Two-by-two typologies with tied middle cells form partially ordered scales.

Evidence

This discussion also allows me to introduce the concept of a partially ordered scale. Some ordinal scales are not completely ordinal. The partial ordering is (1, 1) at the top, (0, 0) at the bottom, but no clear ranking of the (0, 1) and (1, 0) cells in the middle. This is intuitively obvious by performing the common procedure of adding the values of the row and column variables, which produces sums of 2, 1, and 0. — Gary Goertz, Social Science Concepts and Measurement, 1284

Categorization

• DEFINE: Introduces the technical term ‘partially ordered scale’ and shows how the tie in the two middle cells produces it.
• XREF: connects to: A racial binary can be vertically ordered across multiple axes of subordination