Cardinal versus Ordinal

What do we mean when we say that a variable is “quantitatively measurable”?We do not necessarily mean that there is only a single way of measuring or scaling it. Temperature is certainly quantitatively measurable, but there are alternative ways of doing so. For example, 320 Fahrenheit is 00 Celsius, and each degree up or down of Celsius corresponds to 1.8 degrees up or down of Fahrenheit. The two scales differ, but only in zero point and unit interval. Similarly, altitude could be measured from sea level or from the center of the earth (shift of zero point) and in feet or meters (shift of unit interval). Both temperature and altitude are more technically called cardinal magnitudes, variables which have the following property: that, regardless of shift of zero-point and unit interval, the relative magnitudes of differences remain the same. In case of altitude, for example, there’s a bigger difference between the heights of the base and crest of Mount Everest than between the ground floor and roof of even the tallest building. This remains true whether we scale altitude in feet or meters or whether we measure it from sea level or from the center of the earth. If people can state that they prefer two million to one million—but not by how much—their utility is said to be an “ordinal” magnitude. Put another way, if Total Utility is an ordinal magnitude we cannot say anything about the  size of Marginal Utility but we can still say whether Marginal Utility is positive or negative.

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