The value of existential risk mitigation: interactive model

Muñoz Morán’s model (Rethink Priorities, 2023), reproduced, with switches for the alternatives raised in The Unjournal’s evaluation

What is it worth to cut the risk of human extinction a little, for a few years? This page works out the answer under the model in Muñoz Morán’s 2023 report for Rethink Priorities, and lets you change each assumption to see how the answer moves. ? Choose settings on the left, or start from a preset.

The answer is the purple box, E(M): the expected value the action adds to the future, counted in years of today’s world. ? (how it’s computed). Each setting in use is tagged by where its value comes from: the 2023 report, Rethink Priorities’ 2026 model, an illustrative choice of ours, or you.

Hover over or tap any ? for an explanation, and use “Hide settings” to give the charts the full width. When you have a scenario you find plausible, you can share it or submit it.

  • The model in one line. In each year \(t\) the world goes extinct with probability \(r_t\); if it survives, that year produces value \(v_t\). A mitigation multiplies \(r_t\) by \((1-f)\) for \(P\) years. Its value is \(\mathbb{E}(M)=\mathbb{E}(w')-\mathbb{E}(w)\) ?: how much it raises the expected value of the future (formulas).
  • Left panel: pick a risk scenario and a value-growth path, then the mitigation’s efficacy \(f\) (the share of each year’s risk it removes), its persistence \(P\) (how many years its effect on risk lasts) and the horizon \(T\) (the last year counted). Only the settings that matter for your choices are shown. The page opens on the report’s defaults: Time of Perils, constant value, \(f = 0.0001\) (one basis point), \(P = 5\) years. “Hide settings” at the top of the panel folds it away; the “Settings” tab at the left edge brings it back.
  • Beyond the paper (amber box): each switch starts off, so the page opens as a replica of the report. Turn them on one at a time.
  • Units: \(v_c = 1\) is one year of a world like today’s (the report’s footnote 14 suggests roughly 8 billion people at 0.85 QALYs each). All results are multiples of \(v_c\).
  • Results, top to bottom: the headline numbers; how risk and value change over time; when the mitigation’s value arrives; how it depends on persistence; the report’s scenario grid at your settings; the two optional analyses (switches 2 and 4); and which inputs matter most.
  • Share, submit or comment: the share section at the bottom gives a link that reopens these settings, a text summary, downloads, and a form for adding your scenario to the shared list. Comment on anything with Hypothes.is (the < tab at the top right). Hypothes.is annotations are public, so don’t post anything confidential there; and a share link carries your settings, so anyone you send it to sees them.
  • Precision: headline numbers are shown to three significant figures (hover for more digits). The inputs aren’t known nearly that well; the extra digits are there for checking against the report, not because the answer is that precise.
  1. The report’s numbers reproduce. Under Time of Perils with constant value, \(f = 0.0001\) and \(P = 5\), the mitigation is worth about 0.009 years of today’s world; with cubic value growth, about 55,000. See replication.
  2. Most of the value sits in the far future. Under the report’s default scenario, 95% of \(\mathbb{E}(M)\) arrives after year 500 and 37% after year 10,000, even with constant value: the benefit is a higher chance of reaching the long low-risk era.
  3. Under Rethink Priorities’ 2026 central values (preset below; Earth-bound branch only), the same mitigation is worth about 0.36 years of today’s world, 40 times the report’s default, and 99.6% of it arrives after year 500. A donation tool that discounts the 500+ year window to 0.10 keeps about a tenth of it.
  4. Sign uncertainty matters more than the mean suggests. With a spread on \(f\) equal to its mean and a 10% chance of a delayed backfire (switch 2), there’s about a 19% chance the action is net harmful, while the mean falls only about 11%. The report reports means only.
  5. A pure delay of risk can be worthless or harmful. If the risk you avert is paid back right after the window (switch 3 with \(\beta = 1\), \(D = P\)), the value falls to almost zero with constant value and turns negative with cubic growth, because the risk comes back when each year is worth more.

