ordinal preferences just tell you which outcomes you like more than others: apples more than oranges.
Interval scale preferences assign numbers to outcomes, which communicates how close outcomes are in value: kiwi 1, orange 5, apple 6. You can say that apples have 5 times the advantage over kiwis that they do over oranges, but you canāt say that apples are six times as good as kiwis. Fahrenheit and Celsius are also like this.
Ratio scale (ārationalā? š) preferences do let you say that apples are six times as good as kiwis, and you need this property to maximize expected utility. You have to be able to weigh off the relative desirability of different outcomes, and ratio scale is the structure which let you do it ā the important content of a utility function isnāt in its numerical values, but in the ratios of the valuations.
Isnāt the typical assumption in game theory that preferences are ordinal? This suggests that you can make quite a few strategic decisions without bringing in ratio.
From what I have read, and from self-introspection, humans mostly have ordinal preferences. Some of them we can interpolate to interval scales or ratios (or higher-order functions) but if we extrapolate very far, we get odd results.
It turns out you can do a LOT with just ordinal preferences. Almost all real-world decisions are made this way.
ordinal preferences just tell you which outcomes you like more than others: apples more than oranges.
Interval scale preferences assign numbers to outcomes, which communicates how close outcomes are in value: kiwi 1, orange 5, apple 6. You can say that apples have 5 times the advantage over kiwis that they do over oranges, but you canāt say that apples are six times as good as kiwis. Fahrenheit and Celsius are also like this.
Ratio scale (ārationalā? š) preferences do let you say that apples are six times as good as kiwis, and you need this property to maximize expected utility. You have to be able to weigh off the relative desirability of different outcomes, and ratio scale is the structure which let you do it ā the important content of a utility function isnāt in its numerical values, but in the ratios of the valuations.
Isnāt the typical assumption in game theory that preferences are ordinal? This suggests that you can make quite a few strategic decisions without bringing in ratio.
From what I have read, and from self-introspection, humans mostly have ordinal preferences. Some of them we can interpolate to interval scales or ratios (or higher-order functions) but if we extrapolate very far, we get odd results.
It turns out you can do a LOT with just ordinal preferences. Almost all real-world decisions are made this way.