Decision theorists typically assume that a person’s
behaviour can be fully explained in terms of her beliefs and desires. How much these theorems really tell us
is a matter of debate, as discussed above. But on an optimistic
reading of these results, they assure us that we can meaningfully talk
about what goes on in other people’s minds without much evidence
beyond information about their dispositions to choose. Perhaps there is always a way to contrive decision models such that
acts are intuitively probabilistically independent of states. Recall that Savage was trying
to formulate a way of determining a rational agent’s beliefs
from her preferences over acts, such that the beliefs can ultimately
be represented by a probability function.
Such a “weak” notion of
sustainability appears to be compatible with policies based on
discounting of future effects. A second construction method defines an alternative X as
“at least as good as” an alternative Y if and only
if X is chosen from the binary set that contains
Y. The third property requires that an element X that is
chosen from every set in a particular class must also be chosen from
their union. The second property states that if X and Y are
both chosen from
B,
a subset of
A,
then one of them cannot be chosen in
A
without the other also being chosen. In other words, if
≽
satisfies transitivity then
≻
and ∼ are also transitive, and furthermore, IP-transitivity,
PI-transitivity and acyclicity hold. The choice of a discount rate can have a large impact on the
calculated values.
- The
Bayesian decision maker is assumed to make her choices in accordance
with a complete preference ordering over the available options. - Another important thing to notice about Jeffrey’s way of
calculating desirability, is that it does not assume probabilistic
independence between the alternative that is being evaluated, \(p\),
and the possible ways, the \(p_i\)s, that the alternative may be
realised. - For example,
consider the predicament of a mountaineer deciding whether or not to
attempt a dangerous summit ascent, where the key factor for her is the
weather. - Methods of self-restraint, self-command and
self-improvement have been extensively described (Schelling 1984,
Elster 1989, 2000). - In addition to Transitivity and Completeness, vNM
introduce further principles governing rational preferences over
lotteries, and show that an agent’s preferences can be
represented as maximising expected utility whenever her preferences
satisfy these principles.
In a multi-stage process, the inputs
may be more adequately represented as strategies for how to vote at
each stage. In a general framework, that covers these various options,
the individual inputs are usually called strategies. A
voting pattern is an assignment of a strategy to each
participant, in the form of an n-tuple. The decision procedure concerns a set of alternatives that
society has to choose between. In preference-to-choice and
choice-to-choice procedures, the outcome is an element of that
alternative set, or possibly a tie outcome (meaning that no social
choice was made).
Preference and Preference Structure
Economists have traditionally been skeptical
of any talk of a person’s desires and beliefs that goes beyond
what can be established by examining the person’s preferences,
which they take to be the only attitude that is directly revealed by a
person’s behaviour. For these economists, it is therefore
unwelcome news if we cannot even in principle determine the
comparative beliefs of a rational person by looking at her
preferences. Consider first an ordering over three regular options, e.g., the three
holiday destinations Amsterdam, Bangkok and Cardiff, denoted \(A\),
\(B\) and \(C\) respectively. This information suffices to ordinally represent
your judgement; recall that any assignment of utilities is then
acceptable as long as \(C\) gets a higher value than \(B\) which gets
a higher value than \(A\). But perhaps we want to know more than can
be inferred from such a utility function—we want to know how
much \(C\) is preferred over \(B\), compared to how much \(B\) is
preferred over \(A\). For instance, it may be that Bangkok is
considered almost as desirable as Cardiff, but Amsterdam is a long way
behind Bangkok, relatively speaking.
In the former case, it would seem reasonable for the social planner
to use (individual) preferences as inputs into the procedure, whereas
its outcome will be a (social) choice. A practical
reason for this is that in order to obtain a workable solution to a
social problem, the planner can use information not only about what
each individual would prefer most but also about how they value other
alternatives. Two major types of combinations of preferences are relevant in
social science and social philosophy. First, an official such as a
social planner may have the task to satisfy the preferences or choices
of individuals as far as possible, which is not easily done if their
opinions diverge. Such an official will need some form of aggregation
procedure that can be used to make a decision that is based on
individual wishes. Secondly, individuals can make a joint
decision, which is normally done by using some form of voting
procedure.
At each advance he gets
$10,000.” In this way he may “eventually reach
settings that will be so painful that he would then gladly relinquish
his fortune and return to 0” (Quinn 1990, 79). Hedden (2015) argues that defending EDU would force one to
make untestable distinctions between actual and ultimate
preferences. The other definition requires that we introduce, prior to
“good” and “bad”, a set of neutral
propositions. Goodness is predicated of everything that is better than
some neutral proposition, and badness of everything that is worse than
some neutral proposition. The best-known variant of this approach was
proposed by Chisholm and Sosa (1966).
