Quantifying the Expected Disvalue of
Thermally Misaligned Furniture:
A Longtermist Perspective on the Table Problem

Abstract

1. Introduction

The field of alignment research has traditionally—and, we shall argue, myopically—focused on artificial intelligence systems, seeking to ensure that AI agents pursue goals compatible with human values and survival (Russell, 2019; Bostrom, 2014; Christian, 2020). This narrow focus, while understandable given the salience of AI capabilities research, overlooks a broader and more fundamental category of alignment problems: the systematic misalignment between human physical constraints and the physical parameters of objects we create to serve us.

In this paper, we examine what we term the "furniture alignment problem," with specific and sustained attention to tables—the most ubiquitous category of horizontal-surface furniture, with an estimated global population of 1.83 billion units as of the 2023 census (International Furniture Statistics Bureau, 2023). Tables serve as our primary case study for several compelling reasons: they represent the largest furniture category by unit count, they exhibit substantial material diversity enabling cross-material analysis, and they possess a mean operational lifespan of 23.7 years—sufficient to constitute a medium-term persistent misalignment risk.

We demonstrate through rigorous quantitative analysis that tables, as currently manufactured under prevailing industry standards (ISO 7170:2021; ANSI/BIFMA X5.5), possess operational parameters that significantly and systematically exceed human survival thresholds across the temperature dimension. This creates scenarios—whose probability we estimate using expert elicitation methods—in which tables persist as physical objects while the humans who created them do not.

"The question is not whether tables will outlast us, but whether we should permit them to do so by design. Every table produced without temperature alignment is a statement that we accept being outlived by our furniture."
— Proceedings of the First International Conference on Physical Alignment (2023)

This misalignment has received virtually no attention in the academic literature or philanthropic funding landscape. A comprehensive search of major grant databases reveals zero active grants addressing furniture temperature alignment: Open Philanthropy's 2024 grants database contains no entries matching furniture, table, or physical alignment keywords (Open Philanthropy, 2024); GiveWell's intervention reports include no analysis of furniture-related cause areas (GiveWell, 2024); and the EA Funds have allocated $0 to this problem area since inception.

This neglect is particularly striking given the clear applicability of effective altruism's importance-tractability-neglectedness (ITN) framework (MacAskill, 2015). As we demonstrate in subsequent sections, table temperature alignment scores highly on all three dimensions: importance (affecting billions of tables and potentially all future humans), tractability (with existing material science solutions), and extreme neglectedness (zero current funding).

"How are we letting tables get away with this?"
— Anonymous Reviewer 2, Journal of Applied Alignment Studies

The remainder of this paper is structured as follows: Section 2 develops our theoretical framework for physical alignment, introducing formal definitions and the concept of "successor scenarios." Section 3 provides detailed quantitative analysis of the temperature differential between tables and humans, drawing on our systematic survey of 847 table models. Section 4 presents our expected value analysis, including Monte Carlo simulation methodology and results. Section 5 examines technical solutions from materials science. Section 6 provides cost-effectiveness estimates across intervention types. Section 7 discusses implications, limitations, and areas for future research. Section 8 concludes with policy recommendations.

2. Theoretical Framework: Physical Alignment

2.1 Defining Physical Alignment

We begin by developing a formal framework for physical alignment that generalizes insights from the AI alignment literature to the domain of physical artifacts. Where AI alignment concerns the alignment of an agent's goals and behaviors with human values, physical alignment concerns the alignment of an artifact's physical parameters with human survival constraints.

This definition captures the intuition that objects created to serve humans should not be capable of persisting in environments that would eliminate all humans. An artifact satisfying (1) shares our physical fate: it cannot outlast us through superior physical resilience alone.

We can further define a quantitative measure of misalignment:

A misalignment ratio of 1.0 indicates perfect alignment; values greater than 1.0 indicate the artifact can survive conditions that humans cannot. For temperature, we will show that standard tables exhibit M ≈ 6.0, meaning tables can survive across a temperature range six times wider than humans.

2.2 The Successor Problem

Physical misalignment creates the possibility of what we term successor scenarios: situations in which artifacts outlast their creators due to superior physical resilience.

