Awareness of unawareness is the title of a new paper by Karni and Viero (that ‘o’ should actually be one of these, but I can’t get it work on here). As mentioned in my previous post, I shall start by describing the paper for a non-economist audience, before giving a more technical discussion at the end.

For non-economists:

This paper addresses the question: How should we model decision making when there are aspects of our environment about which we are unaware? This is a very delicate question to pose. If we are unaware of something, then how can it affect our decision making process? Yet if we include it in our decision model, then we are no longer unaware.

Karni and Viero take an approach where they split the world into two different groups of states (edit – in decision theory, a state of the world is a complete description of your decision making environment. If we don’t know something about the environment, this is equivalent to not knowing which is the true state of the world). In the first group are the states of the world that we are fully aware of and can explain perfectly. In the second group are the states that we cannot fully conceive of yet. In the future we might learn more about the world, and some of the states move from the second group to the first.

To facilitate the modelling process, the states in the second group can be treated together as a lump of things that we don’t really know about yet. Although we don’t know anything about these states, we might still be able to form an estimate about how likely it is that they are important. Similarly, we might have a sense about whether these unknown outcomes are likely to be good or bad – we might be either fearful or optimistic about the unknown.

The Karni and Viero framework gives us a formal system within which we can quantify and describe these ideas of increasing or decreasing ignorance, and fear or optimism about the unknown. This might not sound like much but it is important get the foundations in place before we can start answering bigger, real world, questions about how ignorance and unawareness affect decisions.

There are other models that model the same sort of things as Karni and Viero; each of these frameworks have their own technical strengths and weaknesses. This a good thing – modelling unawareness is a tricky thing to do, and it would be amazing if the first attempt turned out to be the best one. At this point the literature is very young, and remains to be seen which approach will be the most useful for answering more applied questions.

For economists:

Like many axiomatic decision theory models, the Karni and Viero framework is notationally dense. However, at its heart is a probabilistically sophisticated agent ala Machina and Schmeidler (1995). The basic objects of decision are conceivable acts, which are Anscombe-Aumann acts over feasible consequences. The wrinkle from the standard model is that the state-space includes some states that are not fully describable (i.e. some states may include currently inconceivable consequences). If a new consequence is ‘discovered’ then we can augment both the state space and the consequence space to account for the new discovery.

After a new discovery, Karni and Viero impose some consistency axioms on the decision maker’s preferences. Firstly, risk preferences are unaltered by new discoveries. Secondly, new discoveries do not change preferences over acts that are unaffected by the new information. Thirdly, relative likelihoods of measurable events are not affected when new discoveries allow for finer partitions of these events (absolute likelihoods may be affected by the discovery). With these additional axioms, Karni and Viero are able to provide a representation theorem for their framework.

At this point of the paper (around p. 10) they reader feels like they have done a lot of work for very little benefit. It is at this stage, however, that the reader can feel their conceivable state space expanding. Karni and Viero introduce the notions of increasing and decreasing ignorance – as the agent’s awareness grows the may either feel like the unknown universe is either expanding or shrinking. Each of these concepts is given an axiomatic foundation and has a neat interpretation in the representation theorems.

The readers conceivable state space expands again as Karni and Viero introduce extended conceivable acts to allow measurement of the utility of unknown consequences. Because of the agent’s ignorance, the set of extended conceivable acts is not an Anscombe-Aumann set of acts, although it is still a convex set. Using this extended set of acts it is possible to provide an axiomatization and representation theorem that allows a characterization of an agent’s attitude towards the unknown – are they fearful or optimistic of what they might discover in the future?

This is a young area of research, and this paper gives the reader good reason to be optimistic of what might be discovered in the future. There is a hint of an application in the conclusion (relating to home-bias of investments), but I am sure that there are also many other applications for this type of model.