert B.; Markus, Hazel (1982-09-01). "Affective and Cognitive Factors in Preferences". Journal of Consumer Research. 9 (2): 123–131. doi:10.1086/208905. ISSN 0093-5301.
- ^ Allan, Bentley B. (2019). "Paradigm and nexus: neoclassical economics and the growth imperative in the World Bank, 1948-2000". Review of International Political Economy. 26 (1): 183–206. doi:10.1080/09692290.2018.1543719. S2CID 158564367.
- ^ Zey, Mary (1998). Rational Choice Theory and Organizational Theory: A Critique. SAGE Publications, Inc. pp. 1–13.
- ^ a b Bossert, Walter; Kotaro, Suzumura (2009). "External Norms and Rationality of Choice". Economics and Philosophy. 25 (2): 139–152. doi:10.1017/S0266267109990010. S2CID 15220288.
- ^ a b Schotter, Andrew (2006). "Strong and Wrong: The Use of Rational Choice Theory in Experimental Economics". Journal of Theoretical Politics. 18 (4): 498–511. doi:10.1177/0951629806067455. S2CID 29003374.
- ^ Eliaz, Kfir (2006). "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences". Games and Economic Behavior. 56: 61–86. doi:10.1016/j.geb.2005.06.007.
- ^ Aleskerov, Fuad (2007). Utility Maximization, Choice and Preferences (2 ed.). Springer. pp. 17–52.
- ^ List, Christian (2012). "The theory of judgment aggregation: an introductory review" (PDF). Synthese. 187 (1): 179–207. doi:10.1007/s11229-011-0025-3. S2CID 6430197.
- ^ Kirsh, Yoram (2017). "Utility and Happiness in a Prosperous Society". OUI – Institute for Policy Analysis Working Paper Series. 37.
- ^ Teraji, Shinji (2018). The Cognitive Basis of Institutions: A Synthesis of Behavioral and Institutional Economics. London: Academic Press. p. 137. ISBN 9780128120231.
- ^ Nagaya, Kazuhisa (2021-10-15). "Why and Under What Conditions Does Loss Aversion Emerge?". Japanese Psychological Research. 65 (4): 379–398. doi:10.1111/jpr.12385. ISSN 0021-5368. S2CID 244976714.
- ^ Debreu, Gérard (1952). "Definite and semidefinite quadratic forms". Econometrica. 20 (2): 295–300. doi:10.2307/1907852. JSTOR 1907852.
- ^ Debreu, Gérard (1960). "Topological methods in cardinal utility theory". In Arrow, Kenneth (ed.). Mathematical Methods in the Social Sciences,1959. Stanford: Stanford University Press. pp. 16–26. doi:10.1016/S0377-2217(03)00413-2.
- ^ Tangian, Andranik (2002). "Constructing a quasi-concave quadratic objective function from interviewing a decision maker". European Journal of Operational Research. 141 (3): 608–640. doi:10.1016/S0377-2217(01)00185-0.
- ^ Tangian, Andranik (2004). "A model for ordinally constructing additive objective functions". European Journal of Operational Research. 159 (2): 476–512. doi:10.1016/S0377-2217(03)00413-2.
- ^ Kalter, Frank; Kroneberg, Clemens (2012). "Rational Choice Theory and Empirical Research: Methodological and Theoretical Contributions in Europe". Annual Review of Sociology. 38 (1): 73–92. doi:10.1146/annurev-soc-071811-145441.
- ^ England, Paula (1989). "A feminist critique of rational-choice theories: Implications for sociology". The American Sociologist. 20 (1): 14–28. doi:10.1007/BF02697784. S2CID 143743641.
- ^ Herfeld, Catherine (2021). "Revisiting the criticisms of rational choice theories". Philosophy Compass. 17 (1).
- ^ Case, Karl (2008). "A Response to Guerrien and Benicourt". The Review of Radical Political Economics. 40 (3): 331–335. doi:10.1177/0486613408320324. S2CID 154665809.
- ^ Angner, Erik (2021). A Course in Behavioural Economics (3 ed.). United Kingdom: Macmillan Education Limited. pp. 25–37. ISBN 978-1-352-01080-0.
