Some Elements on Everything You Always Wanted to Know About Introducing Eductive Reasoning in Negative Feedback Environments

In this paper we show how is put into practice one particular process of beliefs formation that agents are likely to undertake in order to answer the behavioural uncertainties they face. Within extreme situations, agents' expectations can either be based on a focal point, or on a process of complex reasoning in which they "forecast the forecasts of the others" (Binmore, 1987), i.e. the eductive reasoning; intermediary situations are possible. As this type of reasoning results from the accumulation of different successive steps, it is probable that the process stops before reaching infinitum, either involuntarily, because the agents have limited eductive abilities, or voluntarily, because they impose themselves a limit, estimating that their opponents will have lower limits. We introduce here a discussion on the negative feedback systems: they correspond to situations where two successive actions have opposite consequences; they are strategic substitutabilities situations, where the eductive reasoning is supported and stabilized. We try to asses the rule that determines the stopping rule of the eductive reasoning, corresponding to the moment when the reflective beliefs become intuitive (Sperber, 1997). We show that this moment rises from the architecture of the verbal communication and is thus "natural" in negative feedback situations; moreover, it is the consequence of a "number attitude" (Dehaene, 1993)