This post was originally written and published in French, Corrélation et causalité, circonstance et contexte

Let’s imagine we collected a few pieces of information, via connected devices,

• Thursday 18:30: a €45 purchase at a bar-tabac
• Friday 13:15, 1 hour above Porte Saint-Martin
• Saturday 14:00, 1 hour near Place de la République

Trying to make the data “speak”, we might hesitate between a first version

• Thursday 18:30: a €45 purchase of cigarettes
• Friday 13:15, 1 hour at the mosque, at prayer time
• Saturday 14:00, 1 hour in a demonstration that started from Place de la République in the early afternoon

and a second version

• Thursday 18:30: a €45 purchase of tax stamps
• Friday 13:15, 1 hour at the gym
• Saturday 14:00, 1 hour at the hairdresser’s, Place de la République

In other words: with the very same raw signal, we can build two perfectly coherent stories. This is not a literary trick à la Sophie Calle; it is the standard situation as soon as we work with traces (geolocation, timestamps, spending, calls, driving). Data do not necessarily lie. But they underdetermine the narrative, because they allow several possible worlds. In insurance (and more broadly in the economy of prediction), we are used to taking correlations and turning them into decisions—not only to “understand”, but to price, classify, accept, refuse. The point is not to say this is illegitimate in principle. The point is to recall what we do when we only correlate, and what we forget when we have no context.

Correlation and causation

In actuarial practice, the question is not

“what causes what?”

but rather:

“what predicts what, in a stable and defensible way?”

That, at least, is what the memo An Actuarial View of Correlation and Causation — From Interpretation to Practice to Implications explains, written by Dorothy Andrews, Steven Armstrong, Dave Heppen, and Julia Romero for the American Academy of Actuaries. We know this (and I have written it many times on this blog): insurance did not wait for machine learning to live off correlations. A premium is a price (and a signal), built on observed regularities, on frequencies, or on severities. And the economic argument often made is that we segment because, without segmentation, we mix different populations and create adverse selection. So far, nothing mysterious. But very quickly, we have to be more precise, and a complex question arises: what are the desirable properties of a rating variable? And in particular: must the variable be causal in order to be a pricing variable? If we think in causal terms, the story makes sense because it connects to prevention. Having a locked garage can indeed prevent certain losses. And therefore it is legitimate to lower the premium (all else equal) when someone has a garage.

But the memo An Actuarial View of Correlation and Causation clearly explains that, in practice, strict causality is not always required: a variable may be accepted if it is relevant for measuring risk—provided we remain within a professional and regulatory framework. That helps a bit, but we all know the mantra “correlation is not causation” that we keep repeating to students. Naomi Altman and Martin Krzywinski, in their short methodological note Association, correlation and causation, summarize well the gradient association / correlation / causation and the traps of naive interpretation. Except that in insurance we do not merely interpret: modeling tools are the basis for decision-making. We turn correlation into a premium, therefore into an incentive, therefore into unequal treatment, therefore into public debate. And the memo An Actuarial View of Correlation and Causation offers an interesting idea: rather than demanding causality (often out of reach), we can demand a “rational explanation”—an intelligible story, testable to some extent, compatible with the facts and with a non-specialist’s understanding. It is an “in-between” notion, a form of responsibility. We predict, we control, we explain reasonably. But that would be a bit too simple, because (1) correlations can be socially explosive proxies (this is all our work on algorithmic fairness and discrimination), and (2) “reasonable stories” are precisely where we go wrong (this is all our work on model explainability).

Proxies, discrimination, and explanations

In the recent history of algorithms, people often mention the COMPAS recidivism algorithm, which disadvantaged Black people even though “being African-American” was not an explicit variable, or the Amazon AI recruiting tool, which disadvantaged women even though “being a woman” was not an explicit variable. The memo uses these examples to remind us that removing a sensitive variable does not necessarily remove the information: the model can reconstruct categories via correlates, i.e., proxies (see also Discrimination by proxy, and tattoos in Japan, which I posted this summer). In pricing, this is structural. Some “neutral” variables (a postal code, a type of phone, time-of-day habits, address stability) may be correlated with protected attributes or socioeconomic determinants. What was presented as “objective risk segmentation” becomes a machine that echoes inequalities. And the memo says so explicitly. Even if a variable is predictive*, its use may be controversial, especially when it leads to indirect discrimination or when it is not “linked” to the behavior we claim to be pricing.

