| There is actually a whole theory around this, and has lots of implications for the designs of hedonic and sensory scales. I work on modeling human sensory perception and preference of food and beverage products, and have had to design scales that work as a true "metric"; Most scales suffer from 3 primary problems: 1) avoidance of the endpoints 2) tendency towards the mean 3) minimum information gain For example; on a 10 point scale, very few (> .5% of respondents) will mark a 1 or 10 (this is problem 1). In addition, 5's are over represented VS the expected amount of 4's and 6's (problem 2). These problems together reduce the amount of information inferable from the collected data. There is a number of ways to measure this, including information theory (think of the avoidence of the end points and tendency towards the mean as a lossy compression algorithm for the true signal) or as a sampling of an unrepresentative population to infer the posterior distribution. A 100 point scale has the same problems as above, and in addition suffers from a lack of consistency (reproducibility) - respondents are likely to give a product a different score (say a 92 and 94) when asked about the same product multiple times. This will frequently lead to non-parametric rank reversals, which 1) prove that a 100 point scale is not a "metric" and 2) show that the amount of information is further reduced at higher optionality. Thus - the discrete scales that work best are: A) 1 - 7 B) 1 - 13 as they both do not suffer from avoidance of the end points, both have no selectable mid-point (forcing respondents to choose a point above or below the median), and are highly replicable (very few respondents will switch rank orders). |