The notion of preference has a central role in many disciplines,including moral philosophy and decision theory. Preferences and theirlogical properties also have a central role in rational choice theory,a subject that in its turn permeates modern economics, as well asother branches of formalized social science. The notion of preferenceand the way it is analysed vary between these disciplines. A treatmentis still lacking that takes into account the needs of all usages andtries to combine them in a unified approach. This entry surveys themost important philosophical uses of the preference concept andinvestigates their compatibilities and conflicts.

• 1. The basic concept of preference
• 2. Preference logic
  • 2.1 Concepts and notation
  • 2.2 Completeness
  • 2.3 Transitivity
  • 2.4 Order typology
  • 2.5 Combinative preferences
  • 2.6 Preference-based monadic value predicates
• 3. Numerical representation of preferences
  • 3.1 Representing preferences ordinally
  • 3.2 Representing preferences cardinally
  • 3.3 Alternative utility-based representations of preference
• 4. Preferences combination
  • 4.1 Managing preference conflicts
  • 4.2 Total and partial preferences
• 5. Preferences and choice
  • 5.1 Choice functions and their properties
  • 5.2 Determining choice from preference
  • 5.3 Inferring preference from choice
• 6. Preferences and welfare
• 7. Preference change
  • 7.1 Evidence for preference change
  • 7.2 Time preferences
  • 7.3 Doxastic preference change
  • 7.4 Valuational preference change
• 8. Preference criticism
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. The Basic Concept of Preference

In common parlance, the term “preference” assumesdifferent meanings, including that of comparative evaluation,prioritisation or favouring, and choice ranking (See for instancetheOxford English Dictionary). In this entry, we discuss thenotion of preference assubjective comparative evaluations,of the form “Agent \(A\) prefers \(X\) to \(Y\)”. Thischaracterisation distinguishes preference from other evaluativeconcepts.

Preferences areevaluations: they concern matters of value,typically in relation to practical reasoning, i.e. questions aboutwhat should be done, or should have been done. This distinguishespreferences from concepts that concern matters of fact.

Furthermore, preferences aresubjective in that theevaluation is typically attributed to an agent – where thisagent might be either an individual or a collective. Thisdistinguishes them from statements to the effect that “\(X\) isbetter than \(Y\)” in an objective or otherwise impersonalsense. The logic of preference has often also been used to representsuch objective evaluations (e.g. Broome 1991b), but the substantialnotion of preference includes this subjective element.

Finally, preferences arecomparative in that they express theevaluation of an item \(X\) relative to another item\(Y\). This distinguishes them from monadic concepts like“good”, “is desired”, etc. which only evaluateone item.

Most philosophers take the evaluated items to be propositions. Incontrast to this, economists commonly conceive of items as bundles of goods, represented as vectors.^[1] However, this approach has a difficult ambiguity. Ifpreferences are subjective evaluations of the alternatives, then whatmatters are the results that can be obtained with the help of thesegoods, not the goods themselves. Whether an agent has a preferencee.g. for a batch of wood over a crate of bricks will depend on whethershe intends to use it to generate warmth, build a shelter or create asculpture. Economists have tried to solve this ambiguity by couplingpreferences over goods with household production functions (Lancaster1966, Becker and Michael 1973); but as these functions are verydifficult to determine, it is often thought more parsimonious to stickwith the sentential or propositional representations of states of theworld.

Serious engagement with preferences began in the 20thcentury. In the social sciences, the preference concept becameimportant for explanatory and predictive purposes with IrvingFisher’s (1892) and Vilfredo Pareto’s (1909)methodological criticisms of hedonistic cardinal utility. Previously,economists largely agreed that decisions were motivated by theindividual’s quest for pleasure, and that the difference inquantity of pleasure derived from different alternatives was animportant influence on decisions. In that framework, the notion ofpreference, to the extent that it was used at all, was merely derivedfrom hedonistic utility: \(X\) is preferred to \(Y\) iff\(X\) yields more utility than \(Y\). Pareto argued thatbecause an accurate measurement procedure for cardinal hedonic utilitywas not available, social scientists should constrain themselves tomerely ordinal comparisons (Bruni and Guala 2001). This argumentturned preference into a fundamental notion of the social sciences,replacing (hedonic) utility.

Economists in the 1930s (Hicks and Allen 1934) radicalisedPareto’s idea and argued that cardinal utility should beexcluded in order to expunge economics from psychological hedonism.However, their concept of preference retained psychological content:people are assumed to act purposefully and therefore to havepreferences that really constitute mental evaluations, rather thanbeing ex-post rationalisations of behaviour (Lewin 1996). Furthermore,Ramsey (1926) and later von Neumann and Morgenstern (1944) devisedformal tools allowing the representation of preference magnitudes asutility functions on an interval scale. This new utility, however, was very different fromthe older hedonic concept: the preference concept was basic. The cardinal utility function was constructed to reflect the preference ordering, but was not completely determined by it.

Psychologists also sought to move away from the old psychophysicalassumptions and began seeing mental concepts like preferences withincreased suspicion. Instead, they sought not only to connect andmeasure psychological events, but indeed replace them by thebehavioural criteria with which they were hitherto connected. (See theentry onbehaviorism). Again, it was an economist, Paul Samuelson, who formulated thisprinciple most explicitly for the concept of preference. In 1938 hesuggested to “start anew … dropping off the last vestigesof the utility analysis” (1938, p. 62). Preferenceswere supposed to be defined in terms of choice, thus eliminatingreference to mental states altogether. Although this approach was highly influential atthe time, economists have largely not followed Samuelson in thisradical proposal (Hausman 2012), and it might indeed be the case thatSamuelson himself later changed his mind (Hands 2014). With theincreasing convergence of (parts of) economics and psychology, theordinal psychological interpretation of preferences appears tocurrently dominate in these disciplines. However, there is an ongoingdiscussion amongst philosophers whether the current concept ofpreference used by economists is this mental,“folk-theoretic” notion or a separate theoretical concept(Mäki 2000, Ross 2014, Thoma 2021).

In philosophy, the concept of preference gained increased attention inthe wake of the conceptual developments in the social sciences.Because the hedonic utility notion was increasingly questioned,utilitarian philosophers sought alternative foundations for theirethical theories. Today,preferentialism defends satisfactionof individual preferences as the only intrinsic value bearer, and thusis a subcategory of the broad welfarist family of value theories,which identify intrinsic value with well-being. Few people defend theview that well-being is constituted by the satisfaction ofany preference, but a number of authors defend refinedversions of preferentialism (e.g. Rawls 1971, Scanlon 1998).Philosophers have also discussed the formal properties of preferencesinpreference logic. To this we turn in the next section.

2. Preference logic

Although not all philosophical references to preference make use offormal tools, preferences are almost always assumed to have structuralproperties of a type that is best described in a formalized language.The study of the structural properties of preferences can be tracedback to Book III of Aristotle’sTopics. Since the earlytwentieth century several philosophers have studied the structure ofpreferences with logical tools. In 1957 and in 1963, respectively,Sören Halldén and Georg Henrik von Wright proposed thefirst complete systems of preference logic (Halldén 1957, vonWright 1963). The subject also has important roots in utility theoryand in the theory of games and decisions. The preferences studied inpreference logic are usually the preferences of rational individuals,but preference logic is also used in psychology and behaviouraleconomics, where the emphasis is on actual preferences as revealed inbehaviour.

2.1 Concepts and notation

There are two fundamental comparative value concepts, namely“better” (strict preference) and “equal in valueto” (indifference) (Halldén 1957, 10). These terms areused to express the wishes of persons, but they are also used forother purposes, for instance to express objective or intersubjectivelyvalid betterness that does not coincide with the pattern of wishes ofany individual person. However, the structural (logical) properties ofbetterness and value equality do not seem to differ between the caseswhen they correspond to what we usually call “preferences”and the cases when they do not. The term “preferencelogic” is standardly used to cover the logic of these conceptseven in cases when we would typically not use the term“preference” in a non-formalized context.

The relations of preference and indifference between alternatives areusually denoted by the symbols \(\succ\) and \(\sim\) or alternatively by\(P\) and \(I\). In accordance with a long-standingphilosophical tradition, \(A\succ B\) is taken torepresent “\(B\) is worse than \(A\)”, as wellas “\(A\) is better than \(B\)”.

The following four properties of the two exclusionary comparativerelations are usually taken to be part of the meaning of the conceptsof (strict) preference and indifference:

It follows from (1) that strict preference is irreflexive, i.e. that\(\neg(A\succ A)\).

The relation \(\succcurlyeq\), “at least as good as” (or moreprecisely: “better than or equal in value to”), can bedefined as follows:

The alternative notation \(R\) is sometimes used instead of\(\succcurlyeq\).

For reasons of convenience, weak preference is usually taken to be theprimitive relation of preference logic. Then both (strict) preferenceand indifference are introduced as derived relations, as follows:

\(\succ\) is thestrict part of \(\succcurlyeq\) and \(\sim\) itssymmetric part.