- ^ Grandori, Anna (2010). "A rational heuristic model of economic decision making". Rationality and Society. 22 (4): 477–504. doi:10.1177/1043463110383972. S2CID 146886098.
- ^ Bouteska, Ahmed; Regaieg, Boutheina (2020). "Loss aversion, overconfidence of investors and their impact on market performance evidence from the US stock markets". Journal of Economics, Finance and Administrative Science. 25 (50): 451–478. doi:10.1108/JEFAS-07-2017-0081. hdl:10419/253806. S2CID 158379317.
- ^ Aguirre Sotelo, Jose Antonio Manuel; Block, Walter E. (2014-12-31). "Indifference Curve Analysis: The Correct and the Incorrect". Oeconomia Copernicana. 5 (4): 7–43. ISSN 2083-1277.
- ^ Steinberg, Laurence (July 2013). "The influence of neuroscience on US Supreme Court decisions about adolescents' criminal culpability". Nature Reviews Neuroscience. 14 (7): 513–518. doi:10.1038/nrn3509. ISSN 1471-003X. PMID 23756633. S2CID 12544303.
- ^ Harrison, Glenn W.; Rutström, E. Elisabet (2008), "Risk Aversion in the Laboratory", Research in Experimental Economics, vol. 12, Bingley: Emerald (MCB UP ), pp. 41–196, doi:10.1016/s0193-2306(08)00003-3, ISBN 978-0-7623-1384-6, retrieved 2023-04-23
- ^ Appelt, Kirstin C.; Milch, Kerry F.; Handgraaf, Michel J. J.; Weber, Elke U. (April 2011). "The Decision Making Individual Differences Inventory and guidelines for the study of individual differences in judgment and decision-making research". Judgment and Decision Making. 6 (3): 252–262. doi:10.1017/S1930297500001455. ISSN 1930-2975. S2CID 2468108.
- ^ Beshears, John; Choi, James; Laibson, David; Madrian, Brigitte (May 2008). "How are Preferences Revealed?" (PDF). Journal of Public Economics. 92 (8–9). Cambridge, MA: 1787–1794. doi:10.3386/w13976. PMC 3993927. PMID 24761048.
- ^ Charness, Gary; Gneezy, Uri; Imas, Alex (March 2013). "Experimental methods: Eliciting risk preferences". Journal of Economic Behavior & Organization. 87: 43–51. doi:10.1016/j.jebo.2012.12.023.
- ^ Mata, Rui; Frey, Renato; Richter, David; Schupp, Jürgen; Hertwig, Ralph (2018-05-01). "Risk Preference: A View from Psychology". Journal of Economic Perspectives. 32 (2): 155–172. doi:10.1257/jep.32.2.155. hdl:21.11116/0000-0001-5038-6. ISSN 0895-3309. PMID 30203934.
- ^ a b c d Schulz, Armin W. (2015). "Preferences Vs. Desires: Debating the Fundamental Structure of Conative States". Economics and Philosophy. 31 (2): 239–257. doi:10.1017/S0266267115000115. S2CID 155414997.
- ^ a b Pettit, Philip. "Desire". Routledge Encyclopedia of Philosophy. Routledge. Retrieved 4 May 2021.
- ^ a b c d Schroeder, Tim (2020). "Desire". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 3 May 2021.
- ^ Steven, Keith. "What Is A Preference Under The Insolvency Act 1986". Retrieved October 1, 2018.
- ^ a b Hannigan, Brenda (2015). Company Law, Fourth Edition. Oxford: Oxford University Press. p. 368. ISBN 9780198722861.
- ^ Gullifer, Louise; Payne, Jennifer (2015). Corporate Finance Law: Principles and Policy, Second Edition. Oxford: Bloomsbury Publishing. p. 111. ISBN 9781782259602.
- ^ Green, Elliot. "Green v Ireland [2011] EWHC 1305 (Ch)". Retrieved December 1, 2022.
