Advice to pivot into AI Safety is uncalibrated and thus suspect

1.1 Break-even \(p_\rho^*\) (closed form)

The sign of \(\Delta \mathrm{EV}_\rho(p)\) is determined by the bracket. Thus the break-even per-application success probability is \[ \boxed{\,p_\rho^*=\frac{c\,\rho}{r\,\Delta u}\,}. \] Comparative statics (all else equal):

• Higher burn \(c\) or higher discount rate \(\rho\) \(\Rightarrow\) increase \(p_\rho^*\) (making it harder for us to break even).
• Higher shot rate \(r\) or higher upside \(\Delta u\) \(\Rightarrow\) decrease \(p_\rho^*\).
• \(p_\rho^*\) is independent of runway \(\ell\) (though \(\ell\) still scales the level of \(\Delta \mathrm{EV}_\rho\)).

A tiny-probability expansion for intuition. When \((r p+\rho)\ell\ll1\), \[ \Delta \mathrm{EV}_\rho(p)\approx \ell\big(\Delta u\,r p/\rho - c\big), \] So, the same closed-form threshold drops out immediately.

1.2 Worked example

Cool! Now, let’s plug in some plausible representative numbers for Alice, our mid‑career technical researcher considering a pivot into an AI safety role in a developed economy. All dollar values are in thousands of USD.

• Personal+impact weights. Set \(\alpha=1\) (we value \(\$1\) of impact/donations like \(\$1\) of personal spend).
• Baseline. \(w_0=180\), \(d_0=18\), \(i_0=0\)
• Target role. \(w_1=120\), \(d_1=0\), \(i_1=100\)
• Process. \(\ell=\tfrac12\) years (6 months), \(r=24\) apps/year. [TODO clarify]
• Discount & runway costs. \(\rho = 1/3 \approx 0.333\,\mathrm {yr}^{-1}\) (roughly “3-year horizon” feel), \(c=25\).

This gives us \(\Delta u = (120 + 0 + 100) - (180 + 18 + 0) = 22\).

Then the break-even probability is \[ p_\rho^*=\frac{c\rho}{r\Delta u} =\frac{25\cdot(1/3)}{24\cdot 22} \approx \boxed{1.58\%}\ \text{per application.} \] Over a 6-month runway, there’s a \(q_\rho^* = 1-e^{-r p_\rho^* \ell} =1-e^{-12\cdot 0.01579} \approx \boxed{17.3\%}\) chance of at least one success.

At \(p_\rho^*\), her truncated expected sabbatical is \[ \mathbb{E}[\tau]=\frac{1-e^{-r p_\rho^* \ell}}{rp_\rho^*}\approx 0.455\,\text{yrs}\,(\approx 5.5\ \text{months}), \quad \mathbb{E}[\tau\mid\text{success}]\approx 0.240\,\text{yrs}\,(\approx 2.9\ \text{months}), \] This matches our intuition. Choosing \(\rho\approx 1/3\) is a steep discount, but seems to be pretty common in people who are worried about short-timeline AI.

Let’s plot a few values to visualize the trade-offs.

# Discounted EV of an AI-safety pivot (PRIVATE MODEL)
# Replaces the T-horizon version with continuous-time discounting at rate rho.

import numpy as np
import matplotlib.pyplot as plt

# Optional styling: keep portable
try:
    from livingthing.matplotlib_style import set_livingthing_style
    set_livingthing_style()
except Exception:
    pass

# -----------------------------
# Model primitives (edit these)
# -----------------------------
# Process
r    = 24.0      # application opportunities per year
ell  = 0.5       # runway (years)
rho  = 1.0/3.0   # discount rate per year (~"3-year horizon" feel)
c    = 25.0      # runway burn rate (k$/year, donation-equivalent)

# Upside options (k$/year): Δu = (w1 + i1 + d1) - (w0 + i0 + d0) with α=1 already folded in
delta_u_list = [5.0, 22.0, 42.0]  # try a few values to see sensitivity

