What does a sound decision depend on more: on solving the decision problem or on how it was posed? In this short article for teachers Mazur answers: on how it was posed. Before anything is calculated, someone has to settle what is the goal, what is a condition and what is freedom of choice. Such ‘pre-decision decisions’ usually weigh more than the calculation, yet they are rarely noticed — even specialists in mathematical methods tend to concentrate on the difficulties of the solving itself.
The author describes typical errors in the language of this division: the goal is adopted without reflection, only some of the means are taken into account, and too many factors are treated as untouchable conditions. This shows most clearly in curriculum reforms that shift hours between subjects instead of asking whether subjects, lessons and their length are needed at all. A few other examples from school, concerning the selection of what pupils are taught, foreign languages and spelling, show problems posed too narrowly. The remedy has two steps: first a full list of factors, then their proper division; in a curriculum reform this means that every item of content needs justification, not only the proposed change.
The calculation itself is presented concisely. The author distinguishes three groups of quantities: the objective (criterion) quantity, which is to be as large or as small as possible; parameters, that is, conditions over which the decision-maker has no influence; and the decision variable, which the decision-maker is free to choose. The optimal decision is the value of the decision variable at which the criterion reaches an extreme. Underlying this is the distinction between merely reaching a goal and reaching it in the most sensible way: only the latter requires a comparison of means, and the result of the comparison depends on the measure adopted and on the conditions. The background is decision theory, which by then had been developing for a dozen or more years thanks to computing machines, together with the observation that every choice — from small everyday ones to professional and planning choices — has, at bottom, the form of an optimisation problem.
The article is an accessible, short exposition of a theme that the author develops in the book Cybernetyka a zarządzanie (‘Cybernetics and Management’) from the same year. In our reading, the concept of pre-decision decisions also links it to the later division of the decision process into postulation, optimisation and realisation (the articles of 1976 and 1980), in which indicating the goal becomes a separate kind of decision, and goals, ways and means adjust to one another.
Our own account, working version; definitions of concepts are in the dictionary, with their sources.