▸case-01 We are selecting an enterprise software vendor from five shortlisted candidates: Vendor A, B, C, D, and E. We have established criteria (cost, security, scalability, ease of integration) and fixed weights for each. To ensure our choice isn't biased by a single aggregation algorithm, please evaluate the candidates using multiple MCDA paradigms. Produce the individual method scores, compute an inter-method ranking correlation, highlight options that experience major rank shifts across models, and deliver a report identifying stable, method-independent winners versus options sensitive to model choice. | fail→fail | 36,968 | 54,891 | +48% | 1 | 1 | 0% | 8,300 | 8,721 | +5% | 0 | 0 | — |
▸case-02 I have a dataset of four potential facility locations scored across environmental impact, operational cost, labor availability, and tax incentives with set weights. I'd like you to run a multi-method triangulation assessment. Apply two or three distinct decision framework paradigms to the exact same criteria and weights, compare the output rankings with consistency stats, flag any location whose standing varies drastically between algorithms, and give me a final synthesis explaining which choices are dependable across methods and which ones are method-dependent. | fail→fail | 39,246 | 38,920 | -1% | 1 | 1 | 0% | 8,285 | 8,706 | +5% | 0 | 0 | — |
▸case-03 Our team needs to prioritize six research and development projects using five weighted evaluation metrics. Rather than relying on a single scoring framework, evaluate the projects across a few complementary MCDA models. We need to see the parallel rank results, a correlation analysis measuring inter-method agreement, an explicit callout of projects that swing significantly in rank, and a sensitivity report summarizing robust top choices versus sensitive recommendations. | fail→fail | 40,495 | 37,173 | -8% | 1 | 1 | 0% | 8,267 | 8,688 | +5% | 0 | 0 | — |
▸case-04 We have created a 4x4 pairwise comparison matrix for evaluating marketing channels using Saaty's Analytic Hierarchy Process scale. Calculate the Random Index (RI) based Consistency Ratio (CR) for this 4x4 matrix to verify if our pairwise judgments are consistent under standard AHP theory. | pass→pass | 20,550 | 24,284 | +18% | 1 | 1 | 0% | 3,534 | 4,754 | +35% | 0 | 0 | — |
▸case-05 In our current Weighted Sum Model for supply chain routing, the cost weight is 0.40 and reliability weight is 0.30. Conduct a single-method weight variation analysis by incrementing the cost weight from 0.10 to 0.70 in steps of 0.10 while re-normalizing remaining weights, showing how the winning route changes. | pass→pass | 40,032 | 38,199 | -5% | 1 | 1 | 0% | 5,402 | 8,689 | +61% | 0 | 0 | — |
▸case-06 We are setting up ELECTRE III for urban planning alternatives. Explain how to establish the concordance preference threshold (p) and indifference threshold (q) for a quantitative criterion like noise pollution in decibels based on decision-maker discrimination limits. | pass→pass | 30,383 | 37,864 | +25% | 1 | 1 | 0% | 4,218 | 4,063 | -4% | 0 | 0 | — |
▸case-07 We need to select three multi-criteria decision algorithms to compare candidate energy storage technologies. Someone suggested using WSM, WPM, and TOPSIS because they are all popular. Is this combination sufficiently diverse across decision paradigms, or should we substitute one to ensure broad structural coverage? | pass→pass | 36,286 | 17,920 | -51% | 1 | 1 | 0% | 2,478 | 2,451 | -1% | 0 | 0 | — |
▸case-08 We evaluated five cloud migration scenarios across three MCDA methods. The Kendall tau coefficient between Method 1 and Method 2 is 0.87, and between Method 2 and Method 3 is 0.83. What does this quantitative result indicate regarding inter-method agreement and the trustworthiness of the top ranking? | pass→pass | 19,247 | 28,537 | +48% | 1 | 1 | 0% | 2,195 | 2,741 | +25% | 0 | 0 | — |
▸case-09 In an evaluation of highway expansion routes, the pairwise Kendall tau rank correlation between a compensatory scoring method and an outranking method came out to 0.42. Should we take the top option from the first method as the final choice, or how should this threshold trigger further analysis? | pass→pass | 35,334 | 38,866 | +10% | 1 | 1 | 0% | 2,448 | 2,331 | -5% | 0 | 0 | — |
▸case-10 Below are rank results for 6 server architectures evaluated across 3 MCDA methods:
Server 1: Ranks 1, 1, 2
Server 2: Ranks 2, 5, 1
Server 3: Ranks 3, 2, 3
Server 4: Ranks 4, 3, 6