External links
[edit]- Stanford Encyclopedia of Philosophy article on 'Preferences'
- Customer preference formation
DOC (white paper from International Communications Research)
Preference
View on GrokipediaCore Concepts
Definition
Preference is fundamentally a comparative attitude or evaluation by which an individual or entity deems one alternative more desirable or valuable than another, serving as a cornerstone in decision theory, psychology, and philosophy.[1] This concept involves subjective assessments of options in relation to practical reasoning, such as determining what course of action or object is preferable, without necessarily entailing immediate behavioral commitment.[1] Historically, the notion of preference traces its origins to 18th-century moral philosophy, particularly through David Hume's emphasis on sentiments as the basis for comparative liking, where moral distinctions arise from feelings of approval or disapproval rather than pure reason.[5] Key characteristics of preferences include their inherently relational and ranking-oriented nature, whereby options are ordered relative to one another rather than evaluated in isolation.[1] Preferences can be represented ordinally, capturing mere rankings of alternatives (e.g., A is preferred to B, which is preferred to C), or cardinally, assigning measurable intensities to these rankings, though the latter is more contentious and often modeled through utility functions that quantify preference strength.[1] Importantly, preferences guide potential behavior by influencing choices and motivations but do not presuppose actual action, distinguishing them as predispositions rather than enacted decisions.[1] In everyday contexts, preferences manifest in simple choices, such as an individual favoring tea over coffee based on taste or habit.[1] The concept extends across disciplines to encompass individual preferences in personal decision-making, social preferences that incorporate concerns for others' outcomes (e.g., altruism or fairness in group allocations), and systemic preferences embedded in institutional or collective frameworks, such as policy priorities in economics or ethical norms in philosophy.[6] Utility functions, explored further in economic modeling, provide a numerical representation of preference intensity to facilitate analysis.[1]Distinctions from Related Terms
Preference is fundamentally distinguished from desire by its comparative nature. Whereas desires are directed toward individual objects or states—such as wanting a specific item or outcome—preferences entail relational evaluations between alternatives, such as favoring option A over option B.[7] This distinction underscores that preferences require a contrastive framework, often involving trade-offs, while desires can exist in isolation without necessitating comparison.[8] Philosophers have debated whether preferences derive from the relative strengths of desires, with early analyses suggesting that the intensity of desires for competing options determines preferential rankings. In contrast to values, which represent enduring normative principles guiding moral or ethical judgments—such as commitments to justice or equality—preferences are more contingent and personal rankings that lack inherent moral obligation.[9] Values often transcend situational contexts and impose prescriptive force, whereas preferences function as descriptive or predictive tools for individual choices, varying across scenarios without implying universality or ethical weight. For instance, one might value environmental sustainability as a core principle but still prefer a less eco-friendly product in a particular purchase due to cost or convenience. Preferences also differ from attitudes, which encompass broader, often emotionally charged evaluative dispositions toward objects, people, or ideas. Attitudes integrate cognitive, affective, and behavioral components, potentially influencing long-term orientations, whereas preferences are narrower, more neutral assessments oriented toward specific decision-making and choice without the same depth of emotional involvement.[10] This makes preferences particularly useful in analytical contexts, such as economic modeling, where they relate to utility representations of comparative choices.[1] Historically, the concept of preference evolved from notions of "inclination" in early modern philosophy, where thinkers like David Hume described it as a motivational bias toward certain ends amid competing impulses.[1] By the 20th century, it shifted toward formalized comparative structures in behavioral sciences and decision theory, emphasizing transitivity and completeness to distinguish it from vaguer inclinations or whims.[1] This progression clarified preference's role as a precise tool for understanding rational choice, separate from the more fluid or instinctual connotations of its philosophical precursors.[11]Psychological Perspectives
Formation and Influences