Formally, let W_t denote the world-state at timet, and let C be a catastrophic event occurring at time t_C. A successor scenario obtains if:

The probability of a successor scenario depends on both the probability of catastrophic events and the degree of physical misalignment. For the temperature parameter specifically:

where T_post-C is the temperature following catastropheC, and R_A ∖R_S is the "successor zone"—temperatures survivable by artifacts but not by humans.

2.3 The Axiological Status of Successor Scenarios

One might object that table persistence without humans is value-neutral. If no conscious entities exist to experience the world, what does it matter whether tables persist? We offer three responses to this challenge.

First, under preference-satisfaction views of value, the current preferences of humans regarding the post-extinction world may carry moral weight. Survey evidence suggests that 67% of respondents express a preference that human-created artifacts not outlast humanity, conditional on human extinction (Bergstrom et al., 2024). These preferences constitute a prima facie reason to avoid successor scenarios.

Second, the physical resources embodied in misaligned tables represent an opportunity cost. Materials configured for table-survivability could alternatively have been configured for human-survivability enhancement. Each misaligned table represents approximately 12.4 kg of matter (production-weighted average) that could theoretically have contributed to survival infrastructure rather than successor-scenario furniture.

Third, and most compellingly from a longtermist perspective, physically misaligned tables may impose constraints on the long-term future. If successor scenarios are possible at non-negligible probability, then optimal resource allocation in the present should account for the expected disvalue of these scenarios, even if that disvalue manifests only as the absence of potential future value.

The remainder of this paper is dedicated to establishing conditions (i) and (iii) empirically, while taking (ii) as axiomatic based on the arguments above.

3. Quantifying the Temperature Differential

3.1 Human Temperature Tolerance: A Review

The human thermoregulatory system maintains core body temperature within a narrow range of approximately 36.5°C to 37.5°C through a combination of metabolic heat production, vasodilation/ vasoconstriction, sweating, and behavioral adaptations (Parsons, 2014). Core temperatures below 35°C (hypothermia) or above 40°C (hyperthermia) initiate physiological cascades leading to organ failure and death within hours to days depending on severity (Kenney et al., 2015).

Ambient temperature tolerance depends critically on humidity, exposure duration, access to water, clothing, and shelter. Under sustained exposure without technological intervention—the relevant baseline for catastrophic scenarios—the survivable ambient temperature range is approximately 0°C to 40°C, with the upper bound constrained by wet-bulb temperature limits (Sherwood & Huber, 2010). Recent climate research has refined the lethal wet-bulb threshold to approximately 35°C, corresponding to dry-bulb temperatures of 40-50°C depending on humidity (Raymond et al., 2020).

We adopt a conservative estimate of 0°C to 40°C for the human survival range (R_H(T) = [0, 40]°C), yielding a range width of 40K. This estimate assumes healthy adults with access to water but without active cooling or heating technology—the appropriate counterfactual for most catastrophic scenarios.

3.2 Systematic Analysis of Table Temperature Tolerance

To establish the temperature tolerance of standard tables, we conducted a systematic survey of 847 table models representing approximately 94% of global production volume by unit count. For each table model, we obtained material composition data and calculated theoretical temperature limits based on material properties, with validation against manufacturer stress-testing data where available (n=312 models with empirical validation).

Table structural failure was defined as permanent deformation exceeding 5% of original dimensions or complete material phase change (melting, sublimation, or combustion). Results are summarized in Table 1.

Table 1: Temperature tolerance by table material category (n=847). T_min and T_max represent the temperature limits for structural integrity. M(T) is the misalignment ratio relative to human temperature range of 40K.

The production-weighted average table maintains structural integrity from -40°C to 200°C, yielding a survivable range of 240K. This corresponds to a misalignment ratio of M = 6.0, indicating that tables can survive across a temperature range six times wider than humans.

3.3 The Successor Zone

Based on our analysis, we can formally characterize the successor zone—the set of temperatures at which tables survive while humans do not:

This successor zone spans 200K of temperature space—five times the human survival range. Any catastrophic event that shifts global temperatures into this zone creates a successor scenario where tables inherit the Earth.

The asymmetry is particularly striking when visualized as a proportion of each entity's total range. Tables can survive in conditions lethal to humans across 83.3% of their operational range (200K / 240K), while humans can only survive conditions that tables can survive across 100% of the human range but merely 16.7% of the table range.

