A trichotomy of attitudes for decision-making under complete ignorance

This paper investigates ‘complete ignorance’ (CI) in the tradition of the CI literature and provides a characterization of possible attitudes toward ignorance. Pessimism, optimism and a new attitude called neutrality are introduced and defined. These attitudes are shown to define a trichotomy of pure attitudes toward ignorance. Our main assumptions are the Savage independence axiom and a rather weak (linear) scale invariance requirement. We then study the implications of these specific attitudes in terms of decision criteria. Pessimism and optimism are shown to be closely related to the minimax and the maximax criterion respectively. More specifically, we show that under CI a unique variant of the maximin to be called the pessimistic criterion, satisfies independence. That criterion coincide with the Protective criterion, a lexicographical variant of the maximin criterion, introduced by Barber`a and Jackson. An analogous result is obtained for the optimistic criterion. A new ...

• Type: Journal
• Year: 2010
• Where: MSS
• Authors: Ronan Congar, François Maniquet
• Keywords: Hardware, MSS 2010, Neutral Criterion, Optimistic Criterion, Pessimistic Criterion