# -----------------------------
# EV function (exact, closed-form, discounted)
# -----------------------------
def ev_discounted(p, delta_u, r, ell, rho, c):
    """
    Discounted expected value ΔEV_ρ (in k$ PV) of attempting a pivot with max runway ell.
    Formula: ΔEV_ρ(p) = [(1 - exp(-(r*p + rho)*ell)) / (r*p + rho)] * (delta_u*(r*p)/rho - c)
    Handles vector p; rho>0.
    """
    p = np.asarray(p, dtype=float)
    lam = r * p
    S = lam + rho
    scale = (1.0 - np.exp(-S * ell)) / S
    return scale * (delta_u * lam / rho - c)

def p_star_discounted(r, rho, c, delta_u):
    """
    Closed-form break-even p*: p* = (c * rho) / (r * delta_u).
    Returns np.nan if delta_u<=0 (no upside).
    """
    return np.nan if delta_u <= 0 else (c * rho) / (r * delta_u)

def q_over_runway(p, r, ell):
    """Total success probability over runway ell when arrivals ~ Poisson with rate r*p."""
    return 1.0 - np.exp(-r * p * ell)

# -----------------------------
# Plot EV vs p (log x-axis), annotate p*
# -----------------------------
p_grid = np.logspace(-3.0, 0, 1000)  # p from 0.1% to 100%

plt.figure(figsize=(8, 5.5))
for du in delta_u_list:
    ev_vals = ev_discounted(p_grid, du, r, ell, rho, c)
    p_star = p_star_discounted(r, rho, c, du)
    label = f"Δu={du:.0f}k/y"
    if np.isfinite(p_star) and (p_grid.min() <= p_star <= p_grid.max()):
        q_star = q_over_runway(p_star, r, ell)
        label += f"  (p*≈{100*p_star:.2f}%,  q*≈{100*q_star:.1f}%)"
        # Mark the root
        y_star = ev_discounted(p_star, du, r, ell, rho, c)
        plt.plot([p_star], [y_star], "o")
    plt.plot(p_grid, ev_vals, label=label)

plt.axhline(0.0, color="gray", linestyle="--", linewidth=1)
plt.xscale("log")
plt.xlabel("Per-application success probability p (log scale)")
plt.ylabel("ΔEV (present value, k$ donation-equivalent)")
plt.title(f"Discounted EV vs p   (r={r}/y, ell={ell}y, rho={rho:.3f}/y, c={c}k/y)")
plt.legend()
plt.grid(True, which="both", ls=":", alpha=0.6)
plt.tight_layout()
plt.show()

# -----------------------------
# Numeric table for the worked example Δu=22k/y
# -----------------------------
du = 22.0

# Baselines: p=0 (pure burn) and p→1 (immediate success)
ev_p0 = ev_discounted(0.0, du, r, ell, rho, c)
ev_p1_limit = du / rho  # as p→1, ΔEV → Δu/ρ
print(f"Baseline (p=0, pure burn): ΔEV = {ev_p0:.2f} k$ (PV)")
print(f"Upper bound (p→1, immediate success): ΔEV → {ev_p1_limit:.2f} k$ (PV)")
print()

for pct in [0.01, 0.02, 0.03]:
    val = ev_discounted(pct, du, r, ell, rho, c)
    print(f"ΔEV(Δu=22k/y, p={100*pct:.0f}%): {val:+.2f} k$ (PV)")

p_star = p_star_discounted(r, rho, c, du)
if np.isfinite(p_star):
    q_star = q_over_runway(p_star, r, ell)
    print(f"Break-even p* (Δu=22k/y): {100*p_star:.3f}% per application")
    print(f"q* over runway (ell={ell}y): {100*q_star:.2f}%")
else:
    print("No break-even (Δu<=0).")

Baseline (p=0, pure burn): ΔEV = -11.51 k$ (PV)
Upper bound (p→1, immediate success): ΔEV → 66.00 k$ (PV)

ΔEV(Δu=22k/y, p=1%): -3.98 k$ (PV)
ΔEV(Δu=22k/y, p=2%): +2.74 k$ (PV)
ΔEV(Δu=22k/y, p=3%): +8.75 k$ (PV)
Break-even p* (Δu=22k/y): 1.578% per application
q* over runway (ell=0.5y): 17.25%

If you wish to play around with the assumptions check out the interactive Pivot EV Calculator (source at danmackinlay/career_pivot_calculator).

For Alice, the threshold probability \(p_\star\) marks the point where a pivot breaks even; below that, she burns runway faster than expected value, and if she wants to make impact, she might consider donating money instead.

1.3 Are we applying too much as individuals?

I reckon so. Maybe we’ve already passed the break‑even point—maybe not.

