Evaluation of nine consensus indices in delphi foresight research and their dependency on delphi survey characteristics: A simulation study and debate on delphi design and interpretation

The extent of consensus (or the lack thereof) among experts in emerging fields of innovation can serve as antecedents of scientific, societal, investor and stakeholder synergy or conflict. Naturally, how we measure consensus is of great importance to science and technology strategic foresight. The Delphi methodology is a widely used anonymous survey technique to evaluate consensus among a panel of experts. Surprisingly, there is little guidance on how indices of consensus can be influenced by parameters of the Delphi survey itself. We simulated a classic three-round Delphi survey building on the concept of clustered consen-sus/dissensus. We evaluated three study characteristics that are pertinent for design of Delphi foresight research: (1) the number of survey questions, (2) the sample size, and (3) the extent to which experts conform to group opinion (the Group Conformity Index) in a Delphi study. Their impacts on the following nine Delphi consensus indices were then examined in 1000 simulations: Clustered Mode, Clustered Pairwise Agreement, Conger's Kappa, De Moivre index, Extremities Version of the Clustered Pairwise Agreement, Fleiss' Kappa, Mode, the Interquartile Range and Pairwise Agreement. The dependency of a consensus index on the Delphi survey characteristics was expressed from 0.000 (no dependency) to 1.000 (full dependency). The number of questions (range: 6 to 40) in a survey did not have a notable impact whereby the dependency values remained below 0.030. The variation in sample size (range: 6 to 50) displayed the top three impacts for the Interquartile Range, the Clustered Mode and the Mode (dependency = 0.396, 0.130, 0.116, respectively). The Group Conformity Index, a construct akin to measuring stubbornness/flexibility of experts' opinions, greatly impacted all nine Delphi consensus indices (dependency = 0.200 to 0.504), except the Extremity CPWA and the Interquartile Range that were impacted only beyond the first decimal point (dependency = 0.087 and 0.083, respectively). Scholars in technology design, foresight research and future(s) studies might consider these new findings in strategic planning of Delphi studies, for example, in rational choice of consensus indices and sample size, or accounting for confounding factors such as experts' variable degrees of conformity (stubbornness/flexibility) in modifying their opinions.