Tool Cognitive Distance

Category: Persona Comparison · Since: v18.27.0 · Tier: All

Compute the Wasserstein distance between any two cognitive personas. Based on optimal transport theory. Treats persona traits as probability measures and computes the minimum cost of transforming one profile into another.

Why This Matters

Persona comparison was qualitative ("these personas are different"). Now it is quantitative: W₁(first-timer, power-user) = 0.2305. This is a precise cognitive distance grounded in 40+ neuroscience papers. Transport cost predicts actual cognitive processing cost.

Parameters

Parameter	Type	Required	Description
personaA	string	Yes	First persona name
personaB	string	Yes	Second persona name

Response

{
  "personaA": "first-timer",
  "personaB": "power-user",
  "w1Distance": 0.2305,
  "w2Distance": 0.1148,
  "slicedWasserstein": 0.0149,
  "interpretation": "Substantially different cognitive profiles",
  "topDifferentiatingTraits": [
    { "trait": "socialProofSensitivity", "contribution": 0.0328 },
    { "trait": "comprehension", "contribution": 0.0302 },
    { "trait": "riskTolerance", "contribution": 0.0277 }
  ]
}

Metrics

• W₁ Distance: Wasserstein-1 with cognitive ground metric (traits in the same domain are closer)
• W₂ Distance: Bures-Wasserstein for Gaussian measures (captures variance differences)
• Sliced Wasserstein: Fast approximation via random 1D projections (100 projections)
• Top Differentiating Traits: Which traits contribute most to the distance

Related Tools

• cognitive_coverage — Select maximally different personas
• cognitive_interpolate — Blend between personas
• cognitive_load_estimate — Per-persona page complexity