Desirability-Probability Gap in AI Governance

• The desirability-probability gap in AI governance is the mismatch between high-level aspirations and the practical likelihood of achieving them.
• It exposes challenges in policy design, such as regulatory overreach, resource misallocation, and unrealistic expectations of AI outcomes.
• Empirical analyses and formal models emphasize the need for adaptive, participatory, and cost-aware frameworks to bridge this gap.

The desirability-probability gap in AI governance designates the persistent mismatch between aspirational objectives for AI systems or policies ("desirability") and the empirically or technically grounded likelihood that these outcomes can actually be achieved ("probability"). This structural gap manifests when regulatory, technical, or societal actors benchmark AI futures or interventions against normative ideals but neglect feasibility constraints, cost structures, behavioral realities, and uncertainty propagation. The result is a range of evaluative and operational challenges for effective AI governance, including policy overreach, resource misallocation, and public trust deficits.

1. Formalization and Core Definitions

Across multiple domains of AI governance, the desirability-probability gap may be formally defined as the scalar or vector difference between a target value (desirable outcome, typically denoted $D$ or $U^*(\cdot)$) and its assessed probability or feasibility ($P$ or $U(\cdot)$):

$G = D - P,$

where $D$ is a normalized desirability score derived from ethical, policy, or stakeholder creativity, and $P$ is an aggregation of quantified risks, uncertainties, or failure modes under real conditions (Tallam, 9 Mar 2025, Ojanen et al., 17 Dec 2025, Zhang, 2024).

For policy evaluation, as in the European Delphi method, $D_i$ and $P_i$ are mean expert scores for policy option $i$ on Likert scales, and the gap is $G_i = D_i - P_i$ (Ojanen et al., 17 Dec 2025). In system evaluation, $D(S)$ is a weighted blend of metrics such as fairness, human impact, and transparency, while $P(S)$ quantifies the probability of undesirable events—security lapses, bias amplification, or systemic failures (Tallam, 9 Mar 2025). In AI/ML-based decision-making, analogous gaps arise from mismatches between expected utility based on estimated probabilities and costs/rewards whose true values are often poorly specified (Bontempi, 2023).

2. Manifestations Across Governance Contexts

2.1 Policy and Regulatory Design

The gap systematically appears in the policymaking “nirvana approach,” where idealized scenarios (e.g., perfect government oversight, infallible regulatory frameworks) are juxtaposed with real-world institutional and technological constraints:

• "The Grass is Always Greener": Overstating potential of regulatory bodies or human oversight relative to actual capacity, while downplaying advances and adaptability achievable by private actors or market-driven systems. \newline
• "Free Lunch": Presuming that new rules or technological fixes achieve risk elimination at negligible cost, overlooking administrative burden, economic drag, or unforeseen side effects.
• "People Could Be Different": Basing proposals on assumptions of either perfectly rational human actors or perfectly aligned AI, ignoring real behavior and the persistence of bias, non-transparency, or error (Zhang, 2024).

Quantitative studies confirm that desirable interventions—such as digital public infrastructure or robust participatory governance—may be highly rated for their virtue but scored as infeasible in expert Delphi exercises, with the largest observed $G$ values for “AI commons” ($G=2.09$ on a 1–5 scale) (Ojanen et al., 17 Dec 2025).

2.2 Sociotechnical Hype Dynamics

In the governance of transformative AI such as AGI, venture capital, policy, and media actors generate pronounced desirability claims (e.g., utopian or existential risk narratives) in the presence of radical feasibility uncertainty. “Deep hype” sustains a large $D$ with little evidential support for $P$, producing decision environments susceptible to speculation, regulatory capture, or misplaced policy prioritization (Gonçalves, 27 Aug 2025). The gap is amplified by sociotechnical fictions that distort estimation of technical and societal timelines.

2.3 Perceptual Misalignments Between Stakeholder Groups

Survey-based mapping of 71 AI scenarios reveals that both experts and lay publics typically rate the probability of AI impacts higher than their desirability, with mean desirability-probability gaps $\bar{\Delta}_E \approx -29.2\%$ (experts) and $\bar{\Delta}_P \approx -32.4\%$ (public) (Brauner et al., 2024). Experts’ gaps are on average smaller, but the distribution of gaps is broader. The trade-off weighting of benefits vs. risks also diverges: experts assign a risk/benefit weight ratio of approximately 1:3, while for the public it is about 1:2.

3. Theoretical and Analytic Foundations

3.1 Expected Utility Analysis

In formal decision theory, agents select actions $a$ to maximize expected utility $E[U(a)] = \sum_s p(s)U(a, s)$. The “AI/ML gap” arises when probability estimates $p(s)$ are precise but utility or cost matrices $U(a, s)$ are imprecisely elicited or subject to structural misestimation. Monte Carlo and analytic sensitivity analyses show that, in realistic cases, uncertainty in utility/cost assessments can produce a larger degradation in decision quality than uncertainty in probability estimates, particularly in low-entropy (high-certainty) regimes (Bontempi, 2023).

