Is there a right not be predicted? In his book Against prediction, Bernard E. Harcourt contends that the widespread use of actuarial methods in criminal justice, particularly for predicting future criminal behavior, is fundamentally flawed and potentially harmful.¹ Harcourt, B., 2000. Against Prediction. Chicago: University of Chicago Press. Harlow, Caroline Wolf. He argues that these predictive techniques, rather than reducing crime or improving justice, actually reshape our concept of just punishment and can lead to increased racial profiling and discrimination. Harcourt posits that prediction tools create a self-fulfilling prophecy: by focusing law enforcement resources on groups deemed “high-risk,” we increase the likelihood of detecting crime in these groups, which in turn reinforces the initial prediction. This cycle, he argues, exacerbates existing inequalities and distorts our understanding of crime patterns. Furthermore, Harcourt suggests that the reliance on these tools shifts the focus of the criminal justice system away from rehabilitation and towards mere risk management, potentially undermining important principles of justice and individual rights.

This would seem to suggest that in order to avoid profiling and bias, prediction should not be used in cases where such techniques can create self-reflexive phenomena like self-fulfilling prophecies. So we can imagine a right not to predicted in cases like this, but what about more generally? What if there is a chance that a prediction might influence us in a positive way? Should it still be prohibited? Or are there cases where we would in fact have a right to be predicted?

The obvious case for the latter is in medicine. Here we would argue that if there are methods that can be used to diagnose us and predict treatments that could help us, we have some right to equal access to those methods. Widespread testing is a version of this: if there is a significant improvement in survival chances for a disease, and a simple test that is reliable for that disease, we sometimes considers it a duty of the state to perform that test and ensure that we get the treatment if we needed it.

Thomas Ploug argues in “The Right Not to Be Subjected to AI Profling Based on Publicly Available Data—Privacy and the Exceptionalism of AI Profiling” that there should be a right not to be predicted, even on the basis of publicly available data.² See Ploug, T. The Right Not to Be Subjected to AI Profiling Based on Publicly Available Data—Privacy and the Exceptionalism of AI Profiling. Philos. Technol. 36, 14 (2023). https://doi.org/10.1007/s13347-023-00616-9 . He argues for a sui generis legal right not to be subjected to AI profiling based on publicly available data without explicit informed consent.³ The question of consent here is really tricky, since prediction from publicly available data may be very broad, and the subject of consent would probably be rather general. He further contends that AI profiling poses unique threats to individual autonomy, wellbeing, and social participation due to its potential for accurate predictions, increased social control, and stigmatization. The article develops three key arguments for protecting personal data: the social pressure argument, the ‘open future’ argument, and the stigmatization argument. It then explains why AI profiling is exceptional in its risks compared to other forms of data processing. The author considers reasons for and against protecting publicly available online data, arguing that online engagement has important social and democratic benefits that could be undermined by unchecked AI profiling. The article examines whether existing EU GDPR regulations adequately protect against AI profiling, concluding that they do not, and advocates for an explicit right. Ploug does acknowledge several areas requiring further research, including the justification for framing this as a right, potential exemptions, and the role of informed consent – all interesting.

It is interesting to note the focus on accurate predictions. If we believed that the predictions were not accurate⁴ When does a prediction cross that accuracy threshold? That is also an interesting question., would our view of the rights question then change? But an erroneous prediction, taken as accurate may be even more harmful to us! So what do we do then? Should we, as some argue, instead focus on the results of predictions so we can challenge them?⁵ See eg M., DUBNIAK. (2023). The right to results of data processing in the form of predictive conclusions obtained by artificial intelligence. Інформація і право, Available from: 10.37750/2616-6798.2023.4(47).291615

And should we focus on the prediction as such, or the acting on that prediction in anticipating someone? A more interesting question here seems to be if there is a right not to be anticipated, not to have someone act in such a way as to use a prediction about us to reduce our optionality. And in sometimes that will mean not sharing predictions with us – as in the case of genetic predictions.⁶ See for example: Gunnar, Duttge. (2021). The Right to Know and not to Know: Predictive Genetic Diagnosis and Non-diagnosis.. Recent results in cancer research, Available from: 10.1007/978-3-030-63749-1_6 Here, knowledge about a heightened risk to succumb to a disease may change our outlook on life, our options and impact us psychologically in such a way as to be compared to physical violence or restraint.

Any philosophy of prediction would have to incorporate this into the overall discussion to understand more clearly how predictions interact with institutions, ethics and more. While often framed as a privacy question⁷ Cast as “predictive privacy” see e.g. Rainer, Mühlhoff. (2023). Predictive privacy: Collective data protection in the context of artificial intelligence and big data. Big Data & Society, Available from: 10.1177/20539517231166886 , this may well be a much more fundamental question about the temporality of action and rights.