Two common notational conventions should be mentioned. First, chainsof relations can be contracted. Hence, \(A\succcurlyeq B\succcurlyeqC\) abbreviates \(A\succcurlyeq B \wedge B\succcurlyeq C\), and\(A\succ B\succ C\sim D\) abbreviates \(A\succ B \wedge B\succ C\wedge C\sim D\). Second, the ancestral symbol * is used to contractrepeated uses of the same relation; hence \(\succ\)* stands for\(\succ\) repeated any finite non-zero number of times (and similarlyfor the other relations). Thus \(A\succ *C\) denotes that either\(A\succ C\) or there are \(B_1 \ldots B_n\) such that

2.2 Completeness

In most applications of preference logic, it is taken for granted thatthe following property, calledcompleteness orconnectedness, should be satisfied:

or equivalently:

The following weaker version of the property is sometimes useful:

(Completeness holds if and only if bothweakconnectivity andreflexivity of indifference hold.)

Completeness (connectedness) is commonly assumed in many applications,not least in economics. Bayesian decision theory is a case in point.The Bayesian decision maker is assumed to make her choices inaccordance with a complete preference ordering over the availableoptions. However, in many everyday cases, we do not have, and do notneed, complete preferences. Consider a person who has to choosebetween five available objects \(A, B, C, D\), and \(E\). If she knowsthat she prefers \(A\) to the others, then she does not have to makeup her mind about the relative ranking among \(B, C, D\), and\(E\).

In terms of resolvability, there are three major types of preferenceincompleteness. First, incompleteness may beuniquelyresolvable, i.e. resolvable in exactly one way. The most naturalreason for this type of incompleteness is lack of knowledge orreflection. Behind what we perceive as an incomplete preferencerelation there may be a complete preference relation that we canarrive at through observation, introspection, logical inference, orsome other means of discovery.

Secondly, incompleteness may bemultiply resolvable, i.e.possible to resolve in several different ways. In this case it isgenuinely undetermined what will be the outcome of extending therelation to cover the previously uncovered cases.

Thirdly, incompleteness may beirresolvable. The most naturalreason for this is that the alternatives differ in terms of advantagesor disadvantages that we are unable to put on the same footing. Aperson may be unable to say which she prefers—the death of twospecified acquaintances or the death of a specified friend. She mayalso be unable to say whether she prefers the destruction of thepyramids in Giza or the extinction of the giant panda. Inenvironmental economics, as a third example, it is a controversialissue whether and to what extent environmental damage is comparable tomonetary loss.

Two alternatives are called “incommensurable” whenever itis impossible to measure them with the same unit of measurement. Casesof irresolvable incompleteness are often also cases ofincommensurability (Chang 1997). In moral philosophy, irresolvableincompleteness is usually discussed in terms of the related notion ofa moral dilemma.

2.3 Transitivity

By far the most discussed logical property of preferences is thefollowing:

The corresponding properties of the other two relations are definedanalogously:

A weak preference relation \(\succcurlyeq\) iscalledquasi-transitive if its strict part \(\succ\) istransitive.

Many other properties have been defined that are related totransitivity. The following three are among the most important ofthese:

• \(A\sim B \wedge B\succ C \rightarrow A\succ C\quad\text{(IP-transitivity)}\)
• \(A\succ B \wedge B\sim C \rightarrow A\succ C\quad\text{(PI-transitivity)}\)
• There is no series \(A_1 ,\ldots ,A_n\) of alternatives such that\(A_1 \succ \ldots \succ A_n\succ A_1\) \(\text{(acyclicity)}\)

All of these are ways of weakening the transitivity of \(\succcurlyeq\). Thus, if \(\succcurlyeq\) satisfies transitivity then \(\succ\) and \(\sim\)are also transitive, and furthermore, IP-transitivity, PI-transitivityand acyclicity hold.

Furthermore, if \(\succcurlyeq\) is transitive, then no cyclescontaining \(\succ\) are possible, i.e. there are no \(A\) and \(B\)such that \(A\succcurlyeq *B\succ A\). Preferences with such a\(\succ\)-containing cycle are calledcyclic preferences.

Transitivity is a controversial property, and many examples have beenoffered to show that it does not hold in general. A classic type ofcounterexample to transitivity is the so-called Sorites Paradox. Itemploys a series of objects that are so arranged that we cannotdistinguish between two adjacent members of the series, whereas we candistinguish between members at greater distance (Armstrong 1939,Armstrong 1948, Luce 1956). Consider 1000 cups of coffee, numbered\(C_0, C_1, C_2,\ldots\) up to \(C_{999}\). Cup \(C_0\) contains nosugar, cup \(C_1\) one grain of sugar, cup \(C_2\) two grainsetc. Since one cannot taste the difference between \(C_{999}\) and\(C_{998}\), one might consider them to be equally good (of equalvalue), \(C_{999}\sim C_{998}\). For the same reason, we have\(C_{998}\sim C_{997}\), etc. all the way to \(C_1\sim C_0\), butclearly \(C_0 \succ C_{999}\). This contradicts transitivity ofindifference, and therefore also transitivity of weak preference.

In a related example proposed by Warren S. Quinn, a device has beenimplanted into the body of a person (the self-torturer). The devicehas 1001 settings, from 0 (off) to 1000. Each increase leads to anegligible increase in pain. Each week, the self-torturer “hasonly two options—to stay put or to advance the dial one setting.But he may advance only one step each week, and he mayneverretreat.At each advance he gets $10,000.” In this wayhe may “eventually reach settings that will be so painful thathe would then gladly relinquish his fortune and return to 0”(Quinn 1990, 79).

In an important type of counterexamples to transitivity of strictpreference, different properties of the alternatives dominate indifferent pairwise comparisons. Consider an agent choosing betweenthree boxes of Christmas ornaments (Schumm 1987). Each box containsthree balls, coloured green, red and blue, respectively; they arerepresented by the vectors \(\langle R_1,G_1,B_1\rangle,\) \(\langleR_2,G_2,B_2\rangle\), and \(\langle R_3,G_3,B_3\rangle\). The agentstrictly prefers box 1 to box 2, since they contain (to her) equallyattractive blue and green balls, but the red ball of box 1 is moreattractive than that of box 2. She prefers box 2 to box 3, since theyare equal but for the green ball of box 2, which is more attractivethan that of box 3. And finally, she prefers box 3 to box 1, sincethey are equal but for the blue ball of box 3, which is moreattractive than that of box 1. Thus,

and from this follows

The described situation yields a preference cycle, which contradictstransitivity of strict preference. (Notice the structural similarityto Condorcet’s Paradox, see the entry onvoting methods.)

These and similar examples can be used to show that actual humanbeings may have cyclic preferences. It does not necessarily follow,however, that the same applies to the idealizedrationalagents of preference logic. Perhaps such patterns are due toirrationality or to factors, such as lack of knowledge ordiscrimination, that prevent actual humans from being rational. Thereis a strong tradition, not least in economic applications, to regardfull \(\succcurlyeq\)-transitivity as a necessary prerequisite ofrationality.

The most famous argument in favour of preference transitivity is themoney pump argument. The basic idea was developed by F.P. Ramsey(1928a, 182), who pointed out that if a subject’s behaviourviolated certain axioms of probability and preference, then he would be willing to buy a bet that yields a gain to the seller, and a loss to the buyer, no matter what happens. The argument was developed in more detailin Davidson et al. (1955).

The following example can be used to show how the argument works in anon-probabilistic context: A certain stamp-collector has cyclicpreferences with respect to three stamps, denoted \(A, B\), and\(C\). She prefers \(A\) to \(B, B\) to \(C\), and \(C\) to \(A\).Following Ramsey, we may assume that there is an amount of money, say10 cents, that she is prepared to pay for exchanging \(B\) for \(A,C\) for \(B\), or \(A\) for \(C\). She comes into a stamp shop withstamp \(A\). The stamp-dealer offers her to trade in \(A\) for \(C\),if she pays 10 cents. She accepts the deal.

For a precise notation, let \(\langle X,V\rangle\) denotethat the collector owns stamp \(X\) and has paid \(V\) centsto the dealer. She has now moved from the state\(\langle A,0\rangle\) to the state \(\langle C,10\rangle\).

Next, the stamp-dealer takes out stamp \(B\) from a drawer, andoffers her to swap \(C\) for \(B\), against another paymentof 10 cents. She accepts, thus moving from the state\(\langle C,10\rangle\) to \(\langle B,20\rangle\). The shop-ownercan go on like this forever. What causes the trouble is the followingsequence of preferences:

The money-pump argument relies on a particular, far fromuncontroversial, way to combine preferences in two dimensions, whichis only possible if two crucial assumptions are satisfied: (1) Theprimary alternatives (the stamps) can be combined with some othercommodity (money) to form composite alternatives. (2) Irrespectivelyof the previous transactions there is always, for each preferredchange of primary alternatives, some non-zero loss of the auxiliarycommodity (money) that is worth that change. The money-pump can beused to extract money from a subject with cyclic preferences only ifthese two conditions are satisfied.