My reasoning is that although the break‑even \(p_\rho^*\) is low (≈1.6% per application with \(\rho\approx 1/3\,\mathrm{yr}^{-1}\) in the worked example), this is a generous lower bound, and I expect the actual break‑evens to be higher. The threshold is also sensitive to \(\rho\) and \(\Delta u\).

For one thing, the calculations are very sensitive to the upside \(\Delta u\); if your impact valuation is lower, or your wage cut is larger, then \(p_\rho^*\) rises quickly. If you’re simply “wrong” about your impact valuation, you can quickly get negative EV.

Let’s be real: we have no idea what the impact of any given career pivot will be. Perhaps it’s a black swan farming situation where expected value isn’t even a productive framing?

By the same token, opportunity costs are still real. If you’re prepared to pay a substantial pivot cost to achieve a marginal impact, you might instead donate that pivot cost to your favourite AI safety NGO and end up ahead with no risky gambles involved.

For one thing, job applications are not IID; rather, they’re correlated because we apply to similar roles with similar CVs. The effective number of independent shots is lower than the raw number of applications.

And what even is \(p\)? Trying to work out that one was what got me started running this calculation for myself. That is one thing we don’t get from the career advice. Without that, many mid‑career readers will implicitly assume \(p>p_\star\) when in fact \(p<p_\star\).

The remedy isn’t complicated in principle: publish base rates. Employers can publish stage counts; advice organizations can publish calibrations of their advisors’ forecasted \(p\) against realized outcomes. Absent that, the rational prior for a mid‑career person is that generic encouragement to “do AI safety stuff” is EV‑negative unless we have private side information that pushes our \(p\) above our personal \(p_\star\).

2.1 Model

• Each applicant \(k\in{1,\dots,K}\) has a true per‑year impact in the role \(I^{(k)}\sim F\), i.i.d. (measured in donation-equivalent \(\Delta u\)-units per year, matching the Part 1 scale).

• Employers observe \(I^{(k)}\) (or a sufficiently informative proxy) and hire the top \(N\). Applicants do not observe their own \(I^{(k)}\). We treat private candidate losses as independent of \(I^{(k)}\): each failed pivot costs \(c \ell\) of value regardless of talent.

• Let the field‑side annual impact of the hires be \[ S_{N,K}:=I_{(K)}+I_{(K-1)}+\dots+I_{(K-N+1)}. \] We care about \(B(K):=\mathbb{E}[S_{N,K}]\), and in particular its marginal value for one extra applicant. \[ \mathrm{MV}_K:=B(K+1)-B(K). \]

• Each unsuccessful applicant pays the discounted sabbatical-cost PV \[ \boxed{\,C_{\text{fail},\rho}=c\int_0^\ell e^{-\rho t}\,dt=c\,\frac{1-e^{-\rho\ell}}{\rho}\,}. \] Under the sabbatical-then-stop rule, all \((K-N)\) unsuccessful candidates pay the full sabbatical cost.

We do not model org‑side congestion (it’s empirically small because employers stop looking at candidates when they’re overwhelmed (J. Horton and Vasserman 2021)). All the benefit in the model comes from the fact that, all else being equal, more applicants mean a better top‑\(N\).

1. With \(N\) seats fixed, adding one more applicant increases the expected number of failures by exactly 1. Hence the marginal private cost of one extra applicant is \(C_{\text{fail},\rho}\), the expected sabbatical burn per failed candidate.

2. Whether adding applicants is socially worthwhile depends on \(\mathrm{MV}_K\), i.e., on the right hand tail of \(F\).

An interesting question is: how much better does one candidate make the top-\(N\)? For sufficiently many candidates \(K\), this depends only on the tail of the candidate quality distribution, \(F\), because of extreme value theory (which gives us a kind of “law of large numbers for maxima”). Now, what kind of extreme value distribution does \(F\) have? The default would be a light-tailed distribution such as Exponential or Normal, but it’s also plausible that \(F\) has a heavy tail, e.g., a Pareto or Fréchet distribution. Picking a heavy-tailed distribution is a way of capturing the intuition that there are “unicorn” candidates (e.g., 10x engineers) who are much better than the rest. I think the candidate quality distribution is heavy-tailed, but how heavy-tailed it is matters a lot, and I don’t know.

Anyway, let’s introduce some families of distributions and see how \(\mathrm{MV}_K\) behaves.

2.2 Oversubscription threshold

When does persuading one more applicant start to reduce total welfare?