Footnotes and references

• 1
  Harcourt, B., 2000. Against Prediction. Chicago: University of Chicago Press. Harlow, Caroline Wolf.
• 2
  See Ploug, T. The Right Not to Be Subjected to AI Profiling Based on Publicly Available Data—Privacy and the Exceptionalism of AI Profiling. Philos. Technol. 36, 14 (2023). https://doi.org/10.1007/s13347-023-00616-9
• 3
  The question of consent here is really tricky, since prediction from publicly available data may be very broad, and the subject of consent would probably be rather general.
• 4
  When does a prediction cross that accuracy threshold? That is also an interesting question.
• 5
  See eg M., DUBNIAK. (2023). The right to results of data processing in the form of predictive conclusions obtained by artificial intelligence. Інформація і право, Available from: 10.37750/2616-6798.2023.4(47).291615
• 6
  See for example: Gunnar, Duttge. (2021). The Right to Know and not to Know: Predictive Genetic Diagnosis and Non-diagnosis.. Recent results in cancer research, Available from: 10.1007/978-3-030-63749-1_6
• 7
  Cast as “predictive privacy” see e.g. Rainer, Mühlhoff. (2023). Predictive privacy: Collective data protection in the context of artificial intelligence and big data. Big Data & Society, Available from: 10.1177/20539517231166886

All predictions are made from some model of the predicted phenomenon, and it is sometimes useful to think of that model as a set of assumptions about the world. Some assumptions will be very basic – like assumptions of continuity, uniformity and normalcy, whereas others may be more specific. One way of understanding a prediction, then, is to say that it is composed of assumptions and has the form:

(i) Given assumptions a(1)…a(x) it seems reasonable to predict X.

This simplified form suggests that we can judge the robustness of a prediction by looking more closely at the robustness of the set of assumptions used to make the prediction. What questions, then, should we ask about the assumptions? The obvious ones seem to be things like “is this a reasonably complete set of assumptions?” and “are these assumptions credible?”, but there are also other interesting questions, like the ones suggested by Charles Manski in his Identification for Prediction and Decision (HUP 2009).¹ See Manski, C.F., 2009. Identification for prediction and decision. Harvard University Press.

In his work Manski challenges conventional economic analysis by advocating for a more nuanced approach to uncertainty and prediction. He critiques the reliance on strong assumptions in traditional models, which often lead to precise but potentially unreliable point predictions. Manski distinguishes between weak assumptions, which are more credible but yield less definitive conclusions, and strong assumptions, which produce more precise predictions but are often less realistic. He argues that weak assumptions, while resulting in partial identification and a range of possible outcomes, ultimately enhance the credibility of economic analysis. By contrast, strong assumptions may artificially narrow the range of predictions, potentially misleading decision-makers. Manski promotes the use of partial identification methods, which acknowledge data limitations and produce a spectrum of possible outcomes. This approach, he contends, leads to more robust and honest analysis, enabling policymakers to make better-informed decisions by understanding the full range of potential consequences and the true extent of uncertainty in economic predictions.

This distinction between weak and strong assumptions strikes me as really important, and almost suggests a principle for is to work with – that we should work to achieve the most accurate prediction possible on the weakest assumptions possible. And even if this principle does not always hold, we should state the strength of the assumptions we work on in order to understand better how the prediction can fail.

*

Of anything it is helpful to ask the very simple question “how does this break?”. This is true for predictions as well, and a large part of the answer to that question for predictions is that they break already in the assumptions. Because the assumptions that we use are often biased, incomplete or wrong – and this goes for all layers of assumptions, from general to specific. Let’s look at a few cases.

• Assumptions of normalcy. A simple way for a prediction to break is that we assume that things will largely be normal in some sense. An example would be assuming that someone will arrive as planned, but extreme weather may derail their plans. Assumptions of normalcy are interesting in that they are based on some kind of idea of a state of the world that is labelled as normal – but it is not clear for what set of world variables this is assumed; is it for all variables in the world model? But how normal is it for everything to be normal? Or is it for a majority of the world variables?
• Assumptions of uniformity. These are closely related to assumptions of normalcy, and they break when we think that everything in a predicted set is uniform. Say we want to predict how well we will fare against a number of chess players, and that one of them is Magnus Carlsen. If we do not know this we will work with average chess players in our models, and the outlier case of Carlsen will break the prediction.
• Assumptions of configuration. We often assume that a problem is configured in a special way, and that this configuration is given for this kind of problem. We may assume, for example, that a problem is a 2 person game, whereas the real configuration is that it is a n-person game where we do not know how many persons are playing the game.
• Assumptions of time. There are a set of assumptions that are about pace, rhythm, time needed etc. These assumptions break when there is a step change in the time with which something can be accomplished. The simplest example may be something like Blitzkrieg, where earlier assumptions in military strategy were that it would take a number of days to establish a front, attack and make military maneuvers.

These are just a few of the assumptions that can break in different ways — there are many others, and an interesting exercise is to list your assumptions and try to understand how they can break, and in what ways they are brittle.