Another argument for the normative appropriateness of preferencetransitivity suggests that transitivity is constitutive of the meaningof preference, in addition to the minimal properties mentioned insection 2.1. Drawing an analogy to length measurement, Davidson (1976,273) asks: “If length is not transitive, what does it mean touse a number to measure length at all? We could find or invent ananswer, but unless or until we do, we must strive to interpret‘longer than’ so that it comes out transitive. Similarlyfor ‘preferred to’”. Violating transitivity,Davidson claims, thus undermines the very meaning of preferring anoption over others.

Yet another argument rests on the importance of preferences forchoice. When agents choose from an alternative set, then preferences should bechoice guiding.They should have such a structure that they can be used to guide ourchoice among the elements of that set. But when choosing e.g. from\(\{A,B,C\}\), a preference relation \(\succ\) such that\(A\succ B\succ C\succ A\) does notguide choice at all: any or none of the alternatives should be chosenaccording to \(\succ\). The transitivity of preference, it is thereforesuggested, is a necessary condition for a meaningful connectionbetween preferences and choice. A critic, however, can point out thatpreferences are important even when they cannot guide choices. Takee.g. preferences over lottery outcomes: these are real preferences,regardless of the fact that one cannot choose between lotteryoutcomes. Further, the necessary criteria for choice guidance are muchweaker than weak transitivity (Hansson 2001, 23–25; compare alsoversions of decision theory in which transitivity fails, e.g. Fishburn1991). Last, the indifference relation does not satisfy choiceguidance either. That does not make it irrational to be indifferentbetween alternatives. Thus, choice guidance can be an argument for thenormative appropriateness of transitivity only under certainrestrictions, if at all (For further discussion, see Anand 1993).

2.4 Order typology

One more property of preference relations needs to be specified. Arelation isantisymmetric if

The categories summarized in the table below (based on Sen 1970a) arestandardly used to denominate preference relations that satisfycertain logical properties.

2.5 Combinative preferences

Sections 2.1–2.4 were devoted to exclusionary preferences, i.e.preferences that refer to a set of mutually exclusive alternatives. Inpractice, people also have preferences between relata that are notmutually exclusive. These are calledcombinative preferences.

Relata of combinative preferences are not specified enoughto be mutually exclusive. To say that one prefers having a dog overhaving a cat neglects the possibility that one may have both atthe same time. Depending on how one interprets it, this preferenceexpression may say very different things. It may mean that one prefersa dog (and no cat) to a cat (and no dog). Or, if one already has acat, it may mean that one prefers a dog and a cat to just having acat. Or, if one already has a dog, it may mean that one prefers just adog to both a cat and a dog. Combinative preferences are usually takento have states of affairs as their relata. These are represented bysentences in sentential logic. It is usually assumed that logicallyequivalent expressions can be substituted for each other.

Properties such as completeness, transitivity and acyclicity can betransferred from exclusionary to combinative preferences. In addition,there are interesting logical properties that can be expressed withcombinative preferences but not with exclusionary preferences. Thefollowing are some examples of these (some of which arecontroversial):

Combinative preferences can be derived from exclusionary preferences,which are then taken to be more basic. In most variants of thisapproach, the underlying alternatives (to which the exclusionarypreferences refer) are possible worlds, represented by maximalconsistent subsets of the language (Rescher 1967, von Wright 1972). However, it has been argued that a more realisticapproach should be based on smaller alternatives that cover all theaspects under consideration – but not all the aspects that mighthave been considered. This approach may be seen as an application ofSimon’s “bounded rationality view” (Simon 1957,196–200).

The derivation of combinative preferences from exclusionarypreferences can be obtained with a representation function. By this ismeant a function \(f\) that takes us from a pair\(\langle p,q\rangle\) of sentences to a set\(f(\langle p,q\rangle)\) of pairs of alternatives(perhaps possible worlds). Then\(p\succcurlyeq\)\(_f\)q holds if and only if\(A\succcurlyeq B\) for all \(\langle A,B\rangle \in f(\langle p,q\rangle)\) (Hansson 2001,70–73).

2.6 Preference-based monadic value predicates

In addition to the comparative notions, “better” and“of equal value”, informal discourse on values containsmonadic (one-place) value predicates, such as “good”,“best”, “very bad”, “fairly good”,etc. Predicates representing these notions can be inserted into aformal structure that contains a preference relation.

Two major attempts have been made to define the principal monadicpredicates “good” and “bad” in terms of thepreference relation. One of these defines “good” as“better than its negation” and “bad” as“worse than its negation” (Brogan 1919).

The other definition requires that we introduce, prior to“good” and “bad”, a set of neutralpropositions. Goodness is predicated of everything that is better thansome neutral proposition, and badness of everything that is worse thansome neutral proposition. The best-known variant of this approach wasproposed by Chisholm and Sosa (1966). According to these authors, astate of affairs is indifferent if and only if it is neither betternor worse than its negation. Furthermore, a state of affairs is goodif and only if it is better than some indifferent state of affairs,and bad if and only if some indifferent state of affairs is betterthan it.

The negation-related and the indifference-related “good”respectively “bad” do not necessarily coincide. Bothdefinitions have been developed with complete preference relations inmind, but formal models are available that do not require completeness.(Hansson 2001)

A proposal for defining preferences in terms of the monadic predicatesfor “good” and “bad” was put forward by vanBenthem (1982, p. 195). It assumes that goodness and badness aredefined in relation to an alternative set, so that for instance\(G_{\{x,y\}}x\) means that \(x\) is good among the alternatives in\(\{x,y\}\) and \(B_{\{x,z,w\}}x\) that \(x\) is bad among thealternatives in \(\{x,z,w\}\). This gives rise to the followingdefinitions:

\(x \succ y\) if and only if\(G_{\{x,y\}}x \amp \neg G_{\{x,y\}}y\)  (goodness-based preference)

\(x \succ y\) if and only if\(B_{\{x,y\}}y \amp \neg B_{\{x,y\}}x\)  (badness-based preference)

However, these two definitions are not equivalent, and neither of themis plausible in all cases. For instance, let \(x\) be good and not badin the context \(\{x,y\}\), and let \(y\) be neither goodnor bad in the same context. Then \(x \succ y\) holds according tofirst definition but \(\neg(x \succ y)\) according to the second. Toavoid such problems, Hansson and Liu (2014) proposed the followingdefinition:

\(x \succ y\) if and only if either\(G_{\{x,y\}}x \amp \neg G_{\{x,y\}}y\) or\(B_{\{x,y\}}y \amp \neg B_{\{x,y\}}x\) (bivalently based preference)

3. Numerical Representation of Preference

Preferences can be represented numerically.\(A\succ B\) is then expressed by a set if numerical utilityfunctions \(\{u_i\}\), each of which assigns a higher value to \(A\) than to\(B\), while \(A\sim B\) is represented byassigning the same value to the two. Such numerical representationsmight serve different purposes, one being that utility functions canbe analysed with the tools of maximisation under constraints, as donein economics. It is important, however, to stress the limitations ofsuch representations. First, not all preferences can be representednumerically. Second, there are different scales by which preferencescan be represented, which require premises of different strengths.Third, the resulting utility representation must be clearlydistinguished from the older hedonistic concept of utility.

3.1 Representing preferences ordinally

The simplest form of numerical representation stipulates the followingequivalence:

Any function \(u\) that assigns a larger number to \(A\)than to \(B\) will work as such a representation. Consequently,the function \(u\) can be replaced with any functionu’ as long asu’ is apositivemonotone transformation of \(u\). As this transformationproperty is the defining characteristic ofordinal scales, wecall this an ordinal preference representation (See the entry onmeasurement in science.)

A preference relation has an ordinal representation only if itsatisfies both completeness and transitivity. However, even if\(\mathcal{A}\) is finite, there can becomplete and transitive preference relations on \(\mathcal{A}\)that cannot be represented by a utilityfunction (for a counter-example based on a lexicographic preferencerelation, see Debreu 1954).^[2]

Anincomplete preference ordering also has a valuerepresentation of the following type:

The inverse is obviously not true. However, under fairly widecircumstances, given the set ofall utility functions thusdefined, one can find the preference relation (Aumann 1962).

3.2 Representing preferences cardinally

Ordinal numerical representations of preference are just a convenienttool – they do not represent any information that cannot berepresented by the relation \(\succ\) itself. However, there isrelevant information about preferences that is not represented by therelation \(\succ\) itself. For example, when an agent expresses twopreferences, say \(A\succ B\) and \(C\succ B\), one might askhowmuch the agent prefers \(A\) to \(B\), in particular incomparison to how much she prefers \(C\) to \(B\). To answer thisquestion, one needs to determine both a measurement procedure formeasuring preference intensities and a measurement scale forrepresenting these measurements.

