Single-crossing condition
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In monotone comparative statics, the single-crossing condition or single-crossing property refers to a condition where the relationship between two or more functions[note 1] is such that they will only cross once.[1] For example, a mean-preserving spread will result in an altered probability distribution whose cumulative distribution function will intersect with the original's only once.
The single-crossing condition was posited in Samuel Karlin's 1968 monograph 'Total Positivity'.[2] It was later used by Peter Diamond, Joseph Stiglitz,[3] and Susan Athey,[4] in studying the economics of uncertainty.[5]
The single-crossing condition is also used in applications where there are a few agents or types of agents that have preferences over an ordered set. Such situations appear often in information economics, contract theory, social choice and political economics, among other fields.