Presets: Report default · Report, cubic value · Report figures (f = 0.5) · RP 2026 central values ?

Scenario

What the risk scenarios are
  • Constant risk: \(r_t = r_{high}\) forever. Ord’s base case; with constant value, \(\mathbb{E}(w)=v_c(1-r_c)/r_c\).
  • Time of Perils: \(r_{high}\) for the first \(L\) years (report: 100), then \(r_{low}\) forever.
  • Great Filters: \(F\) high-risk eras of length \(\ell_d\) separated by low-risk eras of length \(\ell_s\), then low risk forever. Report: \(F=2\), \(\ell=(100,500,100,\ldots)\).
  • Exponential decay: \(r_t = r_0 e^{-\lambda (t-1)} + r_\infty\). Notebook defaults: \(\lambda = 10^{-4}\), \(r_\infty = 10^{-9}\). The report’s Figure 3 draws a much faster decay than the one used in its tables (see Departures).
Per-year risks come from per-century probabilities: 20% per century gives \(r_{high} = 1-0.8^{1/100} = 0.0022289\); 1% per century gives \(r_{low} \approx 0.0001\).

Risk

Value

Value paths explained

The report (section 2.1 and section 11) uses \(v_t = (\alpha t + 1 - \alpha)^n v_c\) with \(\alpha = 1/100\), so that a sequence defined per century (value \(i^n\) in century \(i\)) is reproduced when periods are years; \(n=0,1,2,3\) give the constant, linear, quadratic and cubic cases. Logistic is \(v_t = c / (1 + \frac{c-s}{s}e^{-\gamma t})\) with \(s\) set so that \(v_1 = 1\); the notebook uses \(c = 10^6\) and \(\gamma = 0.03\).

Beyond the paper: polynomial of order n checks the evaluator’s point that cubic isn’t special (quartic gives even more); exponential grows without bound (the report notes its convergence proof fails here); hard cap is exponential growth that stops at a ceiling; fluctuating multiplies a base path by mean-one AR(1) noise in logs, so the expected path equals the base path but any single realization wobbles.

Mitigation

About f, P and T

The report’s headline table uses \(f = 0.0001\) (“a useful and more realistic efficacy is one basis point”); its figures use \(f = 0.5\) “for entirely pedagogical reasons”. Persistence \(P\) is the number of years the risk stays reduced; the report shows \(P \in \{1, 5, 50, 500, 2000\}\) and suggests persistence above 50 years is unlikely.

The report says the computation “assumes a cap of 120 thousand years”, but the companion notebook uses a different \(T\) for each cell of Table 3 (5,000 to 120,000). The replication page uses those per-cell values; here you choose one \(T\). The horizon table on the right shows how much of the answer sits beyond any given year, with a bound on what lies beyond \(T\) itself.

Beyond the paper

Each switch starts at the report’s assumption (off). ?