Measurement scales that represent magnitudes of intervals betweenproperties, or even magnitudes of ratios between properties, arecalledcardinal scales. Although the discussion in the socialsciences often merely distinguishes between ordinal and cardinalpreference measures, it is important to further distinguish betweeninterval and ratio scales among the latter, as these require differentassumptions to hold. An interval scale allows for meaningfulcomparisons of differences (e.g. “43°C is as much hotter than 41°C as 29°C is hotter than 27°C”). In addition, a ratioscale also allows for meaningful comparisons of ratios (e.g. “12m is twiceas long as 6m”). Although there have been some attempts to measurepreferences on a ratio scale (in particular, see Kahneman andTversky’s (1979)Prospect Theory, which requires anatural zero point and thus a ratio scale), most efforts have focussedon measuring preferences on an interval scale.

The basic idea of interval preference measurement is to assume thatacts have uncertain consequences, and that each act is equivalent to alottery between these outcomes. An agent who expresses a preferencefor an act over others by choosing it thus expresses a preference forthe equivalent lottery over the lotteries equivalent to other acts.The utilities of these acts are then determined as the expectedutilities of the equivalent lotteries, calculated as theprobability-weighted average of the lottery’s consequences. Thisapproach was pioneered by Ramsey (1928) and refined by von Neumann andMorgenstern (1944); other approaches have been presented by Savage(1954/72) and Jeffrey (1965/90). There are substantial differencesbetween these approaches and their respective assumptions. For moredetail, seedecision theory.

3.3 Alternative utility-based representations of preference

As mentioned in section 3.1, all transitive and complete preferencerelations can be represented by a utility function according to thefollowing simple relationship

However, as can be seen from the Sorites paradox discussed in section2.3, this recipe for the representation of preferences is toodemanding for some purposes. If \(u(A)\gt u(B)\), but \(u(A)-u(B)\) isso small that it cannot be discerned, then \(A\succ B\) cannot beexpected to hold. One way to represent this feature is to employ acardinal utility function and to introduce a fixed limit ofindiscernibility, such that \(A\succ B\) holds if and only if\(u(A)-u(B)\) is larger than that limit. Such a limit is commonlycalled ajust noticeable difference (JND).

If the set of alternatives is finite, then \(\succcurlyeq\) has a JNDrepresentation if and only if \(\succcurlyeq\) is complete, andsatisfies the two properties that for all (A, B, C, D):

Another interesting construction is to assign to each alternative aninterval instead of a single number. This requires two real-valuedfunctions, \(u_{max}\) and \(u_{min}\), such that for all \(A,u_{max}(A)\ge u_{min}(A)\). Here, \(u_{max}(A)\) represents the upperlimit of the interval assigned to \(A\), and \(u_{min}(A)\) its lowerlimit. \(A \succ B\) holds if and only if all elements of the intervalassigned to \(A\) have higher value than all elements of the \(B\)interval:

It has been shown that a preference relation \(\succcurlyeq\) has aninterval representation if and only if it satisfies completeness andthe property that for all \(A, B, C, D\):

(Fishburn 1970).

A final generalization is to let the threshold of discriminationdepend on both relata.

If the set of alternatives is finite, then \(\succcurlyeq\) has a doublyvariable threshold representation if and only if it satisfiesacyclicity.

For more details on these representations, see Scott and Suppes (1958)and Abbas (1995).

4. Preferences combination

In practical decision making, there are often several preferencerelations that have to be taken into account. The different preferencerelations represent different aspects of the subject matter concernedby the decision. For instance, when choosing among alternativearchitectural designs for a new building, we will have a whole set ofaspects, each of which can be expressed with a preference relation:costs, sustainability, aesthetics, fire safety etc. In other cases, thevarious preference relations represent the wishes or interests ofdifferent persons. This applies for instance when a group of peoplewith different preferences plan a joint vacation trip.

4.1 Managing preference conflicts

The most convenient way to represent problems with multiple preferenceaspects is to introduce a vector \(\langle \succcurlyeq_1 ,\ldots,\succcurlyeq_n \rangle\) whose elements are the preference relationswe have to take into account. For simplicity, we can assume that allthese preferences are complete (or we can treat incompleteness asindifference). We can call such a vectorconflict free if andonly if it has no elements \(\succcurlyeq_k\) and \(\succcurlyeq_m\)such that \(X \succ_k Y\) and \(Y \succ_m X\) for any alternatives\(X\) and \(Y\). If \(\langle \succcurlyeq_1 ,\ldots ,\succcurlyeq_n\rangle\) is conflict free, then we can define a combined preferencerelation \(\succcurlyeq\) such that (1) \(X\succ Y\) if there is some\(\succcurlyeq_k\) such that \(X\succ_k Y\), (2) \(Y\succ X\) if thereis some \(\succcurlyeq_k\) such that \(Y\succ_k X\), and (3) otherwise\(X\sim Y\). This is a plausible construction for conflict freepreferences, since the combined preference relation does notcontradict any of the strict preferences expressed in the componentvectors.

Forconflictual preference vectors, i.e. vectors that are notconflict free, there is no such simple solution that is plausible inall applications. There are five common ways to deal with conflictsamong preferences.

1. Reduction to a single dimension. Such reductions areusually performed by first translating all preference relations intosome numerical value, and then, for each alternative, adding up thevalues assigned to it for all aspects. In utilitarian moralphilosophy, a fictional value unit, “utile”, is used forthis purpose. In economics, cost-benefit analysis (CBA) instead uses monetary units. However in many casesthere is uncertainty or disagreement on how the reductions should beperformed.

2. Assuming that all conflicts cancel each other out. Thisamounts to extending the above definition of a combined preferencerelation so that \(X\sim Y\) will hold in all cases of conflict,i.e. whenever there are \(\succcurlyeq_k\) and \(\succcurlyeq_m\) suchthat \(X \succ_k Y\) and \(Y \succ_m X\). Although usually notexpressed in this way, this is the effect of applying efficiency asthe sole criterion (e.g. Pareto efficiency as the sole criterion in amulti-person case). This method has the obvious disadvantage that itsometimes lets a small disadvantage in one dimension outweigh a largeadvantage in another dimension.

3. Majoritarian solutions. Another way to deal with conflictsis to look for the alternatives that are favoured by most (but not necessarily all) of the preference relations. This requires that the aspectscovered by the different preference relations are valued equally.Therefore, this solution is commonly used when the elements of thevector correspond to the wishes or interests of different persons, butnot when they correspond to more general aspects of a decision (suchas sustainability and aesthetics in the example of of choosing anarchitectural design).

4. Intuitive weighing. In practice, decision makers oftenweigh different preference dimensions against each other intuitively,without any prior attempt to reduce the multi-dimensionality of thedecision. This way of dealing with multiple preferences has practicaladvantages, but it also has the disadvantage of lacking efficientmechanisms for ensuring consistency in decision-making.

5. Modifying at least one of the conflicting preferencerelations. This is what happens when people involved innegotiations or discussions approach each other’s views in ways thatmake their preference relations less conflicting. The Delphi method isa systematized procedure that can be used to reduce interindividualdifferences in preferences. On an intraindividual level, strivings fora reflective equilibrium can take the form of adjusting preferencerelations that concern different aspects of an issue to eachother. From a psychological point of view, such changes can bedescribed as reductions of cognitive dissonance in value issues.

Voting procedures are often described as methods for aggregating orcombining preferences. Such aggregation can also be performed by abenevolent planner striving to take the wishes and/or interests of allconcerned persons into account. The aggregation of preferences is amajor topic of social choice theory. See the entry onsocial choice theory.

4.2 Total and partial preferences

Consider again the choice among alternative architectural designs fora new building. As indicated above, our preferences can be expressedwith a vector \(\langle \succcurlyeq_1 ,\ldots ,\succcurlyeq_n\rangle\), each of whose elements represents ourpartialpreferences with respect to some particular aspect such assustainability or aesthetics. If we manage to aggregate the vector toa single preference relation \(\succcurlyeq\), then \(\succcurlyeq\)represents ourtotal preferences, or, as they are alsocalled, our “preferencestout court” or“preferences all things considered”.

Some authors have argued that the preference notion in economicsalways refers to total preferences (Hausman 2012). However, there arealso economists who recognize partial preferences, often identifyingthem with preferences over properties or characteristics of economicgoods (Lancaster 1966). In contrast, philosophers often treat partialpreferences as referring to different reasons that one may have toprefer one of the options to another (Pettit 1991, Osherson andWeinstein 2012).

Authors who recognize partial preferences usually give them priority,and consider total preferences to be completely determined by thepartial preferences. In other words, they assume that a totalpreference relation is uniquely determined by the partial preferencerelations through a process of aggregation. There are different viewson the nature of this process. According to aquantitativeapproach, each partial preference is connected with a cardinal partialutility function for the aspect in question, and the total preferencerelation can be obtained by aggregating these partial utilityfunctions using an appropriate set of weights. This requires strongassumptions of preference independence in order to justify additivityof utility (Keeney and Raiffa 1993).