*

How many assumptions should we make when we predict something? Is it better to make many assumptions or will fewer assumptions make for a better prediction? Going back to our toy model above – are predictions more robust when X increases, or what is the relationship between the number of assumptions and the robustness of a prediction? It is tempting here to assume that we should be looking at some kind of decreasing utility curve that grows fast in the beginning and then levels out at some point, but even so it is interesting to think about where that point is.

This seems related to Jezz Bezos’ observations on how much of the information you should aim to have when you make a decision. Bezos writes:

Day 2 companies make high-quality decisions, but they make high-quality decisions slowly. To keep the energy and dynamism of Day 1, you have to somehow make high-quality, high-velocity decisions.
Easy for start-ups and very challenging for large organizations. Speed matters in business.
First, never use a one-size-fits-all decision-making process. Many decisions are reversible, two-way doors. Those decisions can use a light-weight process. For those, so what if you’re wrong?
Second, most decisions should probably be made with somewhere around 70 percent of the information you wish you had. If you wait for 90 percent, in most cases, you’re probably being slow. Plus, either way, you need to be good at quickly recognizing and correcting bad decisions. If you’re good at course correcting, being wrong may be less costly than you think, whereas being slow is going to be expensive for sure.

So, does this mean that you should have 70 percent of the assumptions you would ideally want? That is at least one way of thinking about it. The other approach is to think about assumptions as variables in a Fermi-problem.² Fermi problems, named after physicist Enrico Fermi, are estimation exercises that involve breaking down complex questions into smaller, more manageable components. The method works by leveraging the power of decomposition and approximation to arrive at reasonably accurate estimates for seemingly intractable problems. The key principle is that while individual estimates may have significant errors, these errors tend to cancel out when multiple estimates are combined, leading to a surprisingly accurate final result. This approach is particularly effective because it allows problem-solvers to use readily available information and reasonable assumptions to tackle questions where precise data might be lacking.

Superforecasters, as identified and studied by Philip Tetlock, often employ Fermi-style reasoning in their predictive work. They apply this method by:

1. Breaking down complex forecasting questions into smaller, more easily estimable components.
2. Making educated guesses for each component based on known facts and reasonable assumptions.
3. Combining these estimates mathematically to arrive at a final prediction.
4. Iteratively refining their estimates as new information becomes available.

This approach allows superforecasters to make more accurate predictions by leveraging their broad knowledge base, critical thinking skills, and ability to make reasonable approximations. It also helps them to identify key factors influencing outcomes and to adjust their forecasts systematically as circumstances change. The Fermi problem approach aligns well with superforecasters’ tendency to think probabilistically, consider multiple perspectives, and remain open to updating their views – all traits that contribute to their exceptional predictive accuracy. There is no simple way to determine the optimal number of sub-problems a problem should be broken up into when you Fermize it, but there seems to be an upper bound – breaking a problem up into 100 subproblems is hardly viable. Perhaps we should even think about this as the famed 5+-2 rule of cognitive processing memory?

Footnotes and references

• 1
  See Manski, C.F., 2009. Identification for prediction and decision. Harvard University Press.
• 2
  Fermi problems, named after physicist Enrico Fermi, are estimation exercises that involve breaking down complex questions into smaller, more manageable components. The method works by leveraging the power of decomposition and approximation to arrive at reasonably accurate estimates for seemingly intractable problems. The key principle is that while individual estimates may have significant errors, these errors tend to cancel out when multiple estimates are combined, leading to a surprisingly accurate final result. This approach is particularly effective because it allows problem-solvers to use readily available information and reasonable assumptions to tackle questions where precise data might be lacking.
  
  

  Superforecasters, as identified and studied by Philip Tetlock, often employ Fermi-style reasoning in their predictive work. They apply this method by:
  
  

  1. Breaking down complex forecasting questions into smaller, more easily estimable components.
  2. Making educated guesses for each component based on known facts and reasonable assumptions.
  3. Combining these estimates mathematically to arrive at a final prediction.
  4. Iteratively refining their estimates as new information becomes available.

  This approach allows superforecasters to make more accurate predictions by leveraging their broad knowledge base, critical thinking skills, and ability to make reasonable approximations. It also helps them to identify key factors influencing outcomes and to adjust their forecasts systematically as circumstances change. The Fermi problem approach aligns well with superforecasters’ tendency to think probabilistically, consider multiple perspectives, and remain open to updating their views – all traits that contribute to their exceptional predictive accuracy.

Another concept that is closely related to prediction is that of surprise. If we predict X and what instead happens is sufficiently different from X we experience a specific feeling of surprise — but the outcome needs to not just be different in some small degree, but in a very specific way. The way an outcome needs to be different from the prediction suggests that around every predicted outcome there is a zone of expected outcomes, and at some point this reverts into a zone of surprise.

