# When is it appropriate to use statistical models and probabilities for decision making ?

I enjoy reading rationalist and effective altruist blogs. Members of the community usually back their arguments with data and/or other evidence and tend to be scientifically literate. And although no one is a perfect, detached belief updater, I found that rationalists are probably the community that is closest to that ideal. However, I believe this community often commits a fallacy while attempting to think rationally. It is **the fallacy of applying cost benefit analysis under deep uncertainty**. What is deep uncertainty ? I found a great definition in the textbook [Decision making under deep uncertainty](https://link.springer.com/content/pdf/10.1007%2F978-3-030-05252-2.pdf) by Marchau et al., so I’m simply going to quote it :

> Complete certainty is the situation in which we know everything precisely. This is almost never attainable, but acts as a limiting characteristic at one end of the spectrum.
> 
> **Level 1 uncertainty** represents situations in which one admits that one is not absolutely certain, but one does not see the need for, or is not able, to measure the degree of uncertainty in any explicit way (Hillier and Lieberman 2001, p. 43). These are generally situations involving short-term decisions, in which the system of interest is well defined and it is reasonable to assume that historical data can be used as predictors of the future. Level 1 uncertainty, if acknowledged at all, is generally treated through a simple sensitivity analysis of model parameters, where the impacts of small perturbations of model input parameters on the outcomes of a model are assessed. Several services in our life are predictable, based on the past such as mail delivery and garbage collection. These are examples of this level of uncertainty.
> 
> **In the case of Level 2 uncertainties**, it is assumed that the system model or its inputs can be described probabilistically, or that there are a few alternative futures that can be predicted well enough (and to which probabilities can be assigned). The system model includes parameters describing the stochastic—or probabilistic—properties of the underlying system. In this case, the model can be used to estimate the probability distributions of the outcomes of interest for these futures. A preferred policy can be chosen based on the outcomes and the associated probabilities of the futures (i.e., based on “expected outcomes” and levels of acceptable risk). The tools of probability and statistics can be used to solve problems involving Level 2 uncertainties. Deciding on which line to join in a supermarket would be a Level 2 problem.
> 
> **Level 3 uncertainties** involve situations in which there are a limited set of plausible futures, system models, outcomes, or weights, and probabilities cannot be assigned to them—so the tools of neither Level 1 nor Level 2 are appropriate. In these cases, traditional scenario analysis is usually used. The core of this approach is that the future can be predicted well enough to identify policies that will produce favorable outcomes in a few specific, plausible future worlds (Schwartz 1996). The future worlds are called scenarios. Analysts use best-estimate models (based on the most up-to-date scientific knowledge) to examine the consequences that would follow from the implementation of each of several possible policies in each scenario. The “best” policy is the one that produces the most favorable outcomes across the scenarios. (Such a policy is called robust.) A scenario does not predict what will happen in the future; rather it is a plausible description of what can happen. The scenario approach assumes that, although the likelihood of the future worlds is unknown, the range of plausible futures can be specified well enough to identify a (static) policy that will produce acceptable outcomes in most of them. Leaving an umbrella in the trunk of your car in case of rain is an approach to addressing Level 3 uncertainty.
> 
> **Level 4 uncertainty** represents the deepest level of recognized uncertainty. A distinction can be made between situations in which we are still able (or assume) to bound the future around many plausible futures (4a) and situations in which we only know that we do not know (4b). This vacuum can be due to a lack of knowledge or data about the mechanism or functional relationships being studied (4a), but this can also stem from the potential for unpredictable, surprising, events (4b). Taleb (2007) 8 V. A. W. J. Marchau et al. calls these events “black swans.” He defines a black swan event as one that lies outside the realm of regular expectations (i.e., “nothing in the past can convincingly point to its possibility”), carries an extreme impact, and is explainable only after the fact (i.e., through retrospective, not prospective, predictability). In these situations, analysts either struggle to (Level 4a) or cannot (Level 4b) specify the appropriate models to describe interactions among the system’s variables, select the probability distributions to represent uncertainty about key parameters in the models, and/or value the desirability of alternative outcomes.
> 
> Total ignorance is the other extreme from determinism on the scale of uncertainty; it acts as a limiting characteristic at the other end of the spectrum.

As you can see, the textbook distinguishes 4 levels of uncertainty. Statistical models and probabilities are considered useful up until level 2 uncertainty.

Starting at level 3 the system is considered too uncertain to assign probabilities to scenarios, but the number of scenarios is limited. An example of level 3 uncertainty is, perhaps, the possibility of conflict between two neighboring states. Even though it can be impossible to assign a probability to the event of war because of the immense number of factors that come into play, we know the two possibilities are “war” and “no war”. It is thus possible to take an action that leads to the best results across both scenarios.

In level 4a, the number of scenarios is large. In level 4b, we have no idea what the scenarios are or how many they are. Level 4 is usually what is called deep uncertainty.

I believe many organisations and thinkers use level 2 methods in level 3 or level 4 contexts. Here is an example. In [this blog post](https://www.econlib.org/archives/2016/04/global_warming_13.html), rationalist adjacent economist Bryan Caplan argues that a cost benefit analysis of climate change action shows that it might actually be less costly to do nothing. But climate change is a case of deep uncertainty and cost benefit analysis does not apply. There are many **unknown unknowns** and therefore estimates of the costs of climate change damage are not reliable nor valid. I enjoy reading Caplan but in this case I think his argument leads to a false sense of certainty.

Another example of this fallacy, in my opinion, are [80000 hours’ rankings of urgent world issues](https://80000hours.org/problem-profiles/). For example, they consider that AI risk is a more pressing issue than climate change. Although I admit that is possible, I don’t think their justification for that belief is valid. All of the systemic risks they attempt to rank involve unknown unknowns and are thus **not quantifiable**. One also has to keep in mind that we are very likely exposed to other systemic risks that we do not yet know about.

My goal with this blog post is not to give a lecture on decision making under uncertainty. Firstly, because I don’t consider myself knowledgeable enough in this domain yet and haven’t finished reading the book. Secondly, because I think the book is excellent (and freely available !) and that I won’t do a better job than the authors in teaching you their subject. My goal is to raise awareness about this problem in the rationalist community in order to improve discourse about systemic risks and decision making under uncertainty.

As a Data scientist, I believe it is important to be aware of the limits of the discipline. To this date, I think our quantitative methods are unable to fully inform decisions under deep uncertainty. But I am hopeful that progress will be made. Perhaps we can develop reinforcement learning agents capable of evolving in environments of deep uncertainty ?