Defining the Mean-Preserving Spread: 3-pt versus 4-pt
Eric Bennett Rasmusen, Emmanuel Petrakis
The standard way to define a mean-preserving spread is in terms of changes in the probability at four points of a distribution (Rothschild and Stiglitz ). Our alternative definition is in terms of changes in the probability at just three points. Any 4-pt mean- preserving spread can be constructed from two 3-pt mean-preserving spreads, and any 3-pt mean-preserving spread can be constructed from two 4-pt mean- preserving spreads. The 3-pt definition is simpler and more often applicable. It also permits easy rectification of a mistake in the Rothschild-Stiglitz proof that adding a mean- preserving spread is equivalent to other measures of increasing risk.
Rasmusen, Eric Bennett and Emmanuel Petrakis (1992), "Defining the Mean-Preserving Spread: 3-pt versus 4-pt," in John Geweke (ed.), Decision Making under Risk and Uncertainty: New Models and Empirical Findings, Amsterdam: Kluwer.