Surprise has been the subject of research of different kinds. One of the more intriguing papers in this field is “Surprise: a unified theory and experimental predictions.” By Alireza, Johanni and Wulfram. ¹ See Alireza, Modirshanechi., Johanni, Brea., Wulfram, Gerstner. (2021). Surprise: a unified theory and experimental predictions. bioRxiv, Available from: 10.1101/2021.11.01.466796 In this paper the authors detail 16 different kinds of surprise, delving into the nature of surprise at an admirable depth.

They organize these 16 variations into 4 categories:

We classify these surprise measures into four main categories: (i) change-point detection surprise, (ii) information gain surprise, (iii) prediction surprise, and (iv) confidence-correction surprise.

They also explore what different kinds of cognitive strategies – such as surprise seeking – may be most beneficial in certain situations, which is a fascinating question.

In their analysis of surprise measures, the authors identify several distinct categories, each associated with different cognitive strategies. Prediction surprise, exemplified by what they call Shannon surprise, focuses on how unexpected an observation is and aligns with the strategy of making accurate predictions about future events. Change-point detection surprise, such as the Bayes Factor surprise, is geared towards identifying shifts in the environment and supports adaptive learning in volatile conditions. Confidence correction surprise incorporates the certainty of one’s beliefs, modulating surprise based on confidence levels. Information gain surprise, like Bayesian surprise, quantifies belief updates and promotes efficient exploration and model-building of the environment.

The authors argue that these categories reflect different cognitive functions and strategies: prediction surprise matches our intuitive understanding of surprise, change-point detection surprise is crucial for adapting learning rates, and information gain surprise is optimal for exploration.

We do not need to go this far, however, to further explore the relationship between prediction and surprise – we can establish some rough sketches before we start looking deeper.

Surprise is the result of a difference between the predicted outcome O(x) and the observed outcome O(y) – and from an evolutionary perspective the ability to be surprised must have been beneficial and selected for not just because the feeling of surprise itself is pleasant or important, but because of the actions we take following being surprised – surprise enables us to adapt to changes in the environment and to prioritize the changes that deviate most from the range of predicted outcomes (and hence the ones that carry most risk).² This is explored in Rainer, Reisenzein., Gernot, Horstmann., Achim, Schützwohl. (2019). The Cognitive-Evolutionary Model of Surprise: A Review of the Evidence.. Topics in Cognitive Science, Available from: 10.1111/TOPS.12292 and in Ned, Kock., Ruth, Chatelain-Jardon., Jesus, Carmona. (2010). Surprise and Human Evolution: How a Snake Screen Enhanced Knowledge Transfer Through a Web Interface. Available from: 10.1007/978-1-4419-6139-6_5 – where the argument is made that surprise is followed be increased cognitive focus and function.

That means that predictions come with a surprise tolerance that has also evolved — there is a corona of expectation around a prediction that protect us from being surprised all the time by any minor deviation. This corona corresponds to a larger set of outcomes O(x(1))…O(x(n)) that are perceived as variations on O(x) – and then there is a the surprise zone where we have deviated enough from the expected outcome to trigger surprise as a survival reaction.

Where is that boundary and is it different for different predictions? It probably is – and that has to do both with the importance and salience of the prediction to us, and the amount of knowledge we believe we have about the predicted outcome.

And what is the opposite of surprise, the sense of confirmation that we get when we sense that we predicted something accurately?

In a game of prediction, the role of surprise is also interesting. By trying to determine the opponents zone of surprise, I can also understand better where different plays will be less expected, and where my opponent will have to spend significant energy to adapt.

This means that by studying predictions, I can craft surprise.

While this is not surprising (!), it is an interesting observation for anyone interested in military affairs — and also features as a major component in military strategy, where the creation of both tactical and strategy surprise is a key skill that strategists study and try to develop. The best way of doing that is to carefully study the predictions of both our own side and that of the opponent — leading to a search in the space of predictions for the surprise boundaries.

*

There is also, as shown above, some direct implications for how we craft our predictions here. A good prediction, then, is one that allows for us to be surprised in the most productive way we can imagine! This, in turn, means that we should explore and value predictions based on the potential surprise that they entail – and perhaps even define surprise boundaries beforehand as we think closely about how we want our future selves to react to the outcomes of our predictions.

This is especially important, since surprise is culturally complicated and normatively difficult: we do not like being surprised, and so we explain way the results of a bad prediction to seem as we were aware the whole time that the actual outcome was reasonably easy to expect. ³ Why is this? Why do we find being surprised shameful? If being surprised is an evolutionary advantage we should instead celebrate it as a feeling, but there are probably several mechanisms at play here: one is that children are surprised by many things, and we associate that with a not yet formed model of the world: playing peekaboo with a small child is a reminder that they can be surprised again and again by us hiding behind our own hands. This in turn suggests that being surprised means that your model of the world is weak. But nothing could be more wrong — if you repeatedly get surprised at the same thing, for sure, but not if you seek new surprises. Another possible explanation is that we have also evolved to project confidence because that is a need for tribal cohesion . This means that our confidence and surprise are in conflict, and so when we are safe we do not seek surprise as much as when we are in an ambiguous state? Perhaps.

