One useful metaphor is to represent AI creativity as a two-part quantity, similar in form to a complex number: 

ZE = R + iI 

In this notation, R is the weighted average of normalized quantitative indicators, and I is the weighted average of normalized qualitative indicators. The symbol i does not mean that qualitative judgment is imaginary or unreal. It means that qualitative meaning occupies a different assessment dimension from quantitative counting. In other words, R represents countable traces of participation, while I represents interpreted creative value. 

The two components may be defined as: 

R = Σ wjxj; I = Σ vkqk 

A scalar overall magnitude could then be calculated as: 

|ZE| = √(R2 + I2) 

This magnitude can serve as a compact overall AI creativity index, while the ratio or angle between R and I can show whether the evidence is mostly quantitative, mostly qualitative, or balanced. For example, a high R and low I may indicate much activity with limited creative value. A low R and high I may indicate a compact but meaningful contribution. A high R and high I may indicate rich, sustained, and valuable co-creative participation. 

4.3. Calibrating Weights with Design of Experiments 

The weighting coefficients should not remain arbitrary. They can be calibrated through Design of Experiments methodology. DOE is useful because it varies multiple factors systematically and estimates not only main effects, but also interactions among factors. In this context, the “factors” are selected creativity-assessment parameters, and the “response” is an independent assessment of AI creativity, such as expert rating, user continuation behavior, downstream adoption, or a combined validation score. 

A simple first experiment could select only one or two parameters for each part of the model. For example, R might include number of substantive turns and number of reframing events, while I might include originality/usefulness rating and revision-depth rating. Each factor can be varied or selected at two levels, such as low and high. A two-level factorial design can then estimate main effects and interaction effects. 

For four selected factors, a simple linear interaction model may be written as: 

Y = β0 + β1x1 + β2x2 + β3q1 + β4q2 + β12x1x2 + β13x1q1 + β14x1q2 + β23x2q1 + β24x2q2 + β34q1q2 + ε 

In this equation, Y is the independently rated e-ngagement response. The β coefficients estimate the contribution of each factor and interaction. If β13 is large, for example, it may mean that the number of substantive turns matters more when originality/usefulness is also high. This is exactly the type of cross-effect that a simple weighted sum would miss. 

If each factor is tested at three levels, such as low, medium, and high, the experiment can support a second-degree response surface model: 

Y = β0 + Σβizi + Σβijzizj + Σβiizi2 + ε 

This second-degree model can reveal curvature. For example, more generated versions of output may indicate perceived higher AI creativity up to a point, but after that point the effect may flatten or become negative if the interaction becomes redundant. Similarly, moderate conceptual distance may be more useful than either very low distance or extreme irrelevant distance. This makes DOE especially valuable because it can show not only which parameters matter, but how much they matter, when they matter, and how they influence one another. 

4.4 Minimal Example for a First Calibration Game 

A minimal calibration experiment could begin with only two factors: one quantitative and one qualitative. For example: 

The simplest model would be: 

Y = β0 + β1x1 + β2q1 + β12x1q1 + ε 

This small design can already answer useful questions. Does number of versions matter by itself? Does conceptual depth matter more? Does revision activity matter only when it produces meaningful improvement? If the interaction term β12 is significant, then AI creativity is not simply a sum of activity plus quality; it depends on their combination. 

A slightly richer calibration approach could use two quantitative and two qualitative factors. The project team could create a small set of AI/OI sessions or simulated tasks, code each session using the selected parameters, obtain independent AI creativity ratings, and fit the model. The resulting coefficients would become provisional empirical weights.