An alternative strategy employstools from social choicetheory to map a vector of partial preferences into a totalpreference relation. This approach only makes use of ordinalinformation, and disregards any utility information that has no impacton the partial preference relations. Unsurprisingly, the impossibilityresults of social choice theory affect this method. Steedman andKrause (1986) have shown that there is no rule for deriving totalpreferences from a preference vector that satisfies four seeminglyplausible conditions and also yields a transitive and complete totalpreference ordering. When applied to an intrapersonal conflict thismeans that an agent may be rational in the sense of having a completeand transitive (partial) relation for each of the aspects, but maystill be irrational either in the sense of not satisfying plausibleconditions on the relations between partial and total preferences, orin the sense of not having a complete and transitive total preferenceordering for her overall appraisal of the options in question. Thisargument connects with a long philosophical tradition, including Platoand Bishop Butler, that draws an analogy between intrapersonalconflicts and citizens’ conflicting preferences within a state.

There are also authors who reject the idea that total preferences areuniquely derivable from partial preferences. Instead they claim thattotal preferences areconstructed at the moment ofelicitation, and thus influenced by contexts and framings of theelicitation procedure that are not encoded in pre-existing partialpreferences (Payne, Bettman and Johnson 1993). Total preferences seemto be influenced by direct affective responses that are independent ofcognitive processes (Zajone 1980). For instance, food preferences seemto be partly determined by habituation and are therefore difficult toexplain as the outcome of a process exclusively based on well-behavedpartial preferences. According to this view, partial preferences arein many casesex post rationalisations of total preferences,rather than the basis from which total preferences are derived.

A closely related standpoint was expressed by Nozick (1981, 244):“Reasons do not come with previously assigned weights; thedecision process is not one of discovering such precise weights but ofassigning them. The process not only weighs reasons, it (also) weightsthem.” According to Kranz (1991, 34), “[p]eople doandshould act as problem solvers, not maximizers, because they havemany different and incommensurable … goals to achieve”.Much in the same vein, Levi (1986, 246) maintained that “anagent may terminate deliberation and take decisions without havingresolved the moral, political, economic and aesthetic conflictsrelevant to their predicaments”.

5. Preferences and choice

There is a strong tradition, particularly in economics, to relatepreference to choice. Preference is linked to hypothetical choice, andchoice to revealed preference. We begin this section by presentingchoice functions and some of their main properties. We then proceed todiscuss how choice functions and their properties can be derived frompreferences. Finally, we view the relationship from the other end, andintroduce some approaches to inferring preferences from observedchoices.

5.1 Choice functions and their properties

Given an alternative set \(\mathcal{A}\), we can represent(hypothetical) choice as a function \(\mathbf{C}\) that, for any givensubset \(\mathcal{B}\) of \(\mathcal{A}\), delivers those elements of\(\mathcal{B}\) that a deliberating agent has not ruled out forchoice. For brevity’s sake we will call them ‘chosenelements’. The formal definition of a choice function is asfollows:

A large number of rationality properties have been proposed for choicefunctions. The two most important of these are described here.

This property states that if some element of a subset \(\mathcal{B}\)of \(\mathcal{A}\) is chosen from \(\mathcal{A}\), then it is alsochosen from \(\mathcal{B}\). According to property \(\alpha\),removing some of the alternatives that are not chosen does notinfluence choice. This property has often been assumed to hold, butcounterarguments have been raised against it. Consider the followingexample. Erna is invited to an acquaintance’s house fordinner. Her choice for dessert is between an apple (which is the lastpiece of fruit in the fruit basket) \((X)\) and nothing instead\((Y)\). Because Erna is polite, she chooses \(Y\). Had she faced achoice between an apple \((X)\), nothing \((Y)\) and an orange\((Z)\), she would have taken the apple. Thus her choices are:

and

which violate property \(\alpha\). More generally, property \(\alpha\) hasbeen contested with reference to cases when alternatives are preferredfor their position in an alternative set, when the set of alternativesitself constitutes important information about the alternative chosen,or when certain alternatives provide the chooser with the freedom toreject them (Sen 1993, 501–503).^[3]

The second property states that if \(X\) and \(Y\) are bothchosen from the subset \(\mathcal{B}\) of \(\mathcal{A}\),then one of them cannot be chosen in \(\mathcal{A}\)without the other also being chosen.

To exemplify property \(\beta\), suppose that we have threerestaurants, \(X, Y\) and \(Z\), within walking distance, and twoadditional restaurants, \(V\) and \(W\), that we can reach bycar. Furthermore, suppose that we begin by choosing among therestaurants within walking distance. We agree that the choice isbetween \(X\) and \(Y\), but we find no reasons to choose one of themrather than the other, i.e. \(\mathbf{C}(\{X, Y, Z\})=\{X,Y\}\). Then we find out that we do in fact have access to a car.Property \(\beta\) says that if \(X\) is one of the chosen restaurantsin this situation, then so is \(Y\), and vice versa. In other words:\(X\in \mathbf{C}(\{X, Y, Z, V, W\})\) holds if and only if \(Y \in\mathbf{C}(\{X, Y, Z, V, W\})\).

A third property, \(\gamma\), is described in footnote.^[4]

The above properties are mainly found in the social choice literature.A related property in the economic literature is the so-calledWeak Axiom of Revealed Preferences (WARP). It says that if\(X\) is chosen when \(Y\) is available, then there must notbe an alternative set \(\mathcal{B}\) containing bothalternatives for which \(Y\) is chosen and \(X\) is not.

If \(X,Y\in \mathcal{A}\) and \(X\in \mathbf{C}(\mathcal{A})\), thenfor all \(\mathcal{B}\), if \(X\in \mathcal{B}\), and \(Y\in\mathbf{C}(\mathcal{B})\), then \(X\in \mathbf{C}(\mathcal{B})\)  (WARP)

WARP is equivalent to the combination of properties \(\alpha\) and \(\beta\)(Sen 1971, 50). A stronger version, SARP, is discussed in the firstpart of the supplementary document.

The Strong Axiom of Revealed Preference

Counterexamples have been offered to show that these properties arenot plausible in all situations. Consider an agent who chooses to stayat a friend’s house for a cup of tea \((T)\) rather than to gohome \((H)\), but who leaves in a hurry when the friend offers achoice between tea and cocaine \((C)\) at his next visit. Then\(\mathbf{C}(\{T,H\}) =\{T\}\) and \(\mathbf{C}(\{T,H,C\}) =\{H\}\),and hence the visitor violates both properties \(\alpha\) and\(\beta\).

5.2 Determining choice from preference

A choice function that is defined on the basis of a preferencerelation is calledrelational (alsobinary). Themost obvious way to construct a choice function from a preferencerelation \(\succcurlyeq\) is to have the function always choose the elementsthat are best according to \(\succcurlyeq\):

The best choice connection
\(\mathbf{C}^B(\mathcal{B}) = \{X \in \mathcal{B} \mid\forall Y \in \mathcal{B}: (X\succcurlyeq Y)\}\)

\(\mathbf{C}^B\) is a choice function (i.e. satisfies the definingcriteria for a choice function given in section 5.1) if and only if\(\succcurlyeq\) is complete and acyclical. It will then also satisfyproperties \(\alpha\) and \(\gamma\). Furthermore, \(\mathbf{C}^B\)satisfies property \(\beta\) if and only if \(\succcurlyeq\) istransitive and complete (Sen 1970a, 19).

When the underlying preference relation is incomplete, there may notbe an element that is preferred to all other elements. A function\(\mathbf{C}\) constructed according to the best choice connectionwill then be empty, and hence not a choice function. To avoid this, analternative connection constructs the choice function as choosingthose elements that are not dispreferred to any other elements of theset:

The non-dominance choice connection
\(\mathbf{C}^L(\mathcal{B}) = \{X \in \mathcal{B} \mid\forall Y \in \mathcal{B}: \neg(Y\succ X)\}\)

\(\mathbf{C}^L\) is a choice function if and only if \(\succcurlyeq\)is acyclical. It will then satisfy properties \(\alpha\) and\(\gamma\). Furthermore, \(\mathbf{C}^L\) satisfies property \(\beta\)if and only if \(\succcurlyeq\) is transitive and complete (Herzberger1973).

When the preference relation over \(\mathcal{A}\) is cyclical, neither\(\mathbf{C}^B\) nor \(\mathbf{C}^L\) may be a relational choicefunction for \(\mathcal{A}\). In the simplest case, with a cyclicalpreference \(A\succ B\succ C\succ A\), \(\mathbf{C}^B(A,B,C) =\mathbf{C}^L(A,B,C) = \varnothing\). Schwarz (1972) therefore proposesa third relational choice function, which operates even on the basisof cyclical preferences. Its basic idea is to select elements thatare not dominated by non-cyclical preference.