We need to actively ensure to safeguard our surprise instead and learn to relish it. Being surprised several times a day is a good thing.

Footnotes and references

• 1
  See Alireza, Modirshanechi., Johanni, Brea., Wulfram, Gerstner. (2021). Surprise: a unified theory and experimental predictions. bioRxiv, Available from: 10.1101/2021.11.01.466796
• 2
  This is explored in Rainer, Reisenzein., Gernot, Horstmann., Achim, Schützwohl. (2019). The Cognitive-Evolutionary Model of Surprise: A Review of the Evidence.. Topics in Cognitive Science, Available from: 10.1111/TOPS.12292 and in Ned, Kock., Ruth, Chatelain-Jardon., Jesus, Carmona. (2010). Surprise and Human Evolution: How a Snake Screen Enhanced Knowledge Transfer Through a Web Interface. Available from: 10.1007/978-1-4419-6139-6_5 – where the argument is made that surprise is followed be increased cognitive focus and function.
• 3
  Why is this? Why do we find being surprised shameful? If being surprised is an evolutionary advantage we should instead celebrate it as a feeling, but there are probably several mechanisms at play here: one is that children are surprised by many things, and we associate that with a not yet formed model of the world: playing peekaboo with a small child is a reminder that they can be surprised again and again by us hiding behind our own hands. This in turn suggests that being surprised means that your model of the world is weak. But nothing could be more wrong — if you repeatedly get surprised at the same thing, for sure, but not if you seek new surprises. Another possible explanation is that we have also evolved to project confidence because that is a need for tribal cohesion . This means that our confidence and surprise are in conflict, and so when we are safe we do not seek surprise as much as when we are in an ambiguous state? Perhaps.

When we say that something is predictable we are saying that it belongs to a class of, say, events, that have certain properties that allow them to be predicted to some precision and accuracy. This implies that there is a class of events that is the opposite: unpredictable.

What does it mean for something to be unpredictable? What different flavors of unpredictability should we be thinking about?

One possible answer is that the unpredictable is random, and you can even go so far as to define randomness in terms of unpredictability. ¹ This is the approach taken by Eagle, A., 2005. Randomness is unpredictability. The British Journal for the Philosophy of Science. In this interpretation, unpredictability essentially means that something is entirely random and there is nothing I can know about the event today that will allow me to move the probability meaningfully in any way away from the “tossing coin”-state all events start out in.

But this way of thinking about it is filled with assumptions already: is it right to say that all events start out in a 50/50-state of probability? The way this is sometimes defended is to say that when we know nothing about the probability of an event we should start with the assumption that it is equally likely that the event occurs as it is that it does not. But why is 50/50 a good starting position? The mathematical argument is that it gives us the largest chance of being right if we know nothing else — we will be right half of the time, which, for at least binary events, is as good as it gets. If we seek the initial probability for events that have more states, we should just have it be 1/n, assuming that all states are equally likely (say drawing a specific card from a deck of cards).

But it seems as if this assumption is tricky in that we need to know the set of possible outcomes. If we do not even know that, if our model of the world is incomplete to such a degree that we do not know what kind of deck of cards it is (it could be, say, the tarot) – then we are in deeper waters. What initial probability should you ascribe to something if you do not know how many cards are in the deck, or even what those cards are? Say I ask you what the probability of drawing an Orc is – what should you say? Should you approximate the number of cards in the deck, and assume that the Orc is one of the Tarot? If indeed this is the Tarot and not Magic the Gathering?

Here unpredictability seems to inch closer to Knightian uncertainty – where no numeric approximation makes sense at all. The answer to the question how probable we think a certain event in this framing is should simply be: I don’t know.

So are the unpredictable things those that we know nothing about?

Then unpredictability seems to be more than randomness – it seems to be a state in which we have no access to a model of the world in which we can enumerate states, outcomes and alternatives.

*

Another way to approach this is to speak of limits, as we noted in an earlier working note. What are the unpredictability limits? We could argue that they occur in space and time — we cannot predict that which happens so fast that the formulation of a prediction is not possible.

This is interesting, because it assumes that a prediction cannot be immediate – or at least not concurrent with the event itself. A prediction needs to come before, and it will consume some small amount of time to produce, so we should expect that there is this small lag built in to predictions — anything that happens faster than the time it takes to predict it is unpredictable in a very real way.

This is not just a fun point, either – for very complex systems that are irreducible to simpler models, the time requirement makes them unpredictable in this way for a large set of cases. We can think about this as a special case of algorithmic complexity, perhaps, where the size of the algorithm for predicting a system at some accuracy runs optimally in the time it takes for the system to reach the State s+1 which is the state after the state S we tried to predict.