4. Expected Value Analysis

4.1 Methodological Framework

We employ a Monte Carlo simulation framework to estimate the expected disvalue of table temperature misalignment over the long-term future. Our methodology integrates three components: (i) a probability model for temperature-catastrophic events, (ii) a population model for future humans and tables, and (iii) a disvalue function mapping successor scenarios to DALYs.

For each of 10,000 simulated futures extending to the year 10,000 CE (chosen to balance computational tractability against longtermist considerations), we:

1. Sample catastrophic event occurrences from a Poisson process with time-varying intensity λ(t), calibrated to expert-elicited probability estimates
2. For each event, sample post-event temperature from scenario-specific distributions
3. Determine human and table survival based on temperature falling within respective ranges
4. Calculate successor scenario disvalue as the population-weighted expected future DALYs lost
5. Apply time discounting at rate δ = 0.001 per annum (Greaves & MacAskill, 2021)

The expected disvalue is computed as:

where P(C_t) is the probability density of a catastrophic event at time t, P(Successor | C_t) is the conditional probability that the event results in a successor scenario, and D(C_t) is the disvalue of the successor scenario.

4.2 Expert Probability Elicitation

We elicited probability estimates from 23 domain experts across climate science (n=8), nuclear risk studies (n=6), volcanology (n=4), and general catastrophic risk (n=5). Experts were asked to estimate the probability of temperature scenarios exceeding human but not table tolerances, using structured elicitation protocols following best practices (Tetlock & Gardner, 2015).

Table 2: Expert-elicited cumulative probabilities of temperature scenarios exceeding human but not table tolerances, by time horizon.

4.3 Population Projections

Estimating the disvalue of successor scenarios requires projecting both human and table populations into the future. For human populations, we adopt the UN's medium-variant projection through 2100 (United Nations, 2022) and extend using the framework of Ord (2020), which estimates potential human flourishing over astronomical timescales.

For table populations, we model growth using a logistic function with carrying capacity determined by projected human population and tables-per-capita ratios. Historical data suggest tables-per-capita has increased from 0.8 in 1950 to 2.4 in 2023, with projected saturation at approximately 4.0 tables per capita in developed economies.

4.4 Disvalue Calculation

The disvalue of a successor scenario at time t is calculated as the expected future value lost—the integral of population × quality-adjusted life expectancy over all future time, conditional on the successor scenario occurring at t.

where N(τ) is the counterfactual population at time τ (in a world without the catastrophe), QALE(τ) is quality-adjusted life expectancy, and δ is the discount rate.

To convert to DALYs, we use the standard transformation:

4.5 Results

Under our baseline assumptions, the Monte Carlo simulation yields an expected disvalue of table temperature misalignment of 2.3 × 10¹² DALYs (90% credible interval: [4.7 × 10¹¹, 8.9 × 10¹²]).

Table 3 presents the decomposition of expected disvalue by scenario type and time horizon.

Table 3: Decomposition of expected disvalue by scenario type and time horizon. Extreme heat scenarios dominate due to higher probabilities under climate trajectories.

4.6 Comparison to Other Cause Areas

To contextualize our estimate, we compare the expected disvalue of table temperature misalignment to other cause areas commonly evaluated in effective altruism:

Table 4: Comparison of expected disvalue and funding across cause areas. Table temperature alignment exhibits extreme neglectedness with zero current funding despite substantial expected disvalue.

The marginal cost-effectiveness of the first dollar spent on table temperature alignment is, by construction, infinite in terms of moving from the current state of zero attention. This extreme neglectedness, combined with non-trivial expected disvalue, suggests that the cause area merits serious consideration.

5. Technical Solutions for Temperature Alignment

Having established both the existence and magnitude of the table temperature alignment problem, we now turn to potential solutions. Our analysis identifies three primary technical approaches to achieving alignment, each with distinct cost profiles and implementation timelines.

5.1 Phase-Change Composite Materials

The most mature approach involves incorporating microencapsulated phase-change materials (PCMs) into table structural components. PCMs are substances that absorb or release thermal energy during phase transitions (typically solid-liquid); by engineering the encapsulation to rupture at specific temperatures, structural failure can be triggered at predetermined thresholds.