5.3 Inferring preference from choice

The close connections between preference axioms and choice axioms canalso be employed to construct a preference ordering from a choicefunction that satisfies certain axioms. In economics, therevealedpreference approach has been used to define preference in termsof choice. Historically, this approach developed out of the pursuit ofbehaviouristic foundations for economic theories—i.e. theattempt to eliminate the preference framework altogether. Today, itserves to derive preference orderings from an agent’s observedchoices, and to test the empirical validity of the preference axiomsby testing for the violation of choice axioms (Grüne-Yanoff2004).

There are many ways to construct preference relations from observedchoices. The simplest method defines an alternative \(X\) as “atleast as good as” an alternative \(Y\) if and only if\(X\) is chosen from some set of alternatives that also contains\(Y\).

If the choice function is defined over all subsets of \(\mathcal{B},\succcurlyeq^S\) is complete. \(\succ^S\) does not necessarilysatisfy transitivity of strict preference, transitivity ofindifference, IP- or PI-transitivity. Two further methods aredescribed in the supplementary document:

The Strong Axiom of Revealed Preference

The formal relation to choice raises the question of the ontological status of preferences. Are preferences prior to choices, and function potentially as their cause? Or are preferences merely representations of actual or potential choice patterns? Debates about how to interpret preferences in economics have a long history, and in recent years the topic has received renewed attention. This discussion tended to focus on an opposition between behaviourist vs. mentalist interpretations. Many (but certainly not all) economists have interpreted the dominant revealed preference theory in behaviourist terms, claiming for example that “Standard economics does not address mental processes, and as a result, economic abstractions are typically not appropriate for describing them” (Gul and Pesendorfer 2008, 21). Consequently, these authors take the formal relations presented in this section as the determinants of the ontological question what preferences are. Furthermore, they also reject the interpretation of preferences as causes of choice, instead insisting that they only capture choice patterns (Binmore 2008, 19–22).

Mentalists, in contrast, insist that choices and preferences areentities of quite different categories: Preferences arestates ofmind whereas choices areactions. Consequently, theyreject the strong behaviourist program (Hausman 2012). An importantmentalist argument against behaviourist interpretations concerns therole of beliefs in decision making. According to this argument, somechoices are not based on stable preferences over actions, but areconstructed from more basic cognitive and evaluative elements. Asimple choice – like choosing between two pieces ofcandy – might be based on a preference for a world in whichone eats candy \(X\) over a world in which one eats candy \(Y\). Butmore complex choices – e.g. choosing one’s highereducation – depend on what onebelieves these choices tobring about, and how one evaluates these consequences. In those cases,a more complex framework specifies beliefs about the probability orplausibility of possible states of the world, preferences over theconsequences of choices in those worlds, and an aggregation mechanismof these preferences under those beliefs. The need for such acognitive structure to account for preferences has been proposed as anargument against the ontological reduction of preferences to choices(Hausman (2012).

Another argument against behaviourist interpretations points to theapparent existence of preferences over alternatives that one cannotchoose between – for example preferences for winning acertain prize of a lottery, or for particular configurations ofParadise. This contradicts the claim that preferences exclusivelytranspire from choices. One way to substantiate preferences overalternatives that one cannot choose between is to ask people what theyprefer. Their answers can be interpreted as further choiceevidence – as verbal or writingbehaviour. Thisinterpretation treats their answers on a par with all other forms ofbehaviour. Alternatively, their answers can be interpretedasintrospective reports. This interpretation treats answersas agents’ privileged access to their own minds. Furthermore,mentalists also distinguish between those agents who indeed havepreferences as states of minds – e.g. humans, and maybehigher animals – and those agents who donot – e.g. machines, plants or institutions. The formercategory may choose on the basis of their preferences, and hence theabove-discussed effort can aim at eliciting the preferences on whichtheir choices are based. The latter category, despite their lack ofstates of mind, may nevertheless exhibit behaviour that can beinterpreted as relational choice.

Functionalists’ accounts of preferences deny such anintrinsically mental interpretation of preferences, without reducingthem to behaviour. In functionalism, the nature of preferences, likethat of other mental states, is determined by what roles they play– e.g. in evaluating choice alternatives, and in motivatingactions. Yet who assigns these roles, and what justifies suchassignments? Most authors agree that it is “the ontologicalcommitments of our best theory or theories in the relevant area”that perform this assignment (List and Dietrich 2016, 257). Howpreferences are individuated, then, is dependent on the purposes forascribing them. For example, revealed preferences are considered realif they are non-redundantly useful for describing regularities in anindividual’s behaviour:

To show that RPT [revealed preference theory] is useful we must findsome real structures that are usefully measured – where“usefully” means nonredundantly relevant to explanationand prediction–using coefficients and relations defined by itsaxioms. (Ross 2005, 143)

Revealed preference theory is nonredundantly relevant, Ross claims,because it makes sense of patterns like intentionality and agency thatdon’t reduce to physical patterns. To the extent that this isnot merely a predictive but an explanatory task, one needs to admitthe existence of these patterns, thus endorsing “intentionalstance functionalism without sliding into instrumentalism” (Ross2005, 143–4). According to such a view, preferences areidentified by the causal roles they play in generating human, animaland machine behaviour; and they are real to the extent that the besttheories of such behaviour require their attribution.

Recently, some authors have sought to dissolve the simple dialecticbetween mentalism and behaviourism. Guala (2019, 389) argues that thedebate is mainly motivated by a methodological, rather than anontological concern: whether or not economics should accept a healthyinjection of psychological theory and methods depends on theexplanatory tasks at hand. Clark (2020) reasons that whether and howto treat preferences as genuine cognitive variables is a question thatdepends on the epistemic purposes of the investigation (or as hephrased it, “the ultimate aims of economics”). Similarly,Thoma (2021) and Vredenburgh (2020) argue that for their specificpurposes, economists often have good reasons to largely “blackbox” the causes of choice in their modelling of economicbehaviour.

6. Preference and welfare

Preference relates to welfare in rather intricate ways. Welfare is afundamental concept in moral philosophy and economics. It refers tothe fundamental good for individual human beings, and it is thereforean anthropocentric and individualist concept. In order to clarify therelationship between preference and welfare we need to distinguishbetween three variants of the concept of welfare.

According to thematerial view, a person’s welfare is amatter of her material conditions, such as access to food, shelter,healthcare and, generally speaking, the necessities and perhapsluxuries of life. This view of welfare has been criticized for beingmaterialistic in the sense of pursuing material possessions at theexpense of higher values. It also has to face the difficultiesinherent in weighing different material goods against each other.

The other two principal views both treat welfare as a mental ratherthan a material issue. Thewish-based mental view uses eachperson’s wishes (i.e. preferences in the informal sense of thatword) as the criterion of welfare (Sen 1979). A person is consideredto have more welfare, the more her wishes are satisfied. If this viewis applied within a utilitarian framework, then it gives rise topreference utilitarianism. This view of welfare has difficulties indealing with misinformed and self-defeating wishes. It can also havedifficulties with certain types of other-regarding wishes, e.g.malevolent ones. The usual way to deal with this is to require thatpreferences are filtered (“laundered”) and/or refinedbefore they are used to judge a person’s welfare.

The filtering (“laundering”) of preferences can bejustified by the everyday experience that some preferences are muchmore important for a person’s well-being than others. It can beargued that a plausible preference-based account of welfare cannot bebased on total preferences, but would have to be based on a subset of“core” preferences that are important for the individual.The determination of that subset is expectedly contentious. If it isto be determined by others than the individual whose welfare isconcerned, then problems of paternalism will be difficult to avoid.

Refinement of preferences is usually assumed to result in theperson’s (hypothetical) “rational” or “ideallyconsidered” preferences. “My ideally consideredpreferences are those I would have if I were to engage inthoroughgoing deliberation about my preferences with full pertinentinformation, in a calm mood, while thinking clearly and making noreasoning errors.” (Arneson 1989, 83; cf. Brandt 1979 and Rosati 2009) A problemfor this view is that there does not seem to be any easy way todetermine, based on a person’s preferences and circumstances,what her ideally considered preferences would be.

Finally, thestate-dependent mental view identifies aperson’s welfare with some mental state such as happiness orsatisfaction. It is assumed that the relevant states of mind can atleast in principle be judged by external assessors. If such a view isapplied within a utilitarian framework, then it can give rise tohedonistic utilitarianism. This view can be criticized for paternalismand for being uncritical towards arrangements in which individuals arehappy in spite of being oppressed or deprived. Furthermore, thedifficulties involved in comparing mental properties such as happinessin different persons creates a problem for views that depend on suchcomparisons for the determination of welfare. However, recent work onthe measurement of happiness and life satisfaction has challenged thatview, and may have opened up new avenues for research in botheconomics and moral philosophy. (Ng 1997)

Only one of these three views, namely the wish-based one, refers towhat we usually call preferences. However, the other two can also beexpressed in terms of preference (betterness) relations. We can usesuch relations to order material conditions respectively mental statesin terms of how they satisfy the criteria of welfare that we havechosen to apply. It is important to distinguish between on the onehand preferences in the common sense of comparative likings, and onthe other hand the use of a preference relation to express grades ofany property whose structure satisfies the common formal requirementof such a relation.

