Leveraging Order-Theoretic Tournament Graphs for Assessing Internal Consistency in Survey-Based Instruments Across Diverse Scenarios
Bibliographic record
Abstract
This paper introduces Monotone Delta ($\delta$), an order-theoretic measure designed to enhance the reliability assessment of survey-based instruments in human-machine interactions. Traditional reliability measures, such as Cronbach’s Alpha and McDonald’s Omega, often yield misleading estimates due to their sensitivity to redundancy, multidimensional constructs, and assumptions of normality and uncorrelated errors. These limitations can compromise decision-making in human-centric evaluations, where survey instruments inform adaptive interfaces, cognitive workload assessments, and human-AI trust models. Monotone Delta addresses these issues by quantifying internal consistency through the minimization of ordinal contradictions and alignment with a unidimensional latent order using weighted tournaments. Unlike traditional approaches, it operates without parametric or model-based assumptions. We conducted theoretical analyses and experimental evaluations on four challenging scenarios: tau-equivalence, redundancy, multidimensionality, and non-normal distributions, and proved that Monotone Delta provides more stable reliability assessments compared to existing methods. The Monotone Delta is a valuable alternative for evaluating questionnaire-based assessments in psychology, human factors, healthcare, and interactive system design, enabling organizations to optimize survey instruments, reduce costly redundancies, and enhance confidence in human-system interactions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.087 | 0.326 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.007 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".