Every extra applicant slightly improves the chance that the best hires are stronger, but adds one more failed attempt that burns private resources. We compare these in present-value dollars, using the same continuous discount rate \(\rho\) we introduced earlier. This single rate reflects both time preference and any expected shortening of future impact streams (e.g. job changes, role turnover, project endings).

A filled role produces a stream of impact over time. When we discount that stream at rate \(\rho\), the total present value of \(\$1K\)/year of annual impact is \(1K/\rho\). This already accounts for the fact that future years are uncertain and less valuable in expectation.

\[ \boxed{H_\rho=\int_0^\infty e^{-\rho t}\,dt=\frac{1}{\rho}} \qquad\text{(PV weight of one unit of per-year impact).} \]

The planner’s break-even condition for admitting one more applicant is \[ \boxed{\,\mathrm{MV}_K\cdot H_\rho \;\ge\; C_{\text{fail},\rho}=c\,\frac{1-e^{-\rho\ell}}{\rho}\,}. \]

Adding more applicants helps the field only while the discounted value of a slightly better hire (the left side) exceeds the discounted expected cost of one more failed pivot (the right side).

Solving for the critical pool size \(K_\rho^\dagger\) (beyond which the marginal extra applicant has a net negative effect) gives:

• Exponential (\(I\sim\mathrm{Exp}(\lambda)\), mean \(1/\lambda\)): \[ \boxed{\,K_\rho^\dagger = \frac{N}{\lambda}\cdot\frac{1}{\rho\,C_{\text{fail},\rho}}-1\,}. \]

• Fréchet (\(\alpha>1\), scale \(s\); \(C_N=\sum_{k=1}^N\Gamma(k-\tfrac{1}{\alpha})/\Gamma(k)\)): with \(\mathrm{MV}_K\approx \dfrac{s\,C_N}{\alpha}K^{\frac{1}{\alpha}-1}\), \[ \boxed{\,K_\rho^\dagger =\left(\frac{s\,C_N}{\alpha\,\rho\,C_{\text{fail},\rho}}\right)^{\frac{\alpha}{\alpha-1}}.} \] Here \(s\) is the Fréchet scale parameter (units of impact per year), not a survival function. As \(\alpha\downarrow 1\) increases, \(K_\rho^\dagger\) explodes: in very heavy tails, very wide funnels can still be net positive.

With light tails, there’s a finite pool size after which turning up the hype (growing \(K\)) destroys net welfare. Every extra applicant burns \(C_{\text {fail},\rho}\) in private cost while adding \(\mathrm {MV}_K\) that shrinks like \(1/K\).

With heavy tails, the “wider funnel” argument can be correct—but only if the tail is actually heavy and the scale \(s\) is large.

Let’s plot total net welfare.

\[ \boxed{\,W(K)=B(K)\cdot H_\rho - \max\{K-N,0\}\cdot C_{\text{fail},\rho}\,} \] Where \(B(K)=\mathbb{E}[S_{N,K}]\) is in k$/year, \(H_\rho=1/\rho\) converts annual impact to present value, and \(C_{\text{fail},\rho}\) is in k$ (PV).

• Exponential: exact \(B(K)=\dfrac{N}{\lambda}\Big(1+H_K-H_N\Big)\).
• Fréchet (\(\alpha>1\)): large-\(K\) asymptotic \(B(K)\approx s\,C_N\,K^{1/\alpha}\) with \(C_N=\sum_{k=1}^N \dfrac{\Gamma\!\left(k-\tfrac{1}{\alpha}\right)}{\Gamma(k)}\).
• We match the scales to Part 1 by setting the mean impact per hire per year to \(\mu_{\text{ref}}=22\): Exponential: \(1/\lambda=\mu_{\text{ref}}\Rightarrow \lambda=1/\mu_{\text{ref}}\). Fréchet: \(\mathbb{E}[I]=s,\Gamma(1-1/\alpha)=\mu_{\text{ref}}\Rightarrow s=\mu_{\text{ref}}/\Gamma(1-1/\alpha)\).