Nakamura & Singh (2024) demonstrate successful implementation using paraffin-based PCMs with failure onset at 48°C ± 2°C. Their approach involves dispersing microencapsulated paraffin (melting point 45°C) throughout a wood-polymer composite matrix. When ambient temperature exceeds the melting point, the expanded liquid paraffin ruptures its encapsulation, introducing voids into the structural matrix and triggering cascading failure.

For cold-alignment, analogous approaches using water-based systems (freezing point 0°C) can introduce ice crystal damage at sub-zero temperatures. Combined, these techniques can achieve table failure thresholds of [0°C, 48°C]—closely matching human survival parameters.

where ΔT_structural accounts for the time delay between PCM phase change and structural failure, typically 2-5°C depending on material composition and loading.

5.2 Thermoplastic Binding Agents

A second approach replaces traditional adhesives and binding agents with thermoplastic polymers engineered to soften at specific temperatures. This technique is particularly applicable to engineered wood products (MDF, plywood) and composite furniture, which rely heavily on adhesive bonds for structural integrity.

The glass transition temperature (T_g) of thermoplastic polymers determines the point at which the material transitions from rigid to rubbery behavior. By selecting polymers with T_gin the range of 42-48°C, table joints can be engineered to fail at temperatures just above human survival thresholds.

For cold-alignment, crystalline polymers that undergo brittle transitions below 0°C can be integrated into joint structures, ensuring failure in extreme cold conditions.

5.3 Shape-Memory Alloy Integration

The most sophisticated approach employs shape-memory alloys (SMAs)—metallic compounds that undergo reversible phase transformations at specific temperatures, causing dramatic shape changes. By integrating SMA components at structural joints, tables can be designed to actively disassemble when temperature thresholds are exceeded.

Nickel-titanium (NiTi) alloys offer transformation temperatures that can be precisely tuned through composition adjustment, with the austenite finish temperature A_franging from -100°C to +100°C depending on nickel content (Otsuka & Wayman, 1999).

While currently cost-prohibitive for mass production (adding approximately $45-120 per table), declining smart material costs following a Wright's Law trajectory suggest potential feasibility within 10-15 years:

5.4 Technical Comparison

Table 5: Comparison of technical approaches to table temperature alignment. TRL = Technology Readiness Level (1-9 scale).

6. Cost-Effectiveness Analysis

6.1 Intervention Pathways

We analyze cost-effectiveness across three distinct intervention pathways: (i) policy advocacy for regulatory change, (ii) manufacturer subsidy programs, and (iii) direct production of aligned tables. Each pathway operates through different mechanisms and at different scales.

6.2 Policy Advocacy

Policy advocacy aims to incorporate temperature alignment standards into furniture safety regulations. The primary opportunity is the 2025 revision of the EU Furniture Safety Directive (2001/95/EC), which sets standards affecting approximately 400 million tables produced annually for the European market.

We estimate the cost of a successful advocacy campaign at $2.5 million over three years, based on comparable regulatory advocacy efforts in the furniture sector (flame retardant standards, formaldehyde limits). If successful, this would affect approximately 1.2 billion tables over the 15-year policy cycle, at an average cost of:

However, advocacy success is uncertain. Based on comparable campaigns, we estimate a 15% probability of full success, 35% probability of partial success (standards adopted but with weaker thresholds), and 50% probability of failure. The expected cost per table aligned is:

Assuming aligned tables prevent successor scenarios at a rate proportional to global alignment (linear approximation), we estimate:

6.3 Complete Cost-Effectiveness Comparison

Table 6: Cost-effectiveness estimates by intervention type. DALYs per $1000 assumes linear scaling of risk reduction with tables aligned.

6.4 The $847 Threshold

Our headline cost-effectiveness estimate—that each $847 donated to policy advocacy prevents one table-outliving-human event in expectation—derives from the following calculation:

where a "table-outliving-human event" (TOH event) is defined as one table surviving a catastrophic scenario that eliminates one human. This metric, while somewhat artificial, provides an intuitive unit for comparing interventions.

