Experimenting with a strong dual necessity approach to social progress

The paper addresses how ‘subjective’ and ‘objective’ conceptions of social progress should be combined when comparing societies. It advances a strong ‘dual necessity’ hypothesis: both subjective experiences (e.g., life satisfaction) and objective standards (e.g., capabilities, SDGs) are each necessary and only jointly sufficient for social progress, so one should not readily compensate for deficits in the other. The authors propose operationalizing this through a low-substitution aggregation between an objective and a subjective component. They hypothesize that imposing a very low degree of substitution will materially change countries’ social progress rankings relative to (a) rankings based on a single component and (b) rankings based on high substitution. Using the CES function enables systematic comparison across substitution elasticities. The study tests this with widely used indices (WHR with HDI or SDGI), focusing on whether rankings diverge, especially for mid-ranked countries.

The paper situates its approach within debates on measuring social progress and well-being, distinguishing subjective (welfarist/utilitarian; e.g., Layard; World Happiness Report life ladder) and objective traditions (needs, capabilities, sustainability, social cohesion; e.g., Sen; Alkire; Laurent). It draws on Goertz’s concept structure (AND vs OR) and low-compensability aggregation to justify representing dual necessity as two necessary, jointly sufficient components. Prior work has examined correlations and causal links between subjective and objective metrics (e.g., Hall 2013; Kroll 2015; De Neve & Sachs 2020), dashboard approaches, data-driven methods (factor analysis, SEM), and preference-based weighting. The authors contrast these with a normative, low-substitution framework. Earlier research (Cohen Kaminitz 2024) used a minimum function (no substitution); the present study generalizes with CES to span substitution degrees and test empirical implications across different indices.

• Conceptualization: Implement a strong ‘dual necessity’ conception by aggregating one subjective and one objective component with very low substitutability, reflecting two necessary and only jointly sufficient conditions.
• Indices (components): Subjective—World Happiness Report (WHR) life-ladder. Objective—either Human Development Index (HDI, 2019) or Sustainable Development Goals Index (SDGI).
• Data: 141 countries with non-missing observations for the paired indices (e.g., WHR–HDI 2019). Comparable samples used for WHR–SDGI.
• Preprocessing: Standardize component indices (normalized, mean zero) to address differing units and distributions.
• Aggregation: Use a Constant Elasticity of Substitution (CES) function with equal weights on the two components. Vary elasticity of substitution σ to represent: • Low substitution: σ = 0.1 (near complementarity) • High substitution: σ = 3 (substantial substitutability)
• Analyses: • Compare CES-based rankings (low vs high substitution) to each component’s own ranking (HDI or SDGI; WHR). • Examine rank correlations (Kendall’s tau), average absolute deviations between rankings, and identify ‘anomalies’ (large divergence between subjective and objective ranks). Visualize dispersion and quartile-specific correlations.
• Interpretation: Assess whether low substitution meaningfully shifts rankings, especially in mid-ranked countries, thereby supporting discriminant validation of the dual necessity conception.

• WHR vs HDI rankings (2019): Kendall’s tau for all samples ≈ 0.59; quartile correlations (by WHR rank): 1st 0.59; 2nd 0.05; 3rd 0.19*; 4th 0.23 (null of rank correlation rejected at 5% level). Dispersion is larger beyond top ~25, especially mid distribution.
• CES with WHR–HDI: Low vs high substitution CES rankings have high Kendall’s tau (0.93), yet the mean absolute deviation is 4 rank places; for 27 countries differences are statistically significant. Deviations from HDI are especially large for mid-ranked HDI countries (ranks ~40–100).
• Example (WHR–HDI): Hong Kong—HDI rank 5 vs WHR 68. CES low-substitution rank 55 vs CES high-substitution rank 34 (a 22-place gap across elasticities), illustrating that low substitution pulls the composite rank toward the lower-performing component.
• HDI vs SDGI: Overall Kendall’s tau ≈ 0.7 (141 countries), driven by top/bottom; within HDI ranks 35–75, correlation drops to 0.16.
• WHR vs SDGI: Overall correlation high (0.91) in levels; rank correlation (Kendall’s tau) is 0.53; quartile correlations by WHR rank: 1st 0.47; 2nd 0.02*; 3rd 0.17"; 4th 0.16" (null of rank correlation rejected at 5% level). Dispersion rises outside the top ~25.
• CES with WHR–SDGI: Low vs high substitution CES rankings have Kendall’s tau 0.91; mean absolute deviation 4; for 26 countries the difference is statistically significant; deviations are larger in the 2nd and 3rd quartiles.
• Anomalies highlighted (illustrative): • Cases with higher objective than subjective (e.g., Hong Kong; South Korea; Turkey; Sri Lanka; Botswana; Lebanon; Georgia). • Cases with higher subjective than objective (e.g., Saudi Arabia: SDGI 87 vs WHR 26; CES low-substitution rank 70 vs high-substitution 57; Guatemala).
• Overall, incorporating both components shifts rankings relative to single-component indices, and imposing low substitution amplifies these shifts, particularly among mid-ranked countries.

The findings support the hypothesis that modeling social progress with a strong dual necessity (low substitutability) meaningfully affects country rankings compared with using a single component or a high-substitution aggregate. This effect is most pronounced in mid-ranked countries, which often emerge as anomalies when subjective and objective standings diverge. Low substitution draws composite rankings toward the weaker dimension, preventing high performance in one domain from masking deficits in the other. This enhances discriminant validation: the low-substitution composite behaves differently from conventional high-substitutability composites and from either component alone. Policy-wise, the approach underscores balanced progress: improvements in objective outcomes should not come at the cost of subjective well-being (and vice versa). Countries with large gaps receive a clear signal to address the weaker dimension rather than rely on compensating strengths.

The paper establishes the CES function as a practical tool to implement a strong dual necessity conception of social progress, enabling adjustable degrees of substitution and demonstrating the empirical salience of low substitution. Across WHR–HDI and WHR–SDGI applications, low substitution materially alters rankings, especially in the middle of the distribution, and highlights anomalies that merit policy attention. This both validates the distinctiveness of the dual necessity conception and justifies its dedicated measurement. Future research avenues include applying the low-substitution CES framework to other contexts (cities, neighborhoods, schools, workplaces), experimenting with alternative subjective/objective indices, and extending validation (e.g., nomological validation by testing predictive power for behaviors such as migration).

• Comparability: The approach assumes comparability between heterogeneous constructs (subjective experiences and objective conditions), even after standardization. This is a common critique of composite indices and is only partially mitigated by normalization.
• Diagnostic opacity: A single low-substitution rank does not reveal which component drives a country’s position; users must inspect component scores to diagnose causes (e.g., Guatemala’s low composite driven by SDGI).
• Sensitivity to component choice: Results depend on which indices represent the subjective and objective dimensions (e.g., anomalies differ with HDI vs SDGI).
• Elasticity selection: The specific elasticity values (e.g., σ = 0.1 vs σ = 3) are somewhat arbitrary, though chosen to represent very low vs high substitution; findings are robust across similar parameter choices.
• Aggregation caveats: As with any composite index, the summary may conceal within-component complexities and measurement issues; presenting CES ranks alongside component indices is advisable.