* A short aside is needed for non-specialists. In insurance (and more broadly when building predictive models), saying a variable is “predictive” simply means: when we know it, prediction improves—we make fewer errors about the future value of the quantity of interest (claim, cost, frequency, etc.). In “classical” regression, this was long summarized as “the coefficient is significantly different from zero” in the model (i.e., after accounting for other variables). In a simple regression, that is essentially a correlation test (is the rating variable statistically correlated with risk?), and in multiple regression I would speak of “residual correlation” (what the variable adds on top of the others). In machine learning more generally, we reason in terms of out-of-sample performance gains: a variable is predictive if, when we add it, the model predicts better on new data (validation/test), even if its effect is nonlinear, locally unstable, or spread across several correlated variables. In other words: in regression, we often asked for proof “inside the model” (the famous p-value as a marker of statistical significance), whereas in machine learning we mostly ask for proof “in the future” (better generalization)—which can exist even when the variable is just a proxy. And that is precisely where the legitimacy/ethics question comes back.

If the idea is appealing, at this stage practitioners will feel there is still quite a bit of fuzziness about where the boundary should be drawn, between, on the one hand, an actuarial concern (more economic than statistical, it seems to me: reflecting risk, maintaining portfolio balance) and, on the other hand, a political concern (not making people pay for a social destiny, not turning insurance into an instrument of social sorting). And the notion of a rational explanation becomes both a safeguard and a temptation. A safeguard, because it forces you to say something other than “it works.” A temptation, because a “plausible” explanation can also be a comfortable story we tell to make acceptable a correlation whose social effects we do not want to examine. More than a story, I have several times used the word “fable” (borrowed from Ariel Rubinstein), which stresses the exemplary narrative (from which one draws a moral), with the risk of being a lesson rather than a proof. What we call “explanation”, very often, is not a demonstration: it is a narration. And a narration without context can do a lot of damage.

Circumstances and evidence

Interestingly, the question “what counts as evidence?” has stirred the law for centuries. In the English-language literature, it is the notion of “naked statistical evidence.” In Rethinking Evidence, William Twining discusses cases where one has strong statistical information (for instance: “most people cheated”) yet hesitates to convict a particular person on that sole basis. The gatecrasher example has become emblematic: if 501 people out of 1000 got in without paying, can we convict an individual chosen at random, solely because it is “probable”? This is the so-called “Ten Oever” argument (Gerardus Cornelis Ten Oever v Stichting Bedrijfspensioenfonds voor het Glazenwassers- en Schoonmaakbedrijf, 1993).

The court stresses that group averages (e.g., life expectancy) do not describe each individual, and cannot alone justify unequal treatment.

In other words, the fact that women (as a group) tend to live longer than men does not determine the life expectancy of a particular individual—and it is not acceptable for someone to be penalized based on assumptions that may not hold in their specific case. In Einzelfallgerechtigkeit versus Generalisierung, Gabriele Britz discusses discrimination by generalization. This is exactly the argument of actuarial practice, as Frederick Schauer explains in Profiles, Probabilities, and Stereotypes. That said, it seems to me that legal scholars raise an important point: a frequency can make a hypothesis probable without making it probative for a particular case. One can also recall the “blue bus” story (or, in legal references, the case Smith v. Rapid Transit). In the fable, a pedestrian is struck by a bus but cannot identify the company. We only know that, on that line (or in that area), 80% of the buses belong to the “blue buses” company. Is that single proportion enough to conclude that this bus was theirs, and therefore to hold them liable? Laurence Tribe, in Trial by Mathematics, uses this type of scenario to criticize the idea that judicial decisions should be a quasi-mechanical application of probabilistic calculation. If some use this to stage a pseudo “anti-math” debate, I think it mainly questions a social requirement: proof must not only be a probability, it must also be a form of link, so to speak (an attachment, an individualization, a mechanism, a narrative that can be debated contradictorily). Peter Tillers, in his critique (Trial by Mathematics — Reconsidered), nuances the aversion to probabilities in court. The result is not a simple binary verdict (“ban statistics”), but a methodological question: circumstances alone do not always amount to proof, even when they are numerically impressive. In our context, a correlated variable may be a good predictor, but it does not automatically tell us why, and it can be used to support an abusive and unjust story.

Context

Now, let’s be clear: causal inference is not simple, and it raises other issues. Causality is not always accessible (or identifiable), and even when it is, it does not abolish the ambiguities of the social world. The anthropologist Clifford Geertz, in his text on thick description, uses a famous, almost obvious example: the movement of an eyelid. It can be a tic, a wink, a parody… The signal is exactly the same; what changes is the interpretation, therefore the context (codes, intentions, the scene). Unfortunately, it is a weak signal, thin, to use Geertz’s term. We can record it en masse, correlate it, score it. But the act of understanding what it “means” requires a thicker description, or at the very least, contextual hypotheses. This is exactly what the sociologist Erving Goffman asks in Frame Analysis when he poses his guiding question *“What is it that’s going on here?”, *that is, what is the frame in which the scene makes sense? The map I proposed in the introduction (mosque/demo/cigarettes) is an exercise in framing: depending on the frame, the same sequence becomes suspicious or banal. And it seems to me that this mostly highlights a form of political asymmetry. On the one hand, institutions that collect data (insurers, platforms, administrations) can impose an interpretive frame (“this is a risk signal”); on the other hand, the individual often has to defend themselves against an algorithmic narrative with unequal means (explaining their context, challenging an inference, requesting a justification). In other words, the “correlation/causation” debate is then too restrictive: the real issue is “who has the power to tell the story?” and “which stories become operational?”