# Field-level trade-off curves with discounting (PUBLIC MODEL)
# W(K) = B(K) * H_rho - max(K - N, 0) * C_fail_rho
# Where: H_rho = 1/(rho + mu), and C_fail_rho = c * (1 - exp(-rho*ell)) / rho

import numpy as np
import matplotlib.pyplot as plt
from scipy.special import gamma, digamma

# Optional styling: keep portable
try:
    from livingthing.matplotlib_style import set_livingthing_style
    set_livingthing_style()
except Exception:
    pass

# --- Parameters (aligned with Part 1) ---
N   = 24          # number of available roles
rho = 1/3.0       # discount rate per year  (~3-year effective horizon)
c   = 25.0        # k$/year private burn rate
ell = 0.5         # years of sabbatical runway
mu_ref = 22.0     # mean per-hire impact (k$/year, same Δu scale)
fail_cost_rho = c * (1 - np.exp(-rho * ell)) / rho  # PV of one failed pivot

# Impact distribution parameters
alphas = [2.0, 3.0, 4.0]  # Fréchet shapes (heavier→slower diminishing returns)
K_min, K_max = max(N, 20), 600
K = np.arange(K_min, K_max + 1)

EULER_GAMMA = 0.5772156649
def harmonic_number(n): return digamma(n + 1.0) + EULER_GAMMA

# --- Expected top-N impact under different tail assumptions ---
def B_exponential(K, N, mu_ref):
    """
    Impact per year (sum of top-N for Exp(λ) with mean 1/λ = mu_ref).
    Exact identity: B(K) = (N/λ) * (1 + H_K - H_N).
    """
    lam = 1.0 / mu_ref
    HK = harmonic_number(K.astype(float))
    HN = harmonic_number(float(N))
    return (N / lam) * (1.0 + HK - HN)

def C_N_frechet(N, alpha):
    j = np.arange(1, N + 1, dtype=float)
    return np.sum(gamma(j - 1.0 / alpha) / gamma(j))

def B_frechet_asymptotic(K, N, alpha, mu_ref):
    """
    Large-K asymptotic for sum of top-N of Fréchet(α, s), matched so E[I]=mu_ref.
    E[I] = s * Γ(1 - 1/α) => s = mu_ref / Γ(1 - 1/α).
    Then B(K) ≈ s * K^(1/α) * C_N.
    """
    s = mu_ref / gamma(1.0 - 1.0/alpha)
    Cn = C_N_frechet(N, alpha)
    return s * (K ** (1.0 / alpha)) * Cn

# --- Total discounted welfare: W(K) = PV(benefit) - PV(private burn) ---
def total_welfare(BK, K, N, fail_cost_rho, rho):
    H_rho = 1.0 / rho               # PV weight of one unit of annual impact
    failures = np.maximum(K - N, 0)
    return BK * H_rho - failures * fail_cost_rho

def argmax_idx(y):
    i = int(np.nanargmax(y))
    return i, float(y[i])

# --- Compute curves ---
B_exp = B_exponential(K, N, mu_ref)
W_exp = total_welfare(B_exp, K, N, fail_cost_rho, rho)
# Exponential: argmax
i_exp, Wexp_max = argmax_idx(W_exp)
Kexp_star = int(K[i_exp])

# Fréchet: argmax per alpha
frechet_results = []
for a in alphas:
    B_fr = B_frechet_asymptotic(K, N, a, mu_ref)
    W_fr = total_welfare(B_fr, K, N, fail_cost_rho, rho)
    i_star, Wmax = argmax_idx(W_fr)
    K_star = int(K[i_star])
    frechet_results.append((a, W_fr, K_star, Wmax))

Kexp_star = int(K[np.argmax(W_exp)])

# --- Plot ---
plt.figure(figsize=(8.5, 5.2))

# Exponential curve + argmax
plt.plot(K, W_exp, label="Exponential")
plt.scatter([Kexp_star], [Wexp_max], zorder=3)
plt.annotate(f"K*={Kexp_star}", (Kexp_star, Wexp_max),
             xytext=(6, 6), textcoords="offset points")

# Show where failures begin
plt.axvline(N, color="k", linestyle="--", lw=1)
plt.text(N, plt.ylim()[0], f"N={N}", rotation=90, va="bottom", ha="right")

# Fréchet curves + argmax
for (a, W_fr, K_star, Wmax) in frechet_results:
    plt.plot(K, W_fr, label=f"Fréchet α={a:.0f}")
    plt.scatter([K_star], [Wmax], zorder=3)
    plt.annotate(f"K*={K_star}", (K_star, Wmax),
                 xytext=(6, 6), textcoords="offset points")

plt.axhline(0, color="gray", linestyle="--", lw=1)
plt.xlabel("Applicant pool size K")
plt.ylabel("Total discounted welfare W(K) (k$ PV)")
plt.title("Total discounted welfare vs. pool size (single discount rate ρ)")
# Oversubscription thresholds (vertical guides)
lam = 1.0 / mu_ref                         # exponential mean = 1/lam = mu_ref
K_dagger_exp = (N / lam) * (1 / (rho * fail_cost_rho)) - 1

def K_dagger_frechet(alpha):
    s = mu_ref / gamma(1.0 - 1.0/alpha)    # Fréchet scale matched to mean
    Cn = C_N_frechet(N, alpha)
    base = (s * Cn) / (alpha * rho * fail_cost_rho)
    return base ** (alpha / (alpha - 1))

