# Retrospective forecasting

Suppose you had to answer the following question: what were the chances of the Confederate States winning the American Civil War in the eve of the Battle of Gettysburg in 1863?

At first glance, it's not terribly clear what this question means. It's vaguely posed: we haven't made it clear what it means for the Confederacy to "win" the war. We could make this more precise, but it's the comparatively less serious problem with the question. More serious is that we don't know what we're talking about when we ask about the probability of an event taking place when said event happened.

We could, for example, interpret the question as being about the extent to which macroscopic events in the world are influenced by the fact that fundamental physics is not deterministic. For example, it's sensible to ask what the probability of an atom of uranium-235 decaying in a given year was, even if we know that it did decay - in fact, in the ideal setting, this knowledge wouldn't affect our assessment of the chances at all, due to [Fermi's rule](https://en.wikipedia.org/wiki/Fermi%27s_golden_rule). It's an age old question how much this microscopic lack of determinism cascades upwards to a similar lack of determinism on macroscopic scales, but while this question is interesting I also don't have anything novel to say about it.

What I can say is that even if Einstein had been right that God doesn't play dice with the universe, it would still make sense to ask questions such as the one above about the Civil War. The way to make sense of the question in this context is to imagine it as a question conditional only on what we know about the world prior to the Battle of Gettysburg - we exclude any information obtained after the battle. While in a deterministic world [Laplace's demon](https://en.wikipedia.org/wiki/Laplace%27s_demon) could know the outcome of the Civil War with certainty starting from perfect knowledge of an initial state, we don't actually have perfect knowledge about the state of the world in June 1863. We also can't simply condition on the outcome of the war and know it with certainty, since the outcome is something that was only revealed past the deadline to which we restrict ourselves. This puts us in a similar epistemic situation to the paragraph above; except now the question is about the impact of *anything* we don't know on the question we care about rather than only the impact of "irreducible" nondeterminism.

It's important that while we condition only on facts about the state of the world that were available in June 1863, we *don't* do that when it comes to picking a probability distribution over models of the world. In other words, the question we're asking is the following: given our best understanding of how the world works *right now* and how much knowledge we have of the state of the world *dating to before the deadline*, what odds would we give on a particular event taking place?

We can, of course, still cheat by sneaking in what we know happened as part of our understanding inside our model; but this is no different from the usual problem of [overfitting](https://en.wikipedia.org/wiki/Overfitting) and doesn't merit any special consideration.

I won't go into the specific question at the start of the post, but I will direct you to an [old blog post](https://www.overcomingbias.com/2007/11/us-south-had-42.html) by Robin Hanson in which he cites a paper that extracted implied odds of Confederate victory, defined as the Confederacy being able to pay back its debts after the war, from Confederate bond prices posted in the Amsterdam market. Of course markets are often wrong, but we should keep in mind that while we may boast a superior understanding of the world today compared to participants in this market, we're also out of touch with what the state of the world was like in 1863 compared to contemporaries. It's not clear if the net impact would be to make our estimates more or less reliable than theirs.

We might also care about what contemporaries thought of the probability of various different possible futures at the time. In this case, we would have to restrict not only our  information about the state of the world but also our beliefs about models of the world to that of contemporaries. This is only a mild variation on the same exercise, however, and doesn't change the spirit of it.

I'll call this activity "retrospective forecasting". It's acting as if we're forecasting an event that has yet to occur when we in fact know whether it took place or not, and I think it should be one of the primary lenses through which we view (and write about) history.

# Why do retrospective forecasting?

One answer is surprisingly simple and elegant: Bayes' theorem.

Retrospective forecasting is about calculating \\( \mathbb P(\textrm{events} \vert \textrm{model}) \\) for a variety of models we use, or perhaps integrating that against a probability distribution over a family of models if we want to produce a single probability as our final answer. In other words, it's about computing likelihoods. This is important because if we want to do Bayesian updating on our beliefs about which models of the world are how probable, we need to use Bayes' theorem:

\\[ \mathbb P(\textrm{model} \vert \textrm{events}) = \frac{\mathbb P(\textrm{events} \vert \textrm{model}) \times \mathbb P(\textrm{model})}{\mathbb P(\textrm{events})} \\]

Since the likelihood \\( \mathbb P(\textrm{events} \vert \textrm{model}) \\) appears on the right hand side, this means "learning from history" actually *requires* us to do retrospective forecasting. We need to know how likely various events in history were conditional on our models of the world in order to update our beliefs about our models of the world based on what happened in the past. For example, if the disintegration of the USSR is going to be a feather in the cap of free-market economists who believe central planning of an economy is a terrible idea, we must have been able to predict this outcome in advance based on their model of the world. 

There are other reasons to want more retrospective forecasting to be done. I'll give one more in this post: Without having a solid grasp on what contemporaries of an event thought about its chances of turning out one way or another, and how well their beliefs actually aligned with the best that could have been done with the information and understanding in their possession; we are at a loss when we attempt to judge their actions and their character. Was Lincoln a skillful politician who won an inevitable war to preserve the Union and free the slaves, or was he a reckless leader who flipped a coin to decide the fate of the Union instead of pursuing a prudent and more promising course of negotiation? Without retrospective forecasting we can't answer this question.

Another prominent historical figure whose reputation encompasses the whole gamut from genius to incompetence is Napoleon. He's often portrayed as having been successful in the early phase of the Napoleonic Wars due to his military genius, but he grew too enamored with his own success and took the poor decision to launch an invasion of Russia in 1812. The disaster that befell the French army in this expedition paved the way for his eventual downfall two years later.

Perhaps. Or perhaps all of Napoleon's decisions were as reckless as his invasion of Russia, and he merely got lucky when his opponents made one mistake after another when confronting him at [Austerlitz](https://en.wikipedia.org/wiki/Battle_of_Austerlitz), [Auerstedt](https://en.wikipedia.org/wiki/Battle_of_Jena%E2%80%93Auerstedt) and [Friedland](https://en.wikipedia.org/wiki/Battle_of_Friedland). His luck finally ran out when he invaded Russia. Once again, our assessment of a historical figure depends crucially on both our view and their view of the odds that they faced.

I hope the examples of Lincoln and Napoleon are sufficient to make my case.

# Conclusion

The idea of retrospective forecasting is simple, and yet the total lack of it in any history text, written by amateurs and professionals alike, makes it difficult to properly learn from history or to have grounded opinions about the people that lived in the past and the events that they lived through. We're left only with vague verbiage, which is in my opinion a deeply unsatisfying state of affairs.

You can think of this post as a plea to apply the methods and logic of forecasting to the past in an attempt to both learn from it better and to understand it better. The forecasting community so far has been focused almost exclusively on the future, and I think the way of thinking they use actually has broader applicability than that, and I hope it doesn't remain confined to the realm of what is yet to happen.