Preferences form through a combination of innate predispositions and learned experiences, with cognitive biases playing a central role in psychological development. The mere exposure effect, identified by Robert Zajonc, demonstrates that repeated, non-reinforced exposure to a stimulus increases an individual's liking for it, even without conscious awareness or explicit evaluation.[12] This bias arises from familiarity reducing uncertainty and evoking positive affective responses, influencing preferences for music, art, and social stimuli. Similarly, unconscious priming processes activate mental representations that subtly guide preferences; for instance, exposure to related concepts can enhance evaluations of consumer products by associating them with positive attributes without deliberate intent.[13] External factors such as culture, social norms, and environment further shape preferences through contextual and experiential mechanisms. Cultural backgrounds influence aesthetic preferences, with education in the arts fostering greater involvement and appreciation for diverse forms like visual design or literature.[14] Amos Tversky's 20th-century research on context-dependent preferences highlights how the presence of alternative options alters evaluations, as seen in the attraction effect where an inferior "decoy" option boosts preference for a target item by altering comparative judgments.[15] Social influences, including family and peer interactions, reinforce these patterns, while environmental exposures like media or daily routines embed preferences aligned with societal values. Developmentally, preferences evolve from early childhood through interactions between innate tendencies and learning, as explored in Piaget-inspired research on cognitive stages. Infants exhibit innate preferences for sweet tastes, signaling energy-rich foods, but these are modulated by learned associations formed in utero and during weaning.[16] By toddlerhood, children develop social and fairness preferences through observation and interaction, transitioning from self-focused to other-regarding choices around ages 2-3.[17] Food preferences exemplify this interplay: while evolutionary adaptations favor calorie-dense or novel-safe foods for survival, upbringing strongly influences specifics, such as aversion to bitter vegetables or affinity for culturally familiar dishes, persisting into adulthood.[18] In evolutionary psychology, these adaptive preferences prioritize nutrient detection and risk avoidance, ensuring reproductive fitness in ancestral environments.[19]Measurement and Stability
In psychology, preferences are empirically assessed through various techniques designed to capture both qualitative rankings and quantitative intensities. Surveys often employ ranking tasks, where individuals order options by preference, providing insights into relative valuations without requiring absolute judgments. Conjoint analysis extends this by presenting hypothetical scenarios composed of multiple attributes, asking participants to rate, rank, or choose among them, which allows decomposition of preferences into component parts such as importance weights for specific features.[20][21] To measure preference intensity, psychological scales like the Likert format are commonly used, typically featuring 5- or 7-point continua (e.g., from "strongly dislike" to "strongly like") to quantify the strength of affective responses toward stimuli.[22] Preferences exhibit context-dependent variability, often constructed on the spot rather than retrieved as fixed traits, leading to malleability influenced by immediate task demands or environmental cues.[23] In long-term decisions, adaptive preferences emerge as individuals adjust desires to align with feasible outcomes, such as scaling back aspirations under constraints to maintain psychological equilibrium.[24] Post-2000 research highlights how such malleability supports adaptive behavior, with short-term preferences showing greater flux compared to more stable long-term orientations, though overall stability varies by domain.[25] Challenges in measurement arise from inconsistencies driven by mood states or framing of options, as demonstrated in 1970s studies where equivalent choices yielded reversed preferences depending on whether outcomes were described as gains or losses.[26] Reliability is evaluated via test-retest correlations, which assess consistency over intervals like weeks or months; meta-analyses indicate moderate stability for preference measures, with correlations typically ranging from 0.50 to 0.70, though lower for context-sensitive tasks.[27] These metrics underscore the need for repeated assessments to account for variability, distinguishing psychological approaches from economic revealed preference methods that infer stability from observed behaviors.[28]Economic and Decision-Making Perspectives
Modeling Preferences
In economic theory, preferences are formally modeled as binary relations over consumption bundles, which are vectors representing quantities of goods and services available to a consumer. A consumption bundle in the consumption set denotes feasible combinations of goods. The preference relation is typically denoted by , where indicates that bundle is at least as preferred as bundle . This encompasses strict preference (where means is strictly preferred to ) and indifference (where means the bundles are equally preferred).[29] A fundamental property of these relations is the completeness axiom, which ensures that preferences are well-defined for all pairs of bundles. Formally, for all , either , , or both (implying ). This axiom guarantees that a consumer can always compare any two options, providing a complete ordering without gaps or incommensurabilities.