However, alternative frameworks, where this is not thecase, have been developed (e.g. Loomes and Sugden 1982). ≻Sdoes not necessarily satisfy transitivity of strict preference,transitivity of indifference, IP- or PI-transitivity. Relata of combinative preferences typically are not specified enoughto be mutually exclusive. To say that one prefers having a dog overhaving a cat does neglect the possibility that one may have both at thesame time. Depending on how one interprets it, the preferenceexpression may say very different things. Or, if one already has a cat,it may mean that one prefers a dog and a cat to just having a cat.
Types of goods affecting preferences
For practical purposes, however, this method is notvery helpful, as the space of prices and goods bundles is verylarge. Social scientists do not have the resources to observe agents’choices from all relevant preference sets. If they want toderive a transitive preference relation from a choice function notdefined over all subsets (up to three elements), then they have torestrict themselves to consider only choices that satisfy thestrong axiom of revealed preferences (SARP). It says that ifX is chosen when Y is available, and if in someother budget set Y is chosen when Z is available,then there can be no budget set containing alternatives X andZ for which Z is chosen and X is not. Finally, decision theory should be of great interest tophilosophers of mind and psychology, and others who are interested inhow people can understand the behaviour and intentions of others; and,more generally, how we can interpret what goes on in otherpeople’s minds. Decision theorists typically assume that aperson’s behaviour can be fully explained in terms of herbeliefs and desires.
- The postulaterequires that no proposition be strictly better or worse than all ofits possible realisations, which seems to be a reasonablerequirement.
- The most naturalreason for this type of incompleteness is lack of knowledge orreflection.
- Incontrast to this, economists commonly conceive of items as bundles of goods, represented as vectors.[1] However, this approach has a difficult ambiguity.
- Inthe most common forms of voting, the votes refer to elements of thealternative set.
Most commonly used axioms
Thesequestions will be addressed in turn, after the scene has been set withan old story of Ulysses. The decision theories of Savage and Jeffrey, as well as those oftheir critics, apparently concern a single “one shot only”decision; at issue is an agent’s preference ordering, andultimately her choice of act, at a particular point in time. The questionarises as to whether this framework is adequate for handling morecomplex scenarios, in particular those involving a series or sequenceof decisions; these are referred to as sequential decisionproblems. A social choice function takes us from each voting pattern,i.e., total input, to an outcome. The outcome may either beone of the alternatives that the procedure has been set up tochoose between, or it may be the tie outcome (λ).
3 Formal representation
First, an official such as asocial planner may have the task to satisfy the preferences or choicesof individuals as far as possible, which is not easily done if theiropinions diverge. Such an official will need some form of aggregationprocedure that can be used to make a decision that is based onindividual wishes. Secondly, individuals can make a jointdecision, which is normally done by using some form of votingprocedure. Last, certain concepts like taste refinement or self-restraint cannotbe understood without a notion of real preference change. Can there be rationally justifiable claims that certainintrinsic preferences—i.e.
Review Questions
It can actually be seen as a weak version ofIndependence and the Sure Thing Principle, and it plays a similar rolein Jeffrey’s theory. But it is not directly inconsistent withAllais’ preferences, and its plausibility does not depend on thetype of probabilistic independence that the STP implies. The postulaterequires that no proposition be strictly better or worse than all ofits possible realisations, which seems to be a reasonablerequirement. When \(p\) and \(q\) are mutually incompatible, \(p\cupq\) implies that either \(p\) or \(q\) is true, but not both.
Strict versus weak
In contrast, a voting procedure does not consist in combining thepreferences of the participants. The objects of combinations are votes,that in most voting systems take the form of opting for one of thealternatives under consideration. (Of course, individuals can beexpected to vote in a way that reflects their preferences, but it isnevertheless the votes, not the preferences, that areinputs into the voting procedure.) Therefore, it is more adequate torepresent voting as a choice-to-choice procedure.
For example, when an agent expresses twopreferences, say \(A\succ B\) and \(C\succ B\), one might ask howmuch 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. 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 idealized rationalagents of preference logic.
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 xero community a largeadvantage in another dimension. A preference decision involves choosing among multiple capital investment options based on their potential returns and alignment with strategic goals. It typically follows an initial screening process where non-viable projects are eliminated.
Therefore, their theory canrepresent Allais’ preferences as maximising the value of anextended Jeffrey-desirability function. For one thing, in many real-world decision circumstances, it is hardto frame the decision model in such a way that states are intuitivelyprobabilistically independent of acts. For instance, suppose an agentenjoys smoking, and is trying to decide whether to quit or not.
Under certain assumptions, the overallor aggregate preference ordering is compatible with EUtheory. Dietrich and List (2013 & 2015) have proposed aneven more general framework for representing the reasons underlyingpreferences. In their framework, preferences satisfying some minimalconstraints are representable as dependent on the bundle of propertiesin terms of which each option is perceived by the agent in a givencontext.
