Although decision aids exist to support shared decision-making, they are rarely used in practice (Hill et al., 2009; Morecroft et al., 2006). A challenge in shared decision-making highlighted in the studies lies in understanding individual decision-making preferences, which vary among patients (Carey et al., 2012; Davies and Cleary, 2005; Körner et al., 2012; McKinstry, 2000; Murray et al., 2007a; Ramfelt and Lützén, 2005). Gender, age, and socioeconomic status may all influence patients’ preferences for involvement in decision making (McKinstry, 2000; Murray et al., 2007a; Schneider et al., 2006; Singh et al., 2010).
An alternative strategy employs tools 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.
Utility Theory and Decision Theory
On the values side, manycontend that a rational agent may simply find twooptions incomparable due to their incommensurablequalities. Likewise, on the belief side, some contend (notably,Joyce 2010) that the evidence may be such that it does not commit arational agent to precise beliefs measurable by a unique probabilityfunction. Start with the Completeness axiom, which says that an agent cancompare, in terms of the weak preference relation, all pairs ofoptions in \(S\). Whether or notCompleteness is a plausible rationality constraint depends both onwhat sort of options are under consideration, and how we interpretpreferences over these options. If the option set includes all kindsof states of affairs, then Completeness is not immediatelycompelling.
5 Procedural preferences
Possible world modelling hasthe advantages of generality and logical beauty, but it also has thedisadvantage of cognitive unrealism. In practice, we are not capableof deliberating on anything approaching the size of completelydeterminate possible worlds. It can therefore be argued that a morerealistic approach should be based on smaller alternatives that coverall the aspects under consideration—but not all the aspects thatmight have been considered. This approach may be seen as anapplication of Simon’s “bounded rationality view” (Simon1957, 196–200, Hansson 1996b). 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.
2 Completeness
With respect to the car example, Broome would arguethat the desirability of a fully specified option should not vary,simply in virtue of what other options it is compared with. Either thechoice context affects how the agent perceives the option at hand, inwhich case the description of the option should reflect this, or elsethe choice context does not affect the option. The decision procedure concerns a set of alternatives thatsociety has to choose between. In preference-to-choice andchoice-to-choice procedures, the outcome is an element of thatalternative set, or possibly a tie outcome (meaning that no socialchoice was made). In preference-to-preference procedures, the outcomeis a preference relation over the set of alternatives. Such creative and adaptive weighting processes are crossword clue: single entry in a list crossword solver sensitive to taskcomplexity, time pressure, response mode, framing effects, and othercontextual factors.
Decision Theory
- 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.
- However, the ingredients and structure of his theoremwill be laid out, highlighting its strengths and weaknesses.
- Economists have traditionally been skepticalof any talk of a person’s desires and beliefs that goes beyondwhat can be established by examining the person’s preferences,which they take to be the only attitude that is directly revealed by aperson’s behaviour.
- In practical reasoning, it is an important issue whether preferencesare rationally criticisable.
- Nevertheless, Lewis’ argument nodoubt provoked an interesting debate about the sorts of connectionsbetween belief and desire that EU theory permits.
Ulysses’ decision problem is representedin tree (or extensive) form in Figure 1 (where thetwo boxes represent choice points for Ulysses). Even if we suspend doubts about the basic commitments of prominentversions of EU theory (which will be taken upin Section 5), there is a large question as towhat the theory really establishes about how agents should reason inthe real world. This section begins with the negative perspective, byconsidering the gaps left open by EU theory regarding rationalpreference attitudes. The positive perspective will then be discussed, inparticular the substantial contribution that EU theory makes, not justto questions of choice or practical rationality, but also toepistemology and value theory. It can actually be seen as a weak version ofIndependence and the Sure Thing Principle, and it plays a similar rolein Jeffrey’s theory.
However, under fairly widecircumstances, given the set of all utility functions thusdefined, one can find the preference relation (Aumann 1962). 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) vertical analysis of balance sheet 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).
Inany case, it turns out that when a person’s preferences satisfySavage’s axioms, we can read off her preferences a comparativebelief relation that can be represented by a (unique) probabilityfunction. The two central concepts in decision theoryare preferences and prospects (orequivalently, options). Roughly speaking, we say that anagent “prefers” the “option” \(A\) over \(B\) justin case, for the agent in question, the former is more desirable orchoice-worthy than the latter. This rough definition makes clear thatpreference is a comparative attitude; it is one of comparing optionsin terms of how desirable/choice-worthy they are. Beyond this, thereis room for argument about what preferences over options actuallyamount to, or in other words, what it is about an agent (perhapsoneself) that concerns us when we talk about his/her preferences overoptions. This section considers some elementary issues ofinterpretation that set the stage for introducing (in the nextsection) the decision tables and expected utility rule that for manyis the familiar subject matter of decision theory.