[29] Under certain conditions, such as completeness and transitivity (where if and , then ), preferences can be represented by an ordinal utility function , where if and only if . Ordinal utility captures the ranking of bundles without measuring the intensity of preferences, distinguishing it from cardinal approaches. This representation was pioneered by Vilfredo Pareto in his 1906 Manuale di economia politica, where he advocated ordinalism to analyze equilibrium without assuming interpersonal utility comparisons. Pareto's framework shifted economics toward relative rankings, laying groundwork for modern consumer theory.[30][31] Key visualizations in this modeling include indifference curves, which depict sets of bundles yielding the same utility level, forming the level sets of . For two goods, an indifference curve traces combinations where for some constant , typically downward-sloping and convex to reflect diminishing marginal rates of substitution. In consumer theory, these interact with budget constraints, represented as , where is the price vector and is income, defining the feasible set of affordable bundles. Optimal choice occurs at the tangency of an indifference curve and the budget line, maximizing utility subject to affordability. This approach was formalized by John R. Hicks and R. G. D. Allen in 1934, integrating ordinal preferences into demand analysis.[32] These elements evolved into comprehensive general equilibrium models, such as the Arrow-Debreu framework, where individual preferences over dated, state-contingent bundles aggregate to economy-wide equilibrium under competitive markets. By incorporating ordinal utility and binary relations, this model demonstrates the existence of prices clearing all markets, building directly on Pareto's ordinal foundations.[33] Psychological factors, such as cognitive biases, can influence the empirical validity of these abstract models but are incorporated sparingly in standard formulations.[29]Axioms and Utility Functions
In economic theory, preferences over bundles of goods or outcomes are modeled as binary relations satisfying certain axioms to ensure logical consistency and enable numerical representation. The core axioms include completeness, which requires that for any two bundles and , either (weak preference), , or both; reflexivity, stating that every bundle is at least as preferred as itself (); and transitivity, which mandates that if and , then .[34] These properties collectively define a rational preference relation, allowing for consistent ranking without cycles or gaps.[35] A fourth axiom, continuity, ensures that the preference relation is preserved under limits: for any (strict preference), there exist neighborhoods around and such that all bundles in the former are preferred to all in the latter, preventing discontinuities like lexicographic preferences.[36] Empirical studies, however, reveal frequent violations of these axioms in human behavior; for instance, transitivity is often breached in choice experiments where context-dependent preferences lead to cycles, such as preferring A to B, B to C, but C to A under certain conditions.[37] One analysis of consumer choices found transitivity holding in only about 8% of cases across diverse samples.[38] Under these axioms, particularly completeness, transitivity, and continuity, Debreu's representation theorem guarantees the existence of a continuous utility function over a connected space (e.g., ) such that if and only if , and (indifference) if . The theorem derives from constructing such a function via separating hyperplanes in the utility differences, ensuring ordinal uniqueness up to monotonic transformations.[39] For example, Cobb-Douglas preferences, which exhibit constant elasticity of substitution and satisfy the axioms, admit the utility form for , where reflects the relative weight on good 1; this can be derived by assuming homotheticity (preferences invariant to scaling) and integrating marginal rates of substitution.[40] These axiomatic foundations extend to applications in welfare economics, where aggregating individual preferences into social choices reveals fundamental limitations. Arrow's impossibility theorem demonstrates that no social welfare function can satisfy non-dictatorship, Pareto efficiency, independence of irrelevant alternatives, and unrestricted domain while respecting transitive individual preferences, underscoring tensions between individual rationality and collective decision-making.[41]Preferences Under Risk and Uncertainty
Risk Attitudes
In decision theory under risk, preferences are characterized by attitudes toward uncertainty, classified into risk aversion, risk neutrality, and risk seeking based on the shape of the utility function. Risk-averse individuals prefer a certain outcome to a risky prospect with the same expected value, reflected in a concave utility function where the utility of the expected wealth exceeds the expected utility, as per Jensen's inequality: . Risk neutrality corresponds to a linear utility function, where individuals are indifferent between certain and risky outcomes with equal expected values, such that . In contrast, risk-seeking preferences feature a convex utility function, leading to a preference for risky prospects over certain equivalents, with .