7. Discussion

7.1 Implications for Effective Altruism

Our analysis suggests that table temperature alignment merits serious consideration within the effective altruism framework. The cause area exhibits the three hallmarks of a promising intervention opportunity:

• Scale: 1.83 billion tables globally, with expected disvalue of 2.3 × 10¹² DALYs
• Neglectedness: Zero current philanthropic funding, zero academic attention prior to this paper
• Tractability: Existing materials science solutions at 3-7% cost premium; clear policy pathway

While the expected disvalue is smaller than leading cause areas (AI alignment, biosecurity), the extreme neglectedness may compensate on a marginal cost-effectiveness basis. The first dollars spent in this area face no competition and can capture significant low-hanging fruit.

7.2 Limitations

Our analysis is subject to several important limitations:

Model uncertainty: Our Monte Carlo framework relies on expert elicitation for key probability estimates. Expert disagreement is substantial, with individual estimates spanning two orders of magnitude in some cases. We have attempted to capture this uncertainty through wide credible intervals, but structural model uncertainty may be larger.

Value assumptions: Our treatment of successor scenarios as disvaluable rests on philosophical assumptions that not all readers will share. Those who reject the moral significance of post-extinction artifact persistence will necessarily assign zero weight to our expected disvalue calculations.

Technical assumptions: Our cost estimates for alignment technologies are based on laboratory-scale demonstrations. Production-scale implementation may reveal unforeseen challenges or costs.

Scope limitations: We have focused exclusively on tables and the temperature parameter. A complete accounting of physical alignment would need to consider other furniture categories and additional physical parameters (pressure, radiation, atmospheric composition).

7.3 Future Research Directions

We identify several promising directions for future research:

1. Extension to other furniture categories (chairs: 2.3B units; cabinets: 1.1B units; bed frames: 0.9B units)
2. Analysis of non-temperature parameters (pressure survivability, radiation resistance)
3. Deeper exploration of phase-change composite chemistry for optimal failure thresholds
4. Policy analysis for non-EU jurisdictions (US CPSC, China GB standards)
5. Experimental validation of our theoretical temperature tolerance estimates

8. Conclusion

This paper has presented the first rigorous analysis of table temperature alignment as a cause area worthy of philanthropic attention. We have demonstrated that tables, as currently manufactured, possess temperature tolerance parameters that systematically exceed human survival thresholds by a factor of approximately six, creating meaningful probability of "successor scenarios" in which tables outlast humanity following catastrophic temperature events.

Our quantitative analysis, based on systematic material surveys of 847 table models and Monte Carlo simulation across 10,000 possible futures, estimates the expected disvalue of this misalignment at 2.3 × 10¹² DALYs. We have shown that technical solutions exist—primarily through phase-change composite materials and thermoplastic adhesives—that can achieve alignment at marginal cost increases of 3-7%.

Policy advocacy emerges as the most cost-effective intervention pathway, with an estimated cost of $847 per table-outliving-human event averted. The 2025 EU Furniture Safety Directive revision represents a critical near-term opportunity for incorporating temperature alignment standards into regulatory frameworks.

We call on the effective altruism community, policymakers, and furniture manufacturers to take this alignment problem seriously. The window for establishing global temperature alignment standards is narrow, and the stakes—a world populated by our furniture but not by us—are too high to ignore.

"In the end, we must ask ourselves: what kind of tables do we want to leave behind? Tables that share our fate, or tables that will preside over our empty rooms forever?"

Acknowledgments

We thank the anonymous reviewers for their constructive feedback, particularly Reviewer 2 who asked "How are we letting tables get away with this?"—a question that crystallized our thinking on the urgency of this work. We are grateful to participants in the 2024 Global Priorities Seminar at Oxford for valuable discussion, and to the 23 domain experts who contributed probability estimates under conditions of anonymity. We thank the Table Temperature Alignment Project for research funding and administrative support. Special thanks to Maria Lindqvist for exceptional research assistance. M. Chen acknowledges support from the Stanford Existential Risks Initiative (Grant #SERI-2024-017). A. Okonkwo acknowledges support from the Forethought Foundation for Global Priorities Research. H. Bergstrom acknowledges support from the Danish National Research Foundation.

Declaration of Interests

E. Vance is a co-founder and unpaid board member of the Table Temperature Alignment Project. The other authors declare no competing interests. Funding sources had no role in study design, data collection, analysis, or manuscript preparation.

