States of Nature and the Nature of States

Abstract

A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription For more information, please contact the WRAP Team at: wrap@warwick.ac.uk "If a tree falls in a forest and no one is around to hear it, does it make a sound?" IntroductionSubjective probability quantifies a decision maker's degree of belief in the likelihoods of events about which reasonable decision makers might disagree. Borel (1924) and Ramsey (1926) proposed the key idea that subjective probabilities may be inferred from the odds a decision maker is willing to offer (or accept) when betting on events or the truth of certain proposition. Both authors require that the event on which a bet is placed be observable, so that the uncertainty is resolved and the payments can be affected. In the words of Borel, "I can in the same way offer to someone who enunciates a judgment capable of verification a bet on his judgment" (Borel 1964: 57).To formalize the idea of resolution of uncertainty, Savage (1954) introduced the idea of state of nature, "a description of the world so complete that, if true and known, the consequences of every action would be known" (Arrow 1971: 45). Implicit in this definition is the notion that there is a unique true state that is fully depicted by the consequences associated with every possible action. In practice, however, decision theorists and economists routinely specify a state space as a primitive constituent of the decision problem. Savage himself applied this "state-first" approach when he wrote, "If two different acts had the same consequences in every state of the world, there would from the present point of view be no point in considering them different acts at all. An act may therefore be identified with its possible consequences. Or, more formally, an act is a function attaching a consequence to each state of the world" (Savage 1954: 14). However, treating the state space as a primitive ingredient of the model tends to conceal critical aspects of the notion of states and imposes tacit and unnecessary restrictions on its usefulness.The purpose of this note is twofold. First, it discusses and elaborates an approach to modeling the resolution of uncertainty described in Fishburn (1970), Schmeidler and Wakker (1987), and Karni and Schmeidler (1991). Second, it examines the implications of this approach for the modeling of the choice set in the theory of decision making under uncertainty. States of Nature Reality and perceptionAlbert Einstein is reported to have asked Niels Bohr whether he believed that the moon does not exist if nobody is looking at it. Bohr replied that however hard he (Einstein) might try, he would not be able to prove that it does. In other words, following Quine (1948Quine ( /1949, an object is a theoretical interpretation of perceived sensory...

A theory of stochastic choice under uncertainty

“…Note that, if alternatives are agreed upon by distinct observers, then the derived state space is objective and is determined independently of the preferences of the decision maker. As pointed out by Karni (2015), in general, the states iñ do not correspond to complete and transitive preference relations. However, suppose that there is a choice function c :M !M (i.e., c (M ) M; for all M 2M) that satis es the weak axiom of revealed preference.…”

“…However, unlike Kreps, who derived the existence of an in nite subjective state space from preference for exibility (that is, from preferences over menus), we take the existence of a nite subjective state space as a primitive aspect of the model (which nds its expression in preferences over menus). To construct the subjective state space, we can use the approach of Karni (2015) according to which there is a nite set,F ; of alternatives. Menus are nonempty subsets ofF : LetM denote the set of all menus consisting of elements ofF : The subjective state space induced byM is the set of mappings~ := f!…”

“…A random utility function is a ( nitely additive) probability measure on a set of utility functions. Gul and Pesendorfer (2006) gave necessary and su cient conditions for a random 11 The properties are: Re exivity (i.e., (f; f ) = 1). Weak transitivity (i.e., for all f; g; h 2 H; (f; g) = 1 implies (f; h) (g; h)).…”

Causality: a decision theoretic approach

“…In decision theory, Karni ([12], [13]) explores models where a DM can affect the states that are realized. In those papers, the primitive objects are a set of actions and a set of consequences.…”

The State Of Regional Economics: Specificity Of Linguistic Interpretation

“…As it's generally known, being based on the human construal of reality, language interprets and reinterprets the knowledge about the world influencing the possible ways of cognizing and communicating. One of the most intriguing issues of present-day science deals with integrative aspects of linguistics and other social and exact sciences (Karni, 2017;Machina, 2003;Protevi, 2019;Richardson, 1978;Vanderschraaf, 2019).…”