A common problem for attempts to account for welfare in terms ofpreference is that we expect a person’s view of her own welfareto be essentially self-regarding, but her preferences can refer toconcerns that are not self-regarding, such as her concerns for otherpeople, her views on social justice, and her commitments for instanceto traditions, conventions, and moral ideas (Sen 1977). Our choicesare influenced by this wide range of preferences. Therefore, it doesnot seem possible to link preferences strongly to welfare and at thesame time link them strongly to choice.

7. Preference change

Preferences relate to time in several ways. Preference at one point intime can refer to what happens or happened at other points in time.Furthermore, preferences can change over time, due to changes inbeliefs, values, tastes, or a combination of these. Section 7.1explains why preference change requires explanatory and theoretical treatment. In the following sections, three types of explanatory models arediscussed. (For more detail, see Grüne-Yanoff and Hansson 2009.)Time preference models (section 7.2) only refer tothe temporal relationship between the occurrence of a preference andthe objects it refers to.Doxastic change models (section7.3) investigate how a change of an agent’s beliefs leads to achange in her preferences.Valuational change models (section7.4) investigate how a change in an agent’s basic evaluationsleads to a change in her preferences.

7.1 Evidence for preference change

Some authors have argued that preference change is only a superficialperception, and that the underlying preferences remain stable overtime. But there are at least four arguments to the effect thatpeople’s preferences really do change over time. First, manysuccessful explanations of behavioural change have interpreted theempirical behavioural evidence as preference change. Theseexplanations can be differentiated into models ofexternalinfluences and models ofinternal coherence. Externalinfluence models attempt to establish general links between externalevents and agents’ preference formations. They include, forexample, social imitation (Leibenstein 1950), parental influence(Cavalli-Sforza 1973), habit formation (Pollack 1976), and the effectof production patterns on consumption (Duesenberry 1949). Internalcoherence models take certain external influences as given, and modelpreference change as an accommodation of these external influences.They include, for example, religious convictions (Iannaccone 1990) andthe effect of cognitive dissonance on preferences (Elster 1982).

A second argument for preference change is based on the correlationsbetween physiological changes and changes in behaviour. Changes inblood sugar levels, for example, are correlated to feeding behaviour,sexual behaviour varies with hormonal changes, and many behaviouralpatterns change with increasing age (for references and discussion,see Loewenstein 1996). These correlations are not deterministic; suchbehavioural changes can be resisted in many cases. It is plausible toincorporate these potential physiological effects asvisceralpreferences in the general preference framework, and to treat therelevant physiological changes as closely connected with preferencechanges.

Third, most humans have introspective evidence for their ownpreferences changing over time. The favourite activities of a childare replaced by new pleasures as we grow up. Thus was the experienceof Shakespeare’s Benedick: “…but doth not theappetite alter? A man loves the meat in his youth that he cannotendure in his age” (Much ado about nothing Act II,Scene III). Even in adult life, we are literally overcome by suddenand very radical (“transformative”) changes of preference. Paul (2014) has investigated the types of decision-making that this involves. It would be strange toclaim in such cases that it is only our beliefs about the different types ofactivities that change. Explanations in terms of preference change aremuch more in line with how we spontaneously interpret our experiencesof such changes.

Last, certain concepts like taste refinement or self-restraint cannoteasily be understood without a notion of real preference change. Inparticular, self-restraint presupposes that the motivationalcomponents of one’s self can change, for example, throughmaturation or social influence; and that one can and should planone’s future self by curbing certain appetites or by designingthe environment in ways that affect one’s preferences.

7.2 Time preferences

The value that we assign to obtaining an advantage or disadvantageusually varies with the point in time when we obtain it. In typicalcases, values decrease with time. For instance, most of us wouldprefer receiving a large sum of money now to receiving it five yearslater. Analytically, this temporal factor of evaluations is oftenseparated from time-independent factors of evaluations.

The standard approach to this issue in economic analysis treatspreference as based on value. Value is dealt with in a bifactorialmodel, in which the value of a future good is assumed to be equal tothe product of two factors. One of these factors is a time-independentevaluation of the good in question, i.e. the value of obtaining itimmediately. The other factor represents the subject’s pure timepreferences. It is a function of the length of the delay, and is thesame for all types of goods. The most common type of time preferencefunction can be written

where \(r\) is a discount rate and \(t-t_0\) the duration of thedelay. This is theexponetentially discounted utility model (DU), proposed bySamuelson (1937), which still dominates in economic analysis.

The choice of a discount rate can have a large impact on thecalculated values. It is therefore often politically controversial. Asone example of this, the discount rate used in assessing the economiceffects of climate change can have significant consequences for thepolicy recommendations that are based on these assessments.

There is some evidence that the standard discounted utility modeldoes not adequately represent human behaviour. For a simple example,consider a person who prefers one apple today to two apples tomorrow,but yet (today) prefers two apples in 51 days to one apple in 50 days.Although this is a plausible preference pattern, it is incompatiblewith theexponentially discounted utility model. It canhowever be accounted for in a bifactorial model with a decliningdiscount rate. Pioneered by Ainslie (1992), psychologists andbehavioural economists have therefore proposed to replaceSamuelson’s exponential discounting model with a model ofhyperbolic discounting. The hyperbolic model discounts the futureconsumption with a parameter inversely proportional to the delay ofthe consumption, and can therefore cover examples like the above.

Other deviations from the discounted utility model have also beendemonstrated. Experimental evidence indicates that we tend to discountgains more than losses, and small amounts more than large amounts.Discount rates also differ between different goods (such as money andhealth). For some—but only some—types of goods, improvingsequences of outcomes are preferred to declining sequences. For instance, many would prefer an increasing rather than a decreasing living standard across their work life. These areall patterns that cannot be handled in the bifactorial model with itsobject-independent time preferences (Loewenstein et al 2002). Giventhe empirical evidence, it is an open question whether the concept of“time preferences” is at all descriptively adequate.

It is a separate question whether pure time preferences are rational.Critics argue that one should want one’s life,as awhole, to go as well as possible, and that counting some parts oflife more than others interferes with this goal (Pigou, 1920; Ramsey,1928b; Rawls 1971). According to this view, it is irrational to prefera smaller immediate good to a greater future good, because now andlater are equally parts of one life. Choosing the smaller good or thegreater bad makes one’s life, as a whole, turn out worse:“Rationality requires an impartial concern for all parts of ourlife. The mere difference of location in time, of something’sbeing earlier or later, is not a rational ground for having more orless regard for it” (Rawls 1971, 293). Critics of pure temporalpreferences often attribute apparent departures from temporalneutrality to acognitive illusion (which causes people tosee future pleasures or pains in some diminished form) or to aweakness of will (which causes people to choose optionsagainst their better judgment).

Against the temporal neutrality of preferences, some have argued thatthere is no enduring, irreducible entity over time to whom all futureutility can be ascribed; they deny that all parts of one’sfuture areequally parts of oneself (Parfit 1984). Theyargue, instead, that a person is a succession of overlapping selvesrelated to varying degrees by memories, physical continuities, andsimilarities of character and interests, etc. By this view, it may bejust as rational to discount one’s “own” futurepreferences, as to discount the preferences of another distinctindividual, because the divisions between the stages of one’slife may be as “deep” as the distinctions betweenindividuals.

If pure time preferences are rational, the question arises whetherthey are rationally required to adopt a certain form. Economistswidely consider the EDU model to be the rational standard, to theextent that hyperbolic discounting is considered an indicator ofirrationality worthy of policy intervention (Strotz 1956,O’Donoghue and Rabin 2015). Samuelson (1937, 161), the inventorof the EDU, was more cautious:

any connection between utility as discussed here and any welfareconcept is disavowed. The idea that such a [mathematical]investigation could have any influence upon ethical judgments ofpolicy is one which deserves the impatience of moderneconomists.

Recently, some authors developed critiques of the normative validityof EDU. Hedden (2015) argues that defending EDU would force one tomake untestable distinctions between actual and ultimatepreferences. Callender (2021, see also replies in this special issue)argues that EDU is not a universally valid standard, but instead isdependent on contextual factors as yet unspecified; and that many ofthe current policy recommendations derived from this purportednormative standard are questionable.

A quite different critical approach to discounting is connected withthe idea of sustainability. If sustainability is interpreted asmeaning that future generations should have access to the sameresources as those that the present generation has at its disposal,then sustainability is sure to be in conflict with economic policiesbased on exponential discounting. However, there are also views onsustainability that allow us to use up natural resources if we replacethem by non-natural resources such as new technologies that willcompensate for the loss. Such a “weak” notion ofsustainability appears to be compatible with policies based ondiscounting of future effects, but it has been criticized for putting future generations at disadvantage. (Ng 2005)

7.3 Doxastic preference change

Two kinds of beliefs are especially important for doxastic models. Thefirst is the belief that the presence of state \(X\) makes adesired state \(Y\) more likely. Take for example the belief thatfluoride prevents dental cavities. This can lead a person to preferfluoride toothpaste to others. If she comes to disbelieve thisconnection, she may well abandon this preference. More generally, if\(X\wedge Y\) is preferred to\(X\wedge \neg Y\), then a rise of the probability that\(Y\) given \(X\) will result in a rise in the desirabilityof \(X\), and vice versa.