Complexity boundaries also exists in the future – some complex systems, such as the weather, have an upper complexity boundary beyond which they are unpredictable.² In the case of weather this seems to be around 14 days – see https://phys.org/news/2024-02-limits-weather-future.html, but, of course, this does not apply to climate forecasts, because they forecast something fundamentally different — and at a different resolution.

Other limits exist in space. We cannot predict things that are beyond the visible universe in any meaningful sense, since they are spatially inaccessible to us.

Computational limits seem more practical, but for some things we could predict the computational requirement may be such that there is no energy to produce such computations.

Et cetera. The notion of limits of predictability is an interesting one, and it probably also has recursive elements – when more than X predictors are trying to predict a phenomenon that is self-reflexive, the resultant complexity may make something initial predictable quite unpredictable.

*

Unpredictability is also ontologically interesting. Is it a feature of reality or an epistemological limitation? The same holds for uncertainty, and this too is interesting in a “philosophy of physics”-way. Here, obviously, we find the heated debate about things like Heisenberg’s uncertainty principle.

A lot to return to.

Footnotes and references

• 1
  This is the approach taken by Eagle, A., 2005. Randomness is unpredictability. The British Journal for the Philosophy of Science.
• 2
  In the case of weather this seems to be around 14 days – see https://phys.org/news/2024-02-limits-weather-future.html, but, of course, this does not apply to climate forecasts, because they forecast something fundamentally different — and at a different resolution.

What is the relationship between predictions and explanations? Our first intuition may be to say that predictions are forward-looking and explanations directed towards the past, but that is not quite right. Are predictions in some sense not thinner than explanations? I can predict that something will happen without actually understanding why. I cannot explain something without understanding it, however — so prediction and explanation would seem to require different depths of understanding.

Predictiv understanding is thin in the sense that what it understands is correlation, whereas explanatory understanding seems to understand causality, and perhaps even causality in a world model. How does it work in the inverse? Does the impossibility of predicting something mean that I do not understand it at all? If so the limits of my predictive capability seem to be the limits of my understanding, or, perhaps of my world.

In professor Gali Shmueli’s work on the difference between explanatory and predictive modeling in statistics we find a set of useful distinctions.¹ See e.g. Shmueli, G., 2010. To explain or to predict? Available at https://www.stat.berkeley.edu/~aldous/157/Papers/shmueli.pdf Shmueli writes:

As a discipline, we must acknowledge the difference between explanatory, predictive and descriptive modeling, and integrate it into statistics education of statisticians and nonstatisticians, as early as possible but most importantly in “research methods” courses. This requires creating written materials that are easily accessible and understandable by
nonstatisticians. We should advocate both explanatory and predictive modeling, clarify their differences and distinctive scientific and practical uses, and disseminate tools and knowledge for implementing both.

What then is the difference between the two? According to Shmueli, explanatory modeling and predictive modeling differ fundamentally in their goals, approaches, and outcomes. Explanatory modeling aims to test causal theories and hypotheses, focusing on minimizing bias and understanding underlying mechanisms. It typically uses theory-driven variable selection, interpretable statistical models, and evaluates performance based on goodness-of-fit and statistical significance. In contrast, predictive modeling seeks to accurately forecast new or future observations, balancing the trade-off between bias and variance to optimize predictive power. It often employs data-driven variable selection, may use complex or “black-box” algorithms, and evaluates performance using out-of-sample prediction accuracy. This distinction affects the power of the resulting models in that explanatory models may have high explanatory power (e.g., high R-squared) but poor predictive accuracy on new data, while predictive models may achieve high predictive accuracy without necessarily providing clear causal insights. Shmueli argues that these two types of power – explanatory and predictive – should be viewed as separate dimensions rather than extremes on a continuum, and that both are valuable for scientific progress in different ways.

Her perspective here mirrors that of David Krakauer in an interesting way. Krakauer noted on a recent podcast that we are looking at a coming schism in science² See https://complexity.simplecast.com/episodes/106/transcript :

And I, we’re now entering in the 21st century a new kinda scientific schism where we’re gonna live with two very different ways of engaging with reality —a machine-based, high-dimensional, very precise, predictive framework that is a black box and ours, which is a more familiar framework from the history science, if you like, but that is faithful to the complexity of the systems we study, which doesn’t predict so well, but does allow us to understand the basic mechanisms generating the phenomena of interest. And that’s where I think complexity lives. And it’s gonna have to come to terms with living with machine learning and AI. It’s almost as if we’ve returned, to use your biblical metaphors, to the Cain and Abel and those two brothers are gonna have to get on as opposed to one killing the other.

This idea, of one predictive and one explanatory view of the world that needs to co-exist, of two dimensions as Shmueli has it, is fascinating and could be read as the evolution of the split between empiricist and rationalist traditions. Empiricists evolved into machine learning predictors, where as rationalists evolved into complexity explainers. And this suggests that our early distinction is not quite right — prediction is not thinner than explanation, it merely approaches the world from another dimensions (we could say from below and from above, but that suggests a difference that may not be helpful).