# Draw them (only if they’re in-range)
ymin, ymax = plt.ylim()
if K_min <= K_dagger_exp <= K_max:
    plt.axvline(K_dagger_exp, color="C0", ls=":", lw=1)
    plt.text(K_dagger_exp, ymin, "K† (Exp)", rotation=90, va="bottom", ha="center", color="C0")

for a in alphas:
    Kd = K_dagger_frechet(a)
    if K_min <= Kd <= K_max:
        plt.axvline(Kd, color="C1", ls=":", lw=1)
        plt.text(Kd, ymin, f"K† (α={a:.0f})", rotation=90, va="bottom", ha="center", color="C1")

plt.legend()
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()

# --- Print summary ---
print(f"ρ={rho:.2f}/yr (≈{1/rho:.1f}-yr horizon); fail_cost={fail_cost_rho:.2f} k$")
print(f"Exponential: K*={Kexp_star}, W(K*)={np.max(W_exp):.1f} k$")
for (a, W_fr, K_star, W_exp) in frechet_results:
    print(f"Fréchet α={a:.1f}: K*={K_star}, W(K*)={np.max(W_fr):.1f} k$")

ρ=0.33/yr (≈3.0-yr horizon); fail_cost=11.51 k$
Exponential: K*=137, W(K*)=3015.1 k$
Fréchet α=2.0: K*=248, W(K*)=3136.6 k$
Fréchet α=3.0: K*=73, W(K*)=1966.4 k$
Fréchet α=4.0: K*=43, W(K*)=1767.5 k$

• This plots total net welfare \(W (K)\) (as opposed to marginal) and marks the argmax \(K^*\) for each family, i.e. the point where we’d stop widening the funnel if we cared about total welfare. The dashed line at \(K=N\) shows where failures begin: \((K>N\Rightarrow K-N\) people each pay \(C_{\text{fail},\rho})\). Note: the markers annotate \(K^*=\arg\max W(K)\); this generally differs from the oversubscription threshold \(K_\rho^\dagger\), which is defined by \(\mathrm{MV}_K H_\rho = C_{\text{fail},\rho}\).
• Units: \(B(K)\) is in k$ per year and is converted to PV by multiplying by \(H_\rho=\frac{1}{\rho}\). The subtraction uses the discounted per-failure cost \(C_{\text{fail},\rho}=c\,\frac{1-e^{-\rho\ell}}{\rho}\).
• Fréchet curves use the standard large-\(K\) asymptotic \(B(K)\approx s\,K^{1/\alpha}C_N\) (with \(s=\mu_{\text{ref}}/\Gamma(1-1/\alpha)\)). For exact finite-\(K\) values we could add a Monte Carlo estimator, but the large-\(K\) regime is what matters for oversubscription anyway.
• We treat all future uncertainties about role duration, turnover, or project lifespan as already captured in the overall discount rate \(\rho\).

At the field level, Alice is one more data point on the dashboard; if the funnel is already redlining, her marginal impact may be negative.

3.1 Improving field-level calibration (Gauge B)

To decide whether to keep widening the funnel, the field needs a clearer picture of how applicant numbers affect impact. The model highlights that this depends heavily on the distribution of candidate quality (the tail shape of \(F\)) and the private costs of pivoting (\(c\ell\)).

Estimating the tail shape of impact is notoriously difficult and there are no perfect measures. However, we are not even doing a good job at observing imperfect proxies and trends. Let’s consider some we could use:

1. Estimate applicant costs (\(c\ell\)). Advice organizations or funders should survey applicants (both successful and unsuccessful) to estimate the typical time and financial costs incurred during a pivot attempt. This establishes the cost side of the equation.

2. Track realized impact proxies. Employers should track proxies for the value-add of hires over time. Analyzing historical cohorts can help determine if widening the funnel is still yielding significantly better hires, or if returns are rapidly diminishing.

