What is decision theory?
Why is the requirement of probabilistic independence problematic? For one thing, in many real-world decision circumstances, it is hard to frame the decision model in such a way that states are intuitively probabilistically independent of acts. For instance, suppose an agent enjoys smoking, and is trying to decide whether to quit or not.
How long she lives is amongst the contingencies that affect the desirability of smoking. It would be natural to partition the set of states according to how long the agent lives. But then it is obvious that the options she is considering could, and arguably should, affect how likely she finds each state of the Decision theory a brief introduction, since it is well recognised that life expectancy is reduced by smoking.
Perhaps there is always a way to contrive decision models such that acts are intuitively probabilistically independent of states. But therein lies the more serious problem. If we are interested in real-world decisions, then the acts in question ought to be recognisable options for the agent which we have seen is questionable.
In other words, this independence must be built into the decision model if it is to facilitate appropriate measures of belief and desire.
But this is to assume that we already have important information about the beliefs of the agent whose attitudes we are trying to represent; namely what state-partitions she considers probabilistically independent of her acts.
The above problems suggest there is a need for an alternative theory of choice under uncertainty. We first describe the prospects or decision set-up and the resultant expected utility rule, before turning to the pertinent rationality constraints on preferences and the corresponding theorem.
Unlike Savage, Jeffrey does not make a distinction between the objects of instrumental and non-instrumental desire acts and outcomes respectively and the objects of belief states of the world.
Rather, Jeffrey assumes that propositions describing states of affairs are the objects of both desire and belief.
On first sight, this seems unobjectionable: The uncomfortable part of this setup is that acts, too, are just propositions—they are ordinary states of affairs about which an agent has both beliefs and desires. Just as the agent has a preference ordering over, say, possible weather scenarios for the weekend, she has a preference ordering over the possible acts that she may perform, and in neither case is the most preferred state of affairs necessarily the most likely to be true.
It is as if the agent assesses her own options for acting from, rather, a third-person perspective. A possible world can be thought of as an abstract representation of how things are or could be Stalnaker ; see also SEP entry on Possible Worlds.
The agent is not required to have preferences over artificially constructed acts or propositions that turn out to be nonsensical, given the interpretation of particular states and outcomes. A Boolean algebra is just a set of e. An algebra is atomless just in case all of its elements can be partitioned into finer elements.
Some of the required conditions on preference should be familiar by now and will not be discussed further.
The next two conditions are, however, not explicitly part of the two representation theorems that have been considered so far: The postulate requires that no proposition be strictly better or worse than all of its possible realisations, which seems to be a reasonable requirement.
Jeffrey himself admitted as much in his comment: The axiom is there because we need it, and it is justified by our antecedent belief in the plausibility of the result we mean to deduce from it.
The first person to prove a theorem stating sufficient conditions for a preference relation to be representable as maximising the value of a Jeffrey-desirability function was actually not Jeffrey himself, but the mathematician Ethan Bolker Even worse, the same preference ordering satisfying all these axioms could be represented as maximising desirability relative to two probability functions that do not even agree on how to order propositions according to their probability.
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.
It is only by imposing overly strong conditions, as Savage does, that we can achieve this. Broader significance of Expected Utility EU theory Even if we suspend doubts about the basic commitments of prominent versions of EU theory which will be taken up in Section 5there is a large question as to what the theory really establishes about how agents should reason in the real world.
This section begins with the negative perspective, by considering the gaps left open by EU theory regarding rational preference attitudes. The positive perspective will then be discussed, in particular the substantial contribution that EU theory makes, not just to questions of choice or practical rationality, but also to epistemology and value theory.
As such, one might doubt whether the theory is adequate for assessing the rationality of real-world choices, or whether it has any substantial content at all. One way to put the worry is in terms of an infinite regress of decisions. Consider for instance, a decision about how to spend a holiday period: What is the full range of available options and how should one conceive the possible outcomes of these options?
It seems the agent faces an initial choice about representation. But such a choice, if it is to be justified, must surely be governed by a theory of rational decision.Decision Theory has 9 ratings and 0 reviews: 94 pages, ebook/5(9). Leonard Savage’s decision theory, as presented in his () The Foundations of Statistics, is without a doubt the best-known normative theory of choice under uncertainty, in particular within economics and the decision sciences.
In the book Savage presents a set of axioms constraining preferences over a set of options that guarantee the existence of a pair of probability and utility functions relative to which the .
Organizational Theory – an introduction Carl Borge-Andersen, Norwegian School of Management, Oslo Introduction This is article, section, 1 presents an overview of Organizational theory.
Definition of an Organization ” An organization is a social system that is consciously constructed to achieve specific goals”.. 6 Chapter 3: Decision theory We shall Þrst state the procedure for determining the utilities of the consequences, illustrating with data from Example 1. Determine the most preferred and the least preferred consequence.
To these consequences assign utilities of 1 and 0 respectively. Decision Theory: A Brief Introduction by Sven Ove Hansson.
Publisher: KTH Stockholm Number of pages: Description: This text is a non-technical overview of modern decision theory. How a decision "should" be made. Refers to the prerequisites of rational decision-making it is a theory about how decisions should be made in order to be rational.