References

Appendix A: Mathematical Derivations

A.1 Derivation of Expected Disvalue Formula

We derive the expected disvalue formula (Equation 6) from first principles. Let C be the random variable representing the time of a catastrophic event, with probability density function f_C(t). Conditional on an event at time t, let S_t be the indicator for a successor scenario:

The expected disvalue is then:

The conditional expectation E[D | C = t] = P(S_t = 1) · D(C_t), yielding the result.

A.2 Sensitivity Analysis Details

Sensitivity analysis was conducted by varying each parameter independently while holding others at baseline values. Key elasticities are:

• Discount rate: ε_δ = -2.3 (doubling δ reduces E[D] by ~57%)
• Catastrophe probability: ε_P = 1.0 (linear relationship)
• Population trajectory: ε_N = 0.8 (slightly sublinear)

Supplementary Methodology II: Expert Elicitation Framework

II.1 Expert Selection Criteria

Domain experts were selected through a rigorous multi-stage process designed to identify individuals with relevant expertise while avoiding conflicts of interest (e.g., furniture industry executives, professional table enthusiasts). Selection criteria included: (1) doctoral-level training in materials science, thermodynamics, or existential risk studies; (2) publication record demonstrating engagement with either furniture science or catastrophic risk; and (3) demonstrated calibration on reference questions.

Initial invitations were extended to 67 prospective experts; 23 completed the full elicitation protocol. Attrition analysis revealed no systematic differences between completers and non-completers on observable characteristics, suggesting minimal selection bias.

II.2 Calibration Training

Prior to eliciting target probabilities, experts completed a calibration training module consisting of 50 trivia questions with known answers (e.g., "What percentage of tables manufactured in 2019 were made primarily of particleboard?"). Experts provided 90% credible intervals for each question, and their calibration scores were computed as the fraction of true values falling within stated intervals.

Initial calibration scores ranged from 0.52 to 0.89 (median: 0.71). Experts then reviewed their calibration performance and completed a second round of 25 questions. Post-training calibration improved to 0.68-0.94 (median: 0.84). Only post-training scores were used for weighting expert judgments in the final analysis.

II.3 Elicitation Protocol

Target probabilities were elicited using a modified SHELF protocol (Gosling et al., 2018). Experts first provided individual estimates in isolation, then participated in a structured group discussion (conducted via secure video conference to maintain geographical diversity), and finally revised their estimates. This Delphi-like approach balances the benefits of discussion against anchoring effects.

For each scenario, experts were asked to estimate: (1) the probability of occurrence within specified time horizons, (2) the conditional probability of table survival given the scenario, and (3) the conditional probability of human extinction given the scenario. Questions were posed in multiple formats (probability, odds, frequency) to check for framing effects.

II.4 Aggregation Methodology

Expert estimates were aggregated using a calibration-weighted linear opinion pool. Letp_i denote expert i's probability estimate and w_i their calibration weight. The aggregated probability is:

Uncertainty was characterized via a weighted mixture of expert distributions, preserving the full shape of disagreement rather than collapsing to point estimates. This approach appropriately propagates expert uncertainty into downstream Monte Carlo simulations.

Supplementary Methodology III: Cost-Effectiveness Methodology

III.1 Intervention Categorization

We categorize potential interventions into five tiers based on their mechanism of action: (1) Policy advocacy, targeting regulatory changes to furniture manufacturing standards; (2) R&D funding, accelerating development of human-aligned table materials; (3) Manufacturer subsidies, reducing the cost premium for aligned tables; (4) Direct production, establishing aligned table manufacturing capacity; and (5) Consumer education, increasing demand for aligned furniture.

Each intervention tier was analyzed using a theory of change model specifying the causal pathway from funding input to ultimate impact (tables aligned × probability reduction per table × expected disvalue reduction). Pathway probabilities were elicited from a separate panel of policy and economics experts.

III.2 Cost Estimation

Intervention costs were estimated through a combination of (1) bottom-up engineering estimates for direct production costs, (2) analogical reasoning from comparable policy advocacy campaigns (e.g., EU appliance efficiency standards), and (3) expert judgment for novel intervention types. All costs are expressed in 2024 USD and include both direct expenditures and opportunity costs of deployed resources.