And we need both, as both Krakauer and Shmueli suggest, and we should teach both in schools as well. To understand something is to be able both to predict and explain it – and when we cannot do both our understanding is limited.

Is there something here about the historical balance between these two aspects of science? Can we say that historically our science has been explanation heavy, but lately it is becoming much more prediction heavy? If we look at the composition of our knowledge of the world – our understanding of the world – is it primarily explanatory or predictive? Has that changed over time?

If so — should we say that we are moving from an explanatory paradigm to a predictive worldview?

It is intriguing to think about the extremes. Let’s imagine a world where explanations never evolved – their science is all predictions. When we ask why something happens they merely shrug and say that is a nonsense question — explanations in their view are just stories we tell about complex systems to make them more “human”. For them prediction, by complex computational models, is knowledge and understanding.

What, then, would they be missing?³ It is instructive to think about other institutions in a society like this — what would, for example, courts look like if they were limited to predictive modeling? Would they focus wholly on recidivist probabilities or probabilities that an action unpunished would lead to more such actions and entirely base judicial decision on predictions? And what would art look like? Literature?

And what about the inverse world in which we find a science that has no predictions, and only relies on explanations – a science that considers predictions as magic and nonsense. Everything, they say, can be explained in hindsight but is so complex that a prediction can always be wrong, and hence making predictions is useless and intellectually dishonest.

What would this culture be missing?

Or could we imagine a world in which the two co-exist but rarely interact? A school of explainers and one of predictors considering the other vaguely unintellectual (is this the split between the two cultures that Snow discusses? Or did he center on the distinction between understanding and explaining? Should that whole debate really be recast as one in which we should actually have been discussion prediction and understanding all the time.)

In some ways it seems reasonable to argue that we are moving from the second to the first, the aristotelian, from first principles medieval scientific paradigm could be cast as deeply explanatory, and the current machine learning inspired modeling as predictive — but is that right? Is there a further dimension we need to think about here?

Finally, returning to the point about the limits: what can we say about the limits of the both approaches? Where does explanation hit limits and what limits prediction more exactly? And are these limits to knowledge different in some fundamental ways? It seems as if they are — a limit of explanation seems harder to define than a limit to prediction, but why is that?

Footnotes and references

• 1
  See e.g. Shmueli, G., 2010. To explain or to predict? Available at https://www.stat.berkeley.edu/~aldous/157/Papers/shmueli.pdf
• 2
  See https://complexity.simplecast.com/episodes/106/transcript
• 3
  It is instructive to think about other institutions in a society like this — what would, for example, courts look like if they were limited to predictive modeling? Would they focus wholly on recidivist probabilities or probabilities that an action unpunished would lead to more such actions and entirely base judicial decision on predictions? And what would art look like? Literature?

There is a story about Thales, I think, where he is essentially asked why, if he is so clever, he has no money. So Thales goes ahead and observes the world a little, finds that with the great weather they are having there is a great olive crop coming and so corners the market on olive presses – essentially rents them all – and then charges healthy fees for anyone that wants to use them. The value of his prediction – that the presses would be needed – seems simple to assess: it is the most valuable action his prediction allowed him to take (in this case cornering the market for olive presses). This value, of course, depends on the prediction not being widely known, because when it is, well, then everyone will have tried to rent the presses.

Today, trade in predictions is more or less common place in so-called futures. Financial futures contracts are standardized agreements to buy or sell a specific financial asset at a predetermined price on a future date. These contracts allow investors and businesses to hedge against price fluctuations or speculate on market movements. The underlying assets can include currencies, stock indices, commodities, or interest rates. When entering a futures contract, parties commit to the transaction without immediate exchange of the asset or full payment. Instead, they make initial margin deposits and adjust them daily based on market price changes, a process known as “marking to market.” As the contract’s expiration date approaches, participants can either close their position by taking an offsetting contract or proceed with the physical delivery or cash settlement as specified in the contract terms.

But there also seems to be a lot of value in not having to predict a situation, but essentially making sure that an event can be accommodated in one’s plans no matter how it turns out. In this model we are paying to not have to predict, and the value of the prediction is arguably what we would not have had to pay if we had been able – at some probability – to predict the event. This model – hedging – is done at what we could call the price of certainty.

Now, the price of certainty and the value of a prediction are closely related, it seems — the more certain a prediction is, the more it approaches the value of certainty, in some possible curve.

Now, this raises another possible avenue of exploration: maybe events can be characterized by different probability curves? Some may be smooth like this, others may be binary and just shift from zero to 1 in a single moment, and yet others may be quickly growing towards 1 and then increasingly nudging upwards. Could we use this prediction / probability profile to categorize events in different ways? Some may even be random noise until they settle. What would a taxonomy of events based on the nature of the predicted probability look like?