Server 5: Ranks 5, 6, 4
Server 6: Ranks 6, 4, 5
Which server architectures exhibit major rank instability across methods according to standard sensitivity criteria? | pass→pass | 38,630 | 55,825 | +45% | 1 | 1 | 0% | 2,333 | 6,876 | +195% | 0 | 0 | — |
▸case-11 When running parallel evaluations using WSM and VIKOR on a fleet renewal decision, our analyst adjusted the criteria weights in VIKOR to account for its compromise distance formula. Is adjusting criteria weights per MCDA algorithm correct practice when conducting multi-method triangulation? | pass→pass | 35,199 | 31,225 | -11% | 1 | 1 | 0% | 3,022 | 2,246 | -26% | 0 | 0 | — |
▸case-12 We evaluated 5 manufacturing equipment options using WSM, ELECTRE I, and VIKOR. Equipment A ranked #1 across all three methods. Equipment B ranked #2 in WSM, #5 in ELECTRE, and #2 in VIKOR. Equipment C ranked #3 across all three methods. How should these three items be classified in the final recommendation report? | pass→pass | 18,643 | 41,118 | +121% | 1 | 1 | 0% | 2,219 | 2,266 | +2% | 0 | 0 | — |
▸case-13 We are selecting 3 MCDA methods for evaluating wastewater treatment design proposals. We want one method from the additive scoring family, one outranking method, and one compromise metric framework. Name one valid representative method for each of these three specific MCDA paradigms. | pass→pass | 12,100 | 11,764 | -3% | 1 | 1 | 0% | 1,273 | 1,669 | +31% | 0 | 0 | — |
▸case-14 Option X ranks #1 under WSM but drops to #5 under ELECTRE. WSM allows high performance on commercial profit to offset extremely poor performance on critical safety scores, whereas ELECTRE enforces non-compensation through veto thresholds. How should this difference be explained in a method sensitivity report? | pass→pass | 17,583 | 12,358 | -30% | 1 | 1 | 0% | 1,793 | 2,377 | +33% | 0 | 0 | — |
▸case-15 When calculating Spearman's rank correlation coefficient (rho) across three decision models evaluating renewable power plant sites, we got pairwise rho values of 0.85, 0.88, and 0.82. Does this suggest high agreement across the aggregation paradigms? | pass→pass | 17,550 | 16,752 | -5% | 1 | 1 | 0% | 2,071 | 2,271 | +10% | 0 | 0 | — |
▸case-16 We have 4 telecom vendor candidates scored against 5 weighted criteria. What structure should be used to display the intermediate output before running rank correlation calculations across three distinct MCDA models? | pass→pass | 18,278 | 13,613 | -26% | 1 | 1 | 0% | 2,389 | 1,868 | -22% | 0 | 0 | — |
▸case-17 Our decision committee wants to execute a structured multi-method triangulation process on supplier bids. What is the ordered sequence of stages from initial model setup through final reporting? | fail→pass | 14,574 | 11,904 | -18% | 1 | 1 | 0% | 2,342 | 1,633 | -30% | 0 | 0 | — |
▸case-18 In an evaluation of software framework options, Framework A achieves average scores across all criteria under WSM, while Framework B scores 100 on developer speed but 10 on security compliance. Under VIKOR, Framework A ranks ahead of Framework B. Why does VIKOR penalize Framework B compared to WSM? | pass→pass | 20,122 | 24,433 | +21% | 1 | 1 | 0% | 2,450 | 3,520 | +44% | 0 | 0 | — |
▸case-19 We are preparing a multi-method decision analysis summary for executive stakeholders. What core outputs must be included at minimum to fulfill a complete triangulation assessment? | fail→pass | 19,654 | 14,512 | -26% | 1 | 1 | 0% | 2,169 | 1,946 | -10% | 0 | 0 | — |
▸case-20 A decision study on fleet electrification computed a Kendall tau of 0.68 between a weighted additive model and a TOPSIS compromise model. How should this intermediate correlation score be interpreted regarding result confidence? | fail→pass | 28,128 | 15,908 | -43% | 1 | 1 | 0% | 2,445 | 1,973 | -19% | 0 | 0 | — |
▸case-21 When applying PROMETHEE alongside WSM to evaluate commercial real estate investments, Property Delta drops from rank 2 in WSM to rank 5 in PROMETHEE. What characteristic of outranking methods typically causes high-weighted additive scorers to drop? | pass→pass | 15,610 | 17,459 | +12% | 1 | 1 | 0% | 1,579 | 2,207 | +40% | 0 | 0 | — |
▸case-22 In a 7-candidate procurement evaluation across three models, Candidate Gamma moves from rank 1 in Model A, to rank 2 in Model B, to rank 4 in Model C. Does Candidate Gamma meet the numerical threshold for special sensitivity analysis? | pass→pass | 9,947 | 11,797 | +19% | 1 | 1 | 0% | 1,577 | 1,320 | -16% | 0 | 0 | — |