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Summary of a « formal definition or rationality » by Hasties & Dawes

Ecrit par 015035 le 3 janvier 2017

Decision making is the main issue of foreign policy. In order to justify a public choice a decision maker may invoked gods, like the ancients greeks or based its explanation upon rationality. This key concept of international relations theory has been formalized through a set of axioms at the foundation of the decision theory.

pythie

Ancient greeks decision making through the oracle : the Pythie

I propose a summary of these axioms from the Hastie and Dawes book : »Rational choice in an uncertain world », actually the chap 12 : A normative, rational decision theory.

The decision theory axioms rest on the coherence between choice and numerical value. The best choice is the most valuable one. More over, rationality of the decision process rest within the process, not in its product : the decision.

Two economists, Von Neumann and Morgenstern’s theoretical framework, established a set of axioms which enable one to build a function mapping choice and numerical value. If a decision maker’s choice follows these axioms, then it is possible to build a numerical function based on real numbers which represent its personal preferences. Based on this function, it is possible to derive a decision criteria in order to rank all possible decisions. Hence, the best decision will be the one satisfying this criteria, named the expected utility.

As a consequence, a decision maker’s choice which follow these axioms will be coherent regarding his preferences and his decision will optimize his gain, hence he will be rational. The main constraint is to assign a number to each consequence, named the utility. The expected utility of each choice is computed as the sum of these numbers time the consequence probability distribution. The decision process is summarized by : « the decision maker will prefer choice A to choice B if and only if the expected utility  associated with A is greater than that associated with B ».

The set of axioms formalizing the rationality concept of the decision process is : 

  • Property 1 : comparability as meaning that for any two real numbers x and y, x > y, y>x or x=y
  • Property 2 : ordering, the transitive ordering of the numbers
  • Property 3 : additive closure
  • Property 4 : addision is associative
  • Property 5 : addition is symmetric
  • Property 6 : cancellation
  • Property 7 :the archimedean property
  • Property 8 : solvability, if x>y there exists a z such that x<y+z

If the utility function follows these axioms, the number of the utility function will behave in a similar way as the value produce by a pan balance. If the choices concerned objects, the decision maker utility value or preference is the object mass. The real number of the utility function are unique.

A measurement scale with these axioms is technicaclly called a ratio scale. Hence, a scale of utilities can be constructed in which the real numbers represent the values or preferences of consequences in an orderly manner.

In real political life, a decision maker is asked to make judgement about his utilities or preferences upon the consequences and his intelligence agency produces subjective probabilities of occurrence. Then, the best decision may be computed from these numbers. Reciprocally, an intelligence analyst may induced these judgement according to the axioms to predict that actor’s decision.

lepenseur

from : http://www.truthdig.com/cartoon/item/the_overthinker_20110306

In fact, people do not satisfy the axioms in many decision making contexts and theses cases will be studied in another chapter.

To go further on the limits of the rational decision process with Daniel Kahneman : Intelligent Decision Making 2016

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