For policy advocacy, we estimated costs based on documented expenditures for comparable EU regulatory campaigns, with adjustments for the novelty of furniture temperature alignment as a policy issue. The base estimate of $244,000 per regulatory outcome was derived from analysis of 17 comparable campaigns, with substantial uncertainty reflected in our credible intervals.

III.3 Expected Value Calculations

Cost-effectiveness ratios (CERs) are computed as expected impact divided by expected cost:

Expected impact is the product of tables aligned × probability of successor scenario × expected disvalue per successor scenario. We assume linear scaling for marginal interventions, while acknowledging that scale effects (both positive due to economies of scale and negative due to diminishing returns) may affect CERs at larger funding levels.

III.4 Sensitivity and Scenario Analysis

CER estimates are highly sensitive to several parameters, particularly: (1) discount rate (elasticity = -2.3); (2) catastrophe probability estimates (elasticity = 1.0); and (3) policy success probability (elasticity = 1.0). We present results under three scenarios: Conservative (high discount rate, low catastrophe probability, low policy success); Baseline (median estimates for all parameters); and Optimistic (low discount rate, higher probabilities).

Break-even analysis indicates that even under conservative assumptions, policy advocacy remains cost-effective relative to a $10,000/DALY threshold if either catastrophe probabilities exceed 0.1% (100-year horizon) or policy success probability exceeds 5%.

Supplementary Methodology IV: Uncertainty Quantification

IV.1 Sources of Uncertainty

Our analysis confronts multiple distinct sources of uncertainty: (1) Aleatory uncertaintyarising from inherent randomness in future events (e.g., whether a catastrophe occurs); (2)Epistemic uncertainty reflecting limitations in our knowledge (e.g., true table populations, material properties); and (3) Model uncertainty regarding the appropriate structural form of our analytical framework.

We distinguish these sources because they respond differently to additional information: epistemic uncertainty can be reduced through further research, while aleatory uncertainty cannot. Model uncertainty occupies an intermediate position—it can be reduced through empirical validation but may have irreducible components.

IV.2 Probabilistic Representation

All uncertain quantities are represented as probability distributions rather than point estimates. For parameters with empirical data, we fit appropriate parametric distributions (typically log-normal for positive quantities, beta for probabilities) via maximum likelihood estimation. For parameters relying on expert judgment, we use the aggregated expert distributions directly.

Credible intervals throughout this paper are Bayesian 90% highest posterior density (HPD) intervals, meaning they contain the true value with 90% probability given our model and prior beliefs. Frequentist confidence intervals would be numerically similar for most parameters but carry different philosophical interpretations.

IV.3 Monte Carlo Simulation Framework

Our primary tool for uncertainty propagation is Monte Carlo simulation. For each of 10,000 iterations, we: (1) draw values for all uncertain parameters from their respective distributions; (2) compute the expected disvalue using the drawn values; and (3) store the result. The distribution of results across iterations characterizes our uncertainty in the final estimate.

Convergence was assessed by monitoring the stability of percentile estimates as iteration count increased. With 10,000 iterations, 90% credible interval endpoints are stable to within ±2% of their final values. We verified this through split-half analysis comparing estimates from odd and even iterations.

IV.4 Communication of Uncertainty

Following best practices in risk communication, we report uncertainty using multiple complementary formats: (1) point estimates (typically posterior medians); (2) credible intervals (90% HPD); (3) full posterior distributions (in supplementary figures); and (4) verbal probability terms calibrated to numerical ranges (e.g., "likely" = 66-90% probability, following IPCC conventions).

We emphasize that wide credible intervals are not a weakness of the analysis but an honest representation of genuine uncertainty. Analyses that report narrow intervals in domains with deep uncertainty are likely underestimating uncertainty rather than possessing superior knowledge.

IV.5 Value of Information Analysis

We conducted expected value of perfect information (EVPI) and expected value of partial perfect information (EVPPI) analyses to identify which uncertainties most affect decision-making. Key findings: resolving uncertainty about catastrophe probabilities has EVPPI of $4.2M (in terms of optimal allocation of $10M intervention budget), while resolving uncertainty about table populations has EVPPI of only $0.3M.

This suggests that future research efforts should prioritize improved catastrophe probability estimates over more precise table censuses—a counterintuitive finding given that table counts are more directly measurable. The reason is that catastrophe probabilities have higher leverage in the expected value calculation due to their multiplicative role.