Ordinal vs cardinal status: Two examples

Cardinal and Ordinal Numbers

This paper will present a brief set-theoretic construction of the natural numbers before discussing in detail the ordinal and cardinal numbers. It will then investigate the relationship between the two proper classes, in particular the similar difficulties in discussing the size of the classes. We will end with a short section on the cardinalities of well-known infinite sets with which the read...

Ordinal and cardinal solution concepts for two-sided matching

We characterize solutions for two-sided matching, both in the transferableand in the nontransferable-utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade matching to study the role of transfers in matching. A no-trade matching is one in which the avai...

Are social welfare functions ordinal or cardinal ?

On Ordinal, Cardinal, and Expected Utility

By formally defining the relevant mathematical spaces and models we show that the operations of addition and multiplication, and the concepts that depend on these operations, are not applicable on ordinal, cardinal, and expected utility. Furthermore, expected utility’s scale construction rule is self-contradictory.

Ordinal and cardinal measures of health inequality: an empirical comparison.

When measuring health inequality using ordinal data, analysts typically must choose between indices specifically based upon ordinal data and more standard indices using ordinal data, which has been transformed into cardinal data. This paper compares inequality rankings across a number of different approaches and finds considerable sensitivity to the choice between ordinal- and cardinal-based in...