Abstract :
[en] How many degrees can adults reliably distinguish on the confidence scale ranging from 0% to 100% ? Reading the literature, it appears that the confidence scales offered to the respondents to test questions largely vary in terms of number of degrees (Leclercq, 1982). The most “compressive” choice consists in two possibilities, such as adding to the response a Z for “Zekerheid” (Van Naerssen & Van Beaumont, 1965). The other extreme, named “Continuous confidence marking” by De Finetti (1965), consists in allowing the respondent to express his confidence with any precision he likes (.3 as well as .3472, or 30% as well as 34.72%). It is easy to demonstrate that a precision of percentages with two decimals is illusory. This demonstration can be made by a straightforward method: repetition, i.e. asking twice the respondent to provide a confidence degree. This is made after a given delay (one hour, one day, one weak, one month or more) from the first time. The same question and the answer on the first trial are re-presented, and the confidence is re-asked. Of course, and this is a first challenge, this design can be applied only to contents on which the respondent could neither learn nor forget in the time interval. This kind of domain exists. The second challenge is to ensure that, during the two occasions, the mindset of the respondent is the same. Inspired by Shannon and Attneave, a Leclercq Guessing Game (LGG) has been conceived that satisfies these requirements. The design has been applied to a series of university students, eliciting a series of “repetition curves”, the characteristics of which (Mode, Mean, Standard deviation, Skewness) have been studied. This permits to propose an “optimal” number of degrees, i.e. a sensible balance between the concern of subtlety (precision or sensitivity) and reliability (trustfulness or credibility), and to suggest their formats (Percentages, intervals, odds ratios). This has many implications not only in terms of confidence instructions but also in terms of interpretation of results and design of confidence indices such as centration, coherence and calibration, indices that constitute central elements in experimental designs, and in the definition of cognitive mastery.
