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Critical Cost Efficient Index (CCEI): A measure of GARP (Generalized Axiom of Revealed Preference). It was first proposed by Afriat (1972). It is a useful and interesting index to verify the consistency of human rationality.

CCEI is the amount by which the budget constraint must be relaxed in order to remove all violations of GARP, denoted as e in this passage. The data set $$\{p_i,x_i\}$$ is the observations of subjects' decisions, where $$p_i$$ is a price vector and $$x_i$$ is the decision choice made by subject. That the option $$x_i$$ is revealed preferred to $$x_j$$ is equivalent to that $$ep_{i}x_{i}>p_{i}x_{j}$$. $$e^\star$$ is the largest e among the dataset $$\{p_i,x_i\}$$. $$1-e^\star$$ is the "wasting" proportion of the money which is invested inefficiently.



There is one violation of GARP in Figure: Example of CCEI Construction. We say that $$x^1$$ is revealed preferred to $$x^2$$ at the prices when $$x^1$$ is purchased, while $$x^2$$ is revealed preferred to $$x^1$$ at the prices when $$x^2$$ is purchased. Since $$A/B$$ is larger than $$C/D$$, the CCEI of the instance is A/B.