Metadata and telematics

This is not a purely intellectual question. Beyond actuarial practice, one can keep in mind the statement We Kill People Based on Metadata, which caused quite a stir about ten years ago. Beyond the sensational aspect that journalists may enjoy, it says something true about our time and our practices: metadata have enormous inferential power, therefore enormous power to act. This is what Yves-Alexandre de Montjoye argued in Unique in the Crowd, when he showed that with a few spatio-temporal points one can often isolate trajectories, and thus re-identify individuals. Context (where/when) is not a detail; it is a signature. In Privacy in Context, Helen Nissenbaum argues that “privacy” is not only about secrecy, but about the appropriateness of information flows relative to contextual norms (purposes, expectations, roles). In other words, information can be acceptable in one context (driving bonuses, prevention) and problematic in another (surveillance, secondary use, suspicion). In the context that interests me most (professionally), insurance telematics data measure driving events (braking, acceleration, cornering), but also deeply contextual variables (times, road types, areas, parking). The study note Usage-Based Insurance and Telematics by Anthony Cappelleti for the Society of Actuaries details these dimensions, as well as concerns about confidentiality, transparency, data ownership, and secondary uses. The well-rehearsed practitioner’s pitch is seductive: it is “fairer” because it is closer to exposure and behavior. But clearly the ethical problem shifts rather than disappears. Driving at night may be correlated with risk… but also with work constraints. Crossing certain neighborhoods may be correlated with risk… but also with social geography. “Hard braking” may be a driving style… or a road environment. Telematics creates, in my view, a perfect paradox: it collects more context (or could), but it turns that context into variables that, in practice, become circumstances again (interpretable, debatable, sometimes accusatory) and it pushes us to act on those circumstances via prices. The Age of Surveillance Capitalism by Shoshana Zuboff offers an interesting critical framework, as she explains that behavioral prediction can become an infrastructure of extraction and influence beyond initial purposes. Even if one does not endorse her full diagnosis, the warning seems important to me: the more a datum “works”, the stronger the temptation to collect it, keep it, reuse it. The ethical question returns because what began as a technical debate (“correlation or causation”) ultimately becomes a social debate (“what do we accept measuring, and at what price?”). Returning to my introductory example, with my three lines of metadata, they are not “false”, but they are not “true” either, in the sense that they are not sufficient to establish a unique story. But they are thin, in Geertz’s sense, and that is precisely what makes them dangerous: they lend themselves very easily to over-interpretation. Actuarial practice will continue to predict*. Yes, and that is a necessity in insurance. The memo An Actuarial View of Correlation and Causation reminds us that pricing lives on properly exploited associations.

* Second important technical note: there is a crucial specificity in insurance that we easily forget when we talk about “prediction”. The actuary is not trying to guess who will have an accident (or who will die), as one might look for a culprit or an “at-risk” individual. They are looking for collective probabilities and expected costs that make sense for setting a price ex ante: the goal is to spread a random cost across many—i.e., to mutualize. In that logic, “predicting” does not mean anticipating the ultra-rare shock (for example, a catastrophic accident costing several million) in order to send the bill to Sidonie, Jordan, or Pierre-Emmanuel. That makes no insurance sense. On the contrary, we want such events to remain “insurable”: individually unpredictable but modelable on average, so that we can collectively finance, for instance, the equivalent of €30 spread across all motor third-party liability policies. And that is also why a model that is “too good” at the individual level would paradoxically be the death of insurance: if it knew almost exactly who will cost what, we would no longer pool, we would individualize. And we would leave insurance to enter a quasi-certain pricing scheme.

Actuarial practice will also continue to explain—ideally with modesty. James Woodward (in Making Things Happen) recalls the interventionist ideal of causality, and Nancy Cartwright (in How the Laws of Physics Lie) reminds us that regularities depend on conditions and that “laws” can lie if we forget their domain of validity. If we allowed ourselves to go one step further, actuarial practice will continue to justify itself, publicly. That is the value of “rational explanation”: if you cannot prove causally, you must at least defend your choice reasonably, and examine social effects (proxies, indirect discrimination, surveillance). These are the debates we began to have during discussions about the European AI Regulation, and that it would be good to keep pursuing…

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OpenEdition suggests that you cite this post as follows: Arthur Charpentier (February 3, 2026). Correlation, Causation, Circumstance, Context. Freakonometrics. Retrieved February 3, 2026 from https://freakonometrics.hypotheses.org/87986

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