Why a floor? The evaluator argued that if some extinction risk \(c>0\) is always present, survival is bounded by \((1-c)^t\), so value has an “approximate support” in finite time and the question of infinite-series convergence matters less than the truncation error at a chosen horizon. The floor replaces \(r_t\) by \(\max(r_t, c)\). The horizon table reports the share of \(\mathbb{E}(w)\) and \(\mathbb{E}(M)\) beyond 100, 500, 1,000, 10,000 and 100,000 years, plus a bound on everything beyond \(T\).
What the Monte Carlo does The report treats \(f\) as a known positive number. Here \(f \sim \mathrm{Normal}(\mu_f, \sigma_f)\), clipped at 1, so negative draws (the action raises risk during its window) are possible; with probability \(p_b\) a delayed backfire multiplies risk by \((1+b)\) in a later window, with \(b\) lognormal. Each draw’s \(\mathbb{E}(M)\) is computed exactly, and the page reports the full distribution and \(\Pr[\mathbb{E}(M) < 0]\), not only the mean. The defaults are illustrative, not estimates. Seeded, so results are reproducible.
What rebound means In the report the risk path is fixed: nothing you do now changes later risk. Here, after the mitigation window ends, risk is multiplied by \(1 + \beta f P / D\) for the next \(D\) years (so \(\beta = 1\), \(D = P\) adds the same proportional risk-years back later, a pure delay of risk), or by \(1+\beta f\) forever if permanent. Negative \(\beta\) is a virtuous cycle. This is the simplest version of the action-dependent risk the evaluator asked for; it’s one functional form among many.
What this illustrates Rethink Priorities’ Donor Compass splits each fund’s modeled impact into six time windows and multiplies each by a factor the user’s worldview sets (its walkthrough’s example: 1.00, 0.95, 0.85, 0.70, 0.50, 0.10). This switch applies the same aggregation to this model’s \(\mathbb{E}(M)\), so you can see what share lands in the 500+ year window and how much a given set of factors keeps. RP’s current model of global catastrophic risk funds lists this report as an influence; see Departures.

Risk and value paths

Left: the yearly chance of extinction, with and without the action. The action’s effect is the small dip in its first years; both axes are logarithmic. Right: what each year is worth compared with a year of today’s world.

Expected value versus horizon

Each curve is the value of the future if everything ended at that year, with and without the mitigation; the right panel is the cumulative value of the mitigation. Where the curves flatten is where the report’s answer “converges”; how far right that happens shows how much rides on the far future.

When the value arrives (truncation diagnostics)

Read across a row: how much of the future’s value, and of the mitigation’s value, arrives before and after year H. If much of E(M) comes after year 10,000, the answer depends on beliefs about the very far future, which no one can check.

Persistence curve

\(\mathbb{E}(M)\) as persistence \(P\) varies, everything else as set (compare the report’s Figure 8 and Table 3). The circled point is your current \(P\). Returns to persistence diminish when the mitigated years are similar; under Time of Perils the curve kinks where the window leaves the high-risk era.

Scenario grid at the current settings

The report’s Table 3 layout (4 risk cases by 5 value cases), computed with the current \(f\), \(P\), \(T\) and any switches that are on. Each cell is \(\mathbb{E}(M)\) for that pair; the smaller number under it is the ratio to the constant-risk, constant-value cell (the report’s Figure 6 convention). Reading down a column shows how much the risk scenario matters; reading across a row shows how much value growth matters.

Distribution of the value of mitigation under sign uncertainty

Time-bucket discounting

Sensitivity: one input at a time

Each bar halves or doubles one input, holding the others at their current values, and shows the resulting \(\mathbb{E}(M)\) as a log10 ratio to the current \(\mathbb{E}(M)\): a bar reaching 1 means the answer becomes 10 times larger, -1 means 10 times smaller. Longer bars are the inputs that matter most. This is a local sensitivity, not a variance decomposition.

Share or submit your results

Three ways to share what you found. Copy a link that reopens this page with your settings. Copy, email or download a summary of the results. Or submit the scenario to the shared list, with a few words on why you chose these values; we’d especially like scenarios from people who have thought hard about one of the inputs. You can also paste the summary into a Hypothes.is annotation on this page.

Two things to know. The link and the summary carry all your settings, so anyone you send them to sees your assumptions. And Hypothes.is annotations are public, so don’t paste anything confidential into one. The downloads include the engine version, settings schema and build, so a result can be checked against the model that produced it.

Submit this scenario to the shared list

The form sends your current settings and results along with what you write below. We read every submission before anything goes on the shared scenarios page, and we publish it only if you tick the box. Your email address is never published.

Formulas and parameters: Formulas. Exact comparison with the report: Replication. Everything that differs from the 2023 report, and how Rethink Priorities’ current model compares: Departures. How this tool relates to other models, tools and research: Context. Scenarios other people have submitted: Shared scenarios. Questions, corrections and suggestions: Comment.