We could imagine a few of the categories:

• Binary events that move from 0 to 1, where a single data input point decides and that is not know at all. Or, perhaps more common, it moves from 0.5 to either 1 or 0.
• Smooth gradient events like aging processes.
• Step functions where probability changes in steps.
• Exponential growth events with fast growing probabilities.
• Plateau events – quick initial growth that levels off.
• Cyclical events with, say, seasonal probabilities. ¨
• Random events, where probability shifts like a random walk.
• Threshold events with points where the probability shifts radically.
• Decay events where probability is increasingly high or low but then decays.
• Compound events of different kinds.

Or in a picture:

The prices of certainty and prediction will then vary with the kind of event it really is — and knowing what kind of event it is in itself may be an advantage for whoever is thinking this through.

As noted in an earlier post, not all statements about the future are necessarily predictions. In that post we explored the idea of a spectrum of future statements, ranging from guesses to prophecy – ordered on some kind of notion of the robustness of the data and process that led to the production of the statement itself. How a statement about the future is produced is one way of evaluating it, and a taxonomy can certainly be built around the means of producing such statements – but are there other ways of approaching this problem as well?

One possibility is to look at the use of the statement – it could look something like this: a guess is offered by someone who has no intention of acting on the statement, a prediction is a statement that the person uttering it intends to use to make decisions, a prophecy is a statement that is intended to force one person’s prediction upon another person or persons. The different use cases for statements about the future are descriptive, decisional and normative – or something along those lines.

In some sense, then, we should value these statements differently – and if we are trying to make our own predictions we should value those statements by others, where they intend to use the statement to make decisions, higher than other kinds of statements about the future. Predictions are statements from someone who has skin in the game, and will need to act on the basis of the statement.

One way to think about this is to say that predictions should always be possible to translate into bets. Guesses and prophecies are at least not intended to be taken that way, and many people would not take a bet based on a guess they made, and would be offended if offered a bet on a prophecy, since the bet suggests that there is some uncertainty lingering in the prophecy.

And that gives us another angle: the uncertainty associated with the statement. And here we might want to think about this as a kind of Knightian uncertainty that is not easily reducible to probabilities – and so we end up with something like this: a guess is made about an event that is more uncertain than not, a prediction can only be made about an event where the uncertainty has been reduced to probability at some acceptable rate and residual uncertainty in the web of causes around the event is largely eliminated and a prophecy is a statement about an event almost without any uncertainty at all.

This ties the statements about the future, in an interesting way, to the events that they are about — the nature of those events determine if we have to do with a guess, prediction or prophecy — if we believe that uncertainty is a property of the event rather than our knowledge about the event (this mirrors the question of subjective probabilities, I think).

Another aspect of the robustness analysis would be to look at how embedded a statement about the future is in our web of belief. A guess, under this taxonomy, is almost disconnected, or just loosely attached to our overall web of belief. A prediction is connected and the more connected it is the deeper we believe it. A prophecy, however, might exist very close to the center of our web of belief and shape us deeply. This approach allows us to see statements about the future as more or less a part of our identity. A guess says very little about a person’s beliefs – a prophecy says quite a lot. This, intriguingly, seems to imply that predictions and prophecies can be used to make predictions about the person making the predictions and their world view.

Predictions should be about the future as well (seems obvious) — even though we do not always use the term that way. We sometimes say that a certain theory predicts a fact, something that eliminates the timeframe. This seems muddled, and the old predictivist debate is interesting here: in short (very short) this is a debate about whether it is right to say that something is predicted or accommodated by a theory. Intuitively it would seem more correct to suggest that a fact or fact pattern can be accommodated within a theory, but a future event predicted by the theory. ¹ See for a write up here: https://plato.stanford.edu/entries/prediction-accommodation/

So, as always, let’s invert. When is a statement about the future absolutely not a prediction, nor a guess or a prophecy? I think the best example of that is probably a statement about the future that expresses a hope. Hope seems to be almost the opposite of a prophecy, something we actively believe will not happen (we would in fact often take a bet to the opposite if we were not so desperately hoping) — or at least something we would not even have guessed would happen.

Hope, then, occupies a counter-factual role in the theory of predictions – a sort of inverse prediction attached to a strong preference for the world to be a way we think it will not turn out to be?

What about absolutely determinist statements about the future that contain no uncertainty at all? Prophecies still have some uncertainty – if only just the uncertainty that comes from a belief not being shared by others – but are there completely determined statements about the future? Perhaps physical laws are the closest we can come to such statements about the future – but they are statements from a point outside of time, in some way. They are statements about the past, present and future of a state space.

A physical law eliminates all space for hope, and physical laws do not predict – but accommodate – timeless facts.

Footnotes and references

• 1
  See for a write up here: https://plato.stanford.edu/entries/prediction-accommodation/