An odd number of ordinal levels gives exactly one clear crossover point

Evidence

Critical for concept development is the 0.50 point, the half-empty or half-full point. With an odd number of levels there will be a clear crossover point, e.g., 3 in a 1–5 scale. For example, the Aid Transparency Index2 has five categories: (1) very poor, (2) poor, (3) fair, (4) good, and (5) very good. — Gary Goertz, Social Science Concepts and Measurement, 801

Categorization

• DEFINE: The 0.50 point is defined as the half-empty/half-full membership threshold in fuzzy-set terms.
• QUESTION: Does an even number of levels merely shift the ambiguity elsewhere, or does it force two candidates for the crossover? Worth chasing in the chapter’s own treatment of even scales.