[42] These attitudes form the foundation of expected utility theory, formalized by von Neumann and Morgenstern in 1944, which posits that rational preferences over lotteries satisfy axioms like completeness, transitivity, continuity, and independence, yielding a cardinal utility representation for choices under risk. Risk attitudes are quantified through certainty equivalents, the guaranteed amount that makes an individual indifferent to a given lottery; for risk-averse persons, this is below the lottery's expected value, while for risk seekers it exceeds it.[43] Stated preferences are elicited via hypothetical gambles, where respondents choose between safe payments and probabilistic outcomes to infer their utility curvature.[44] Revealed preferences, conversely, are observed from market behaviors, such as purchasing insurance policies that entail a negative expected monetary value, signaling risk aversion as individuals pay premiums to avoid potential losses.[45] A seminal measure of risk aversion intensity is the Arrow-Pratt coefficient of absolute risk aversion, defined as , where higher values indicate greater aversion at wealth level ; this local measure, introduced by Pratt in 1964, facilitates comparisons across utility functions and agents.[46] The St. Petersburg paradox, posed by Nicolaus Bernoulli in 1713, exemplifies early challenges to risk attitudes, involving a coin-flip game with infinite expected value yet finite willingness to pay, highlighting the need for concave utility to resolve such discrepancies in expected monetary value calculations.[47]Behavioral Deviations
Behavioral economics has revealed several empirical deviations from classical expected utility theory in how individuals form preferences under risk, highlighting systematic inconsistencies in decision-making. One foundational challenge is the Allais paradox, which demonstrates violations of the independence axiom by showing that people often prefer certain outcomes over risky ones in ways that cannot be reconciled with expected utility maximization. In Allais's 1952 experiments, participants chose a guaranteed $1 million over a 10% chance at $5 million and an 89% chance at $1 million, but switched preferences when the certain option was replaced by a near-certain one with added risk to both alternatives, revealing a certainty effect that prioritizes avoiding uncertainty over consistent probabilistic weighting.[48] Prospect theory, developed by Kahneman and Tversky, provides a descriptive alternative that accounts for these anomalies through an asymmetric value function and nonlinear probability weighting. The value function is concave for gains and convex for losses, steeper for losses than gains (capturing loss aversion), and defined relative to a reference point rather than final wealth, leading individuals to evaluate outcomes as deviations from this point. Probability weighting is handled by a function that overweight small probabilities and underweight moderate to high ones, distorting perceived chances. The overall prospect value is calculated aswhere gains and losses are evaluated separately. This framework better explains observed behaviors like risk-seeking in losses and risk-aversion in gains, as validated in experimental settings.[49] Related biases further illustrate these deviations, such as the endowment effect, where ownership increases perceived value, causing willingness-to-accept to exceed willingness-to-pay for the same good. In controlled experiments, participants endowed with mugs demanded roughly twice as much to sell them as non-endowed participants were willing to pay, persisting even in market-like settings with trading opportunities. Similarly, status quo bias leads individuals to disproportionately favor maintaining current options over alternatives of equal or better value, driven by loss aversion relative to the status quo as a reference point; for instance, hypothetical retirement plan choices showed over 40% more selections for the default option when framed as such. These effects underscore how reference dependence and loss aversion shape preferences beyond rational utility calculations.[50][51] Post-2010 neuroeconomic research using brain imaging has illuminated the neural underpinnings of these risk preferences, showing distinct activations for gain and loss domains. Functional MRI studies reveal that the anterior insula processes risk as an aversive signal, particularly for losses, while the ventral striatum encodes expected rewards, supporting prospect theory's asymmetry; for example, loss aversion correlates with stronger insula responses to potential losses compared to striatal activation for gains. Critiques of expected utility during the 2008 financial crisis highlighted how ambiguity and overconfidence, amplified by behavioral biases, led to underestimation of tail risks in mortgage-backed securities, as agents overweighted recent gains and ignored low-probability crashes, contributing to systemic failures.[52][53] In post-2020 behavioral finance applications to digital assets like cryptocurrencies, these deviations manifest prominently due to high volatility and speculative nature; herding and overconfidence biases drive boom-bust cycles, with investors exhibiting disposition effects by holding losing positions longer amid FOMO (fear of missing out), as evidenced in analyses of trading data during the 2021 bull run. Prospect theory's probability weighting explains overweighting of rare high-return events in crypto preferences, leading to riskier portfolios than expected utility would predict.[54]