Table 1: Comparative Sensitivity to Error Types (summary)

Source of Error	Impact on Expected Utility	Policy Implication
Probability est.	Bounded by $p_0(1-p_0)$	Gains from further accuracy are diminishing
Utility est.	Potentially unbounded	Robustness requires explicit cost-elicitation

3.2 Multi-Dimensional Frameworks

Advanced frameworks for governance propose four interlocking pillars—transparency & explainability, dynamic regulation, ethical/philosophical oversight, and systems-level intervention—explicitly designed to shrink the gap by coordinating technical risk reduction ($P$) with uplift in stakeholders’ normative goals ($D$) (Tallam, 9 Mar 2025).

4. Empirical and Case Study Evidence

4.1 Policy Delphi Results

Quantitative Policy Delphi panels on European AI governance report the following top desirability-probability gaps ($G_i$) across policy options (Ojanen et al., 17 Dec 2025):

Policy Option	$D_i$ (mean)	$P_i$ (mean)	$G_i (= D_i - P_i)$
Digital public infrastructure & AI commons	3.95	1.86	2.09
Citizen participation mechanisms	3.91	3.23	0.68
Robust global AI governance	3.83	3.33	0.50

Explanations for low $P$ include regulatory “pacing problems,” insufficient institutional resources, and conflicting geopolitical or market incentives.

4.2 Technical and Societal Case Studies

Notable failures attributed to large gaps include:

• Microsoft Tay (2016): High desirability for broad engagement and safety, actualized probability of adversarial misuse near 0.9, leading to reputational loss (Tallam, 9 Mar 2025).
• UK A-Level grading (2020): Standardization and efficiency targeted; bias amplification probabilities realized at unacceptable rates, prompting policy reversal (Tallam, 9 Mar 2025).

4.3 Perceptual Mapping

Quantitative mapping of expert vs. public evaluations for 71 AI impacts underscores widespread negative gaps ($\Delta_{i,g} < 0$ in ~80% cases), with healthcare scenarios showing smaller gaps and warfare, surveillance, and social division larger negative gaps (Brauner et al., 2024).

5. Governance Implications and Design Principles

Robust AI governance requires explicit gap-mitigation strategies:

• Comparative Alternatives Analysis: Avoid “nirvana” or unattainable-ideal benchmarks; systematically compare feasible regimes (status quo, proposal, alternate realistic options) (Zhang, 2024).
• Explicit Cost-Benefit Weighing: Mandate quantification and transparent reporting of both direct and indirect costs in regulatory proposals; optimize regulatory standards with real, resource-bounded risk-reduction calculations (Zhang, 2024, Bontempi, 2023).
• Utility-Aware Methodology: Elicit utilities with uncertainty intervals, update under evolving social norms, integrate into robust optimization and regulatory reporting (Bontempi, 2023).
• Participatory and Adaptive Regulation: Foster structured citizen panels and continuous horizon scanning; prioritize adaptive licensing, scenario-based stress-tests, and co-audited ethics-security processes (Tallam, 9 Mar 2025, Ojanen et al., 17 Dec 2025).
• Demystification and Transparency: Require that grand narratives and claims (especially on AGI) be distinguished as “promissory scenarios,” coupled to technical progress verification and open data (Gonçalves, 27 Aug 2025).

6. Addressing Structural and Perceptual Misalignment

Systematic attention to the desirability-probability gap is essential for both legitimacy and functional performance of governance regimes:

• Alignment of Public Trust: Risk communication should be tailored to differences in risk-weighting between experts and the public; regulatory standards must balance these divergent sensitivities for enduring acceptability (Brauner et al., 2024).
• Monitoring and Agility: Deploy real-time regulatory monitoring, delegated acts, and data-driven feedback to adjust as actual feasibility and societal preferences evolve (Ojanen et al., 17 Dec 2025).
• Democratic Accountability: Expand oversight to avoid concentrated, self-serving policy formulation in high-uncertainty environments such as AGI (Gonçalves, 27 Aug 2025); institutionalize anticipatory governance and broader stakeholder engagement.

7. Future Directions and Open Challenges

Ongoing research suggests several advancements:

• Cross-sectional comparative studies to identify best practices and context-specific gap dynamics (Ojanen et al., 17 Dec 2025).
• Longitudinal tracking of gap metrics as input to regulatory amendments and the design of early warning systems for emerging misalignments (Ojanen et al., 17 Dec 2025).
• Formalization of hybrid utility-probability frameworks integrating quantitative risk assessment, scenario-based stress testing, and adaptive regulation (Tallam, 9 Mar 2025, Bontempi, 2023).

A plausible implication is that narrowing the desirability-probability gap requires not only technical innovation in AI but continuous governance innovation anchored in empirical monitoring, stakeholder pluralism, and robustness against both utopian and dystopian overreach.