If returns are diminishing (as expected in light-tailed distributions) and applicant costs are high, the field should pause efforts to widen the generic funnel. Resources should instead shift towards creating more roles (\(N\)) or improving the impact of existing roles.

3.2 Improving individual-level calibration (Gauge A)

The most direct way to help individuals calibrate their decisions is to provide accurate base rates. This allows candidates to estimate their personal \(p\) and use the decision model presented in Part A.

1. Publish stage-wise acceptance rates. Employers and fellowship programs should publish historical data on the number of applicants, interviews, and offers for different tracks and seniority levels. This is the single most impactful intervention for individual calibration.

2. Provide informative feedback and rank. Base rates provide a population average, but candidates need personalized signals to update their estimate of \(p\). The highest-value information an employer can provide is an applicant’s approximate rank within the pool (e.g., “top quartile,” “middle 50%”) or standardized feedback based on initial screening.

   Providing this feedback is costly for employers — it requires more reviewer time and careful communication. However, these costs must be weighed against the significant deadweight loss incurred by miscalibrated candidates (the Pivot Tax). When organizations don’t pay the cost of providing feedback, they externalize that cost onto the applicants. Furthermore, if the field fails to provide this information, it risks a credibility cost by continuing to operate on opaque mechanisms. Investing in better feedback mechanisms internalizes the cost of calibration and reduces systemic deadweight loss.

Absent this data, advice organizations face a difficult challenge. They want to encourage talented people to enter the field, but without calibration, their encouragement may be misleading.

Some organizations already contribute valuable information. MATS (ML Alignment Theory Scholars), for example, publishes statistics about their application rounds. The 80,000 Hours job board provides context about the opportunity rate (\(r\)) and the scale of the field. Widespread adoption of this transparency is necessary for a calibrated ecosystem.

A potential fallback is for advisors to track and publish their own forecast calibration (e.g., Brier scores) regarding candidate success. However, this is a second-best solution. It provides a noisy signal and places the burden of interpretation on the candidates, who may not be resourced to evaluate such scores. It does not replace the need for ground-truth base rates from employers. If an advice organization does not track outcomes, its advice cannot be calibrated except by coincidence.

5.1 Improving the information environment

The following actions would significantly improve the ability of both individuals and the field to calibrate decisions.

1. Stage-count reports. Employers should commit to publishing quarterly or annual summaries of application funnels, detailing the number of applicants, candidates reaching each interview stage, and hires, segmented by track and seniority. A simple standardized format (e.g., CSV) would suffice. This is the single most important step toward anchoring realistic success probabilities (\(p\)).

2. Standardized feedback and ranking. Employers should develop mechanisms to provide standardized feedback or an indication of relative rank to applicants, even those rejected early. While resource-intensive, this provides a crucial personalized signal of fit. The field must recognize that the cost of providing this information should be weighed against the collective cost of the Pivot Tax and the long-term credibility of the field.

3. Applicant cost surveys. Advice organizations should regularly survey the community to estimate the typical private costs (\(c\ell\)) associated with pivot attempts, including foregone wages and time spent. Publishing these estimates helps determine the field-level oversubscription threshold (\(K^\dagger\)).

We can try to get the information ourselves by gossip and guesstimation, but this is a poor substitute for systematic transparency.

5.2 Secondary improvements: Reducing private costs

Beyond calibration, there are ways to reduce the deadweight loss by lowering the private costs of pivoting or by better utilizing existing signals.

• Utilizing transition grants as signals. Organizations like Open Philanthropy offer career transition grants. These play a dual role in the ecosystem, serving both as funding and as information gates.
  • If received, a grant directly lowers the private cost of pivoting (\(c\)) for the candidate, making the gamble more favorable by reducing the financial barrier to exploration.
  • If denied, it serves as a valuable, albeit noisy, calibration signal. The grantmaker’s assessment, presumably calibrated by observing many such transitions, offers an external signal about the candidate’s prospects. If a major funder declines to underwrite the transition, candidates should use this information to significantly update their estimate of \(p\) downwards, recognizing that their sabbatical will not only be more costly but also less likely to succeed.
• Mechanism design (Soft caps). In capacity-constrained hiring rounds or fellowships, implementing soft caps—where the application window automatically pauses after a certain number of applications—can reduce excessive congestion. Experimental evidence suggests this can reduce applicant-side waste without significantly harming match quality (J. J. Horton et al. 2024).