Luce's Coffee Cups
Luce's Coffee Cups
This is a thought experiment that shows that the Indifference relation is not transitive
Suppose we have 402 cups of coffee:
- $c_0$ with 0 grains of coffee
- $c_1$ with 1 grain of coffee, $c_0 \ I \ c_1$
- $c_2$ with 2 grains of coffee, $c_1 \ I \ c_2$
- ...
- $c_{401}$ with 401 grain of coffee, $c_{400} \ I \ c_{401}$
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But we cannot say that there's no difference in $c_0$ and $c_{401}$
- $c_0 \ \not I \ c_{401}$
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It shows that $I$ is not transitive:
- $a \ I \ b, b \ I \ c \not \Rightarrow a \ I \ c$
The reason for it is that there's a sensitivity threshold that is not taken into account
- This is reflected in SemiOrder Preference Structure
Links
- On Indifference: http://econweb.umd.edu/~ozbay/indifference.pdf