In the world of econometrics, we're accustomed to predicting recessions, estimating causal impacts, and modeling long-term growth. But what if the tools of probabilistic reasoning could also offer insight into humanity's own lifespan? This is the bold proposal behind physicist Brandon Carter’s Doomsday Argument, a theory that, while grounded in philosophical probability, has clear implications for statistical reasoning and long-term forecasting.
The Premise: You Are Not Special
Carter’s Doomsday Argument begins with a deceptively simple premise: suppose that you are a randomly selected individual from the set of all humans who will ever live. If you accept that assumption, known in probability circles as the Self-Sampling Assumption (SSA), then your birth rank (i.e., where you fall in the total timeline of humanity) becomes informative.
Rough estimates suggest that around 117 billion humans have lived to date. If the total number of humans to ever exist were, say, 10 trillion, then you would find yourself in the first 1% of all humans, an extraordinarily unlikely position, assuming you’re randomly sampled. Carter argues, therefore, that it's statistically more plausible that the total number of humans will not be dramatically higher than the current number. This leads to a sobering conclusion: we are likely living in the second half of human history, and extinction or a severe population decline could be relatively near.
The Argument in Econometric Terms
Carter’s logic resembles Bayesian inference, particularly the use of informative priors. If your prior distribution over total human population is uniform (i.e., no assumptions about how long humanity will last), then your observed birth rank updates that prior. It shifts the posterior probability distribution toward a shorter total lifespan for humanity.
Let:
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N = total number of humans who will ever live,
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r = your birth rank (say, 117 billion),
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Then P(N>1 trillion ∣ r=117B) becomes small under SSA.
This is a form of population-based survivorship bias, where your own existence skews what you should rationally expect about the future.
Critiques and Statistical Caution
For econometricians, the argument is appealing, at least at first glance. It uses probabilistic reasoning, prior beliefs, and observational data (your birth rank) to infer an unobservable quantity (humanity’s remaining future). However, the model makes several debatable assumptions:
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Reference Class Problem: What counts as a "human observer"? Does this include unborn generations, future artificial intelligences, or only modern humans?
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Random Sampling Assumption: It’s questionable whether individuals are truly random draws from the total human population.
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Endogeneity of Observation: Your observation of your own place in time is tautological—you can’t observe a future you.
These are familiar challenges in econometrics, particularly in the use of instrumental variables and sample selection models. The Doomsday Argument, while thought-provoking, may overextend the logic of sampling in a domain where we lack experimental design or repeatable data.
Broader Implications
Carter’s argument has rippled beyond cosmology into philosophy, ethics, and even risk management. In an age where existential risks like climate collapse, nuclear war and artificial intelligence are increasingly plausible, the argument adds statistical weight to calls for long-term policy planning.
Econometricians, with their tools for modeling uncertainty and dynamic systems, may find new purpose in applying their methods to global existential forecasting. Could we build models that not only estimate GDP growth but also humanity’s survival probability?
Conclusion
Brandon Carter’s Doomsday Argument remains controversial, but it’s a reminder of the power and peril of probabilistic reasoning. While econometrics typically serves more grounded domains, Carter’s approach invites us to consider how our models and assumptions could be applied to the grandest questions: not just what happens next, but how much longer do we have?