The second kind of belief relevant for doxastic preference changeconcerns prospects that influence the preference for other prospectswithout being probabilistically related. For example, one’spreference for winning a trip to Florida in the lottery will cruciallydepend on one’s belief about the weather there during thespecified travel time, even though these two prospects areprobabilistically unrelated. More generally, if\(X\wedge Y\) is preferred to\(X\wedge \neg Y\), with \(X\) and \(Y\)probabilistically not correlated, then a rise of the probability that\(X\) will result in a rise in the desirability of \(Y\)(even if it does not affect the probability of \(Y)\), and viceversa.

Jeffrey (1977) provides a simple model of preference change as theconsequence of an agent coming to believe a proposition \(A\) tobe true. His model incorporates both kinds of belief relevant fordoxastic preference change. It is based on the notion of conditionalpreferences. Jeffrey treats preferences as a relation overpropositions, viz. sets of possible worlds. They are represented by autility function \(\mathbf{U}\) (see section 2), such that:

\(\mathbf{U}(X)\) in turn is defined as the probability-weightedaverage of the utility \(u\) of all the possible worlds \(w\) in which\(X\) is true. For unconditional preferences the weighing is built onthe probability function \(P\) that represents the agent’sactual information. The conditional preference ordering\(\succcurlyeq_A\), in contrast, is based on \(P_A\), the probabilitydistribution representing the counterfactual scenario that the agentaccepts proposition \(A\) as true. (For more discussion on theexistence and uniqueness conditions of conditional preferences, seeLuce and Krantz 1971, Joyce 1999, chapter 4, Bradley 1999). Jeffreyshows that the posterior utility function \(\mathbf{U}_A\) is relatedto the prior utility function \(\mathbf{U}\) as follows:

Conditional preferences allow modelling doxastic preference change.What matters for an agent’s evaluation and behaviour are hisunconditional preferences, \(\succcurlyeq_t\), which areunconditional only in the sense that they rely on the agent’sactual information at time \(t\). When the agent accepts a newproposition \(A\) at time \(t+1\), hisconditional-on-\(A\) preferences become his unconditionalpreferences at \(t+1\): \(\succcurlyeq_{t+1} = \succcurlyeq_{A}.\)

Jeffrey’s model is restricted in two ways. First, it requires anunchanging evaluative function \(u\) defined over the atoms of thepropositional space, viz. possible worlds. Thus for all doxasticallychanged preference orderings, the preferences over worlds remainidentical. Second, the model only considers the effects of a beliefchange to certainty. But it is plausible that one’s preference– say, for a vacation in Florida – changes just becauseone believes that it is more likely that there will be a hurricanenext week. Jeffrey’s model can be generalised by introducing amore general probability updating rule (e.g., Jeffreyconditionalisation). An alternative solution was proposed by Bradley(2005). It is based on relatively strong assumptions on the relationbetween prior and posterior unconditional preferences.

An important discussion from economics needs mentioning, namely thequestion whether models of doxastic preference change are capable inprinciple to representall preference changes. This questionoriginates with an important paper by Stigler and Becker (1977), whoargued that a wide range of phenomena which are commonly thought of aspreference changes—like addiction, habitual behaviour, fashionsand the effects of marketing—can be explained by stable,well-behaved preferences. In a rather informal fashion, they arguethat such explanations involve only changes in information (moreprecisely: prices and income), while leaving preferences intact. As aresult of this, economists largely abandoned the discussion ofpreference change, believing that all preference change phenomena canbe explained in this way. Prima facie, their proposed explanationsexhibit important similarities to the discussed accounts of doxasticpreference change. The results from that discussion, which show thatmodels of doxastic preference change are subject to relatively strongconstraints, may therefore put doubt on the orthodox position ineconomics that models of doxastic preference change are capable inprinciple to representall preference changes.

7.4 Valuational preference change

If an agent forms a specific preference as a result of someexperience, further changes in her overall preference state are oftennecessary to regain consistency. A model of preference change cantherefore be constructed as an input-output model in the same style asstandard models of belief change. (Hansson 1995, Liu 2011) Changes inpreference are triggered by inputs that are represented by sentencesexpressing new preference patterns. Hence, if the subject grows tiredof her previous favourite brand of mustard, \(A\), and starts to likebrand \(C\) better, then this will be represented by a change with thesentence “\(C\) is better than \(A\)”, in formal language\(C\succ A\), as an input. However, a change in which the previouspreference \(A\succ C\) is replaced by the new preference \(C\succ A\)can take place in different ways. For instance, there may be a thirdbrand \(B\) that was previously placed between \(A\) and \(C\) in thepreference ordering. The instruction to make the new preferencerelation satisfy \(C\succ A\) does not tell us where \(B\) should beplaced in the new ordering. The new ordering may for instance beeither \(C\succ A\succ B\) or \(C\succ B\succ A\). One way to dealwith this is to include additional information in the input, forinstance specifying which element(s) of the alternative set should bemoved while the others keep their previous positions. In our example,if only \(C\) is going to be moved, then the outcome should satisfy\(C\succ A\succ B\). These and other considerations make it necessaryto modify the standard model of belief change in order to accommodatethe subject matter of preferences.

8. Preference criticism

In scholarly discussions, preferences are usually taken to be open torational criticism only insofar as (i) they have been inconsistent,violating some of the rationally justifiable preference axioms, or(ii) they (in combination with beliefs) commit the agent toinconsistent inferences.

Can there be rationally justifiable claims that certainintrinsic preferences – i.e. preferences that are notdependent on other preferences – are wrong, or should bechanged? The Humean position answers no. Hume distinguished reasonfrom the passion, and argued “that reason alone can never be amotive to any action of the will; that it can never oppose passion inthe direction of the will” (Treatise, Book II, PartIII, Section III). Humeans often took this distinction between beliefsand desires to imply not only that beliefs alone cannot motivateaction, but also that desires are not open to similar rationalcriticism as beliefs. Therefore, Humeans conclude, preferences canonly be criticised if they areextrinsic – i.e.instrumentally derived from other preferences on the basis of beliefs– or inconsistent. Such criticism of extrinsic preferences wouldseem ultimately to be a criticism of false beliefs, and it could beargued that it is therefore not really criticism of preferences(Broome 1993).

Several authors have argued for a more substantial criticism ofpreferences, including that of intrinsic ones. Some critics argue thatsome or all preferences are in fact a kind of belief, and hence opento the same rational criticism as beliefs. Two defences have beenpresented to counter this challenge. First, it has been claimed thatthat desires (standing for motivation in general) are fundamentallydistinct from epistemic states in theirdirection of fit.Beliefs are directed to fit the world; hence their insufficient fitprovides the basis for their criticism. Desires are directed to fitthe world to them; hence they lack this basis for criticism (Smith1987). Second, Humeans have argued that treating desires as beliefs isincompatible with Bayesian decision theory and also with other,non-quantitative, decision theories (Lewis 1988, Collins 1991,Byrne/Hajek 1997).

Some proponents of the criticizability of preferences have referred tosecond-order preferences. An addict may prefer not to prefer smoking;a malevolent person may prefer not to prefer evil actions; an indolentmay prefer not to prefer to shun work; a daydreamer may prefer not toprefer what cannot be realised, etc. First-order preferences arecriticisable if they do not comply with second-order preferences. (Foraccounts of second-order preferences, see Frankfurt 1971, Sen 1977.)Second-order preferences may trigger attempts to change one’spreferences. Methods of self-restraint, self-command andself-improvement have been extensively described (Schelling 1984,Elster 1989, 2000). Already Hume described the possibility ofrationally choosing such expedience (Grüne-Yanoff & McClennen2006).

Critics have argued against the possibility of rationally choosingsuch indirect preference-modifying strategies. Millgram (1998) arguesthat knowledge of the way such desires-at-will were brought aboutmakes it impossible for them to actually function as the desires theyare intended to be. He gives the example of a car salesman, who, inorder to be successful in his work, makes himself prefer the varioususeless knick-knacks that the brand he represents offers for its cars.When the salesman is laid off, the car-dealer offers him a car withall the useless extras that he made himself prefer. Because heremembers how he acquired these preferences, he chooses not to act onthem. So, Millgram argues, the desire-at-will was not genuine. What ismissing, he points out, are the backward-directed inferentialcommitments that genuine preferences bring with them. Only if oneforgets that one acquired a specific preference at will, or if onealso acquires the inferential commitments of such a preference, canpreferring-at-will be successful.

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