In other words, they assume that a total
preference relation is uniquely determined by the partial preference
relations through a process of aggregation. This requires strong
assumptions of preference independence in order to justify additivity
of utility (Keeney and Raiffa 1993). The basic idea of interval preference measurement is to assume that
acts have uncertain consequences, and that each act is equivalent to a
lottery between these outcomes. An agent who expresses a preference
for an act over others by choosing it thus expresses a preference for
the equivalent lottery over the lotteries equivalent to other acts. The utilities of these acts are then determined as the expected
utilities of the equivalent lotteries, calculated as the
probability-weighted average of the lottery’s consequences. This
approach was pioneered by Ramsey (1928) and refined by von Neumann and
Morgenstern (1944); other approaches have been presented by Savage
(1954/72) and Jeffrey (1965/90).
Screening Decisions and Preference Decisions:
A quite different critical approach to discounting is connected with
the idea of sustainability. If sustainability is interpreted as
meaning that future generations should have access to the same
resources as those that the present generation has at its disposal,
then sustainability is sure to be in conflict with economic policies
based on exponential discounting. However, there are also views on
sustainability that allow us to use up natural resources if we replace
them by non-natural resources such as new technologies that will
compensate for the loss.
Screening Decisions and Preference Decisions
Richard Bradley (2017) defends a similar principle
in the context of the more general Jeffrey-style framework, and so
does Roussos (2020); but the view is criticised by Steele and
Stefánsson (forthcoming-a, forthcoming-b) and by Mahtani
(forthcoming). Such a model seems at odds with
nonconsequentialist ethical theories for which the
choice-worthiness of acts purportedly depends on more than the moral
value of their consequences. The model does not seem able to
accommodate basic deontological notions like agent relativity,
absolute prohibitions or permissible and yet suboptimal acts.
2 Completeness
It is based on relatively strong assumptions on the relation
between prior and posterior unconditional preferences. Voting procedures are often described as methods for aggregating or
combining preferences. Such aggregation can also be performed by a
benevolent planner striving to take the wishes and/or interests of all
concerned persons into account. The derivation of combinative preferences from exclusionary
preferences can be obtained with a representation function. By this is
meant 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).
Preference criticism
Ulysses must make a choice about the manner in which he will sail past
an island inhabited by sweet-singing sirens. In the former case, Ulysses
will later have the choice, upon hearing the sirens, to either
continue sailing home to Ithaca or to stay on the island indefinitely. In the latter case, he will not be free to make further choices and
the ship will sail onwards to Ithaca past the sweet-singing sirens. Ulysses’ decision problem is represented in tree (or extensive)
form in
Figure 1
(where the two boxes represent choice points for Ulysses). So EU theory or Bayesian decision theory underpins a powerful set of
epistemic norms.
First, many
successful explanations of behavioural change have interpreted the
empirical behavioural evidence as preference change. These
explanations can be differentiated into models of external
influences and models of internal coherence. External
influence models attempt to establish general links between external
events and agents’ preference formations.
Others (e.g., Broome 1991a) argue that Transitivity is part of
the very meaning of the betterness relation (or objective comparative
desirability); if rational preference is a judgment of betterness or
desirability, then Transitivity is non-negotiable. With respect to the
car example, Broome would argue that the desirability of a fully
specified option should not vary, simply in virtue of what other
options it is compared with. Either the choice context affects how the
agent https://simple-accounting.org/ perceives the option at hand, in which case the description of
the option should reflect this, or else the choice context does not
affect the option. In a voting
procedure, the inputs are the votes of the individual participants. In
the most common forms of voting, the votes refer to elements of the
alternative set. However, there are also voting procedures in which
voters state not only their first alternative, but also a list of how
they rank the other alternatives.
The former
category may choose on the basis of their preferences, and hence the
above-discussed effort can aim at eliciting the preferences on which
their choices are based. The latter category, despite their lack of
states of mind, may nevertheless exhibit behaviour that can be
interpreted as relational choice. The formal relation to choice raises the question of the ontological status of preferences. 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 contradicts the claim that preferences exclusively
transpire from choices. One way to substantiate preferences over
alternatives that one cannot choose between is to ask people what they
prefer. Their answers can be interpreted as further choice
evidence – as verbal or writing behaviour. This
interpretation treats their answers on a par with all other forms of
behaviour. This interpretation treats answers
as agents’ privileged access to their own minds. Furthermore,
mentalists also distinguish between those agents who indeed have
preferences as states of minds – e.g. humans, and maybe
higher animals – and those agents who do
not – e.g. machines, plants or institutions.
To say that one prefers having a dog over
having a cat neglects the possibility that one may have both at
the same time. Depending on how one interprets it, this preference
expression may say very different program evaluation things. Or, if one already has a
cat, it may mean that one prefers a dog and a cat to just having a
cat. Or, if one already has a dog, it may mean that one prefers just a
dog to both a cat and a dog.
