The minimax regret criterion was first described by Savage (1951) in the context of uncertainty over world states, and has been advocated more recently for robust decision making with incompletely specified utility functions (Boutilier, Bacchus, and Brafman 2001; Salo and Hamalainen 2001; Boutilier et al.
The minimax regret criterion can be used both for making robust decisions under strict uncertainty and for guiding the elicitation process itself.
Another rival decision theory is the minimax regret criterion.
I will not venture to say here whether the maximin rule, the principle of insufficient reason, or the minimax regret criterion is universally the "most rational" under conditions of uncertainty.
The same reasoning applies to the minimax regret criterion.
Assuming arguendo that this scenario were to develop, at most it would make the principle of insufficient reason and the minimax regret criterion indeterminate.
If the best-case scenario under the dual system was just slightly better, or if the best-case scenario under the unitary system was just slightly worse, the minimax regret criterion would be decisively in favor of the nonguaranteed national forum system.
The principles of insufficient reason and minimax regret criterion would then both be indecisive.
If the difference between the best outcomes were greater than 5, and if the rest of the table remained unchanged, then the minimax regret criterion would prefer the nonguaranteed system.
We have studied availabilities of Laplace criterion, Hurwicz criterion, min-max cost and min-max regret criterion [7-9].
We will name the min-max regret criterion the criterion of min-max risk or losses caused by uncertainty of information, because this criterion guarantees that maximum of losses from the uncertainty of information is as small as possible.