# 🐅2.12🏇 Founder-Venture Separation Structure [Sections 2.1-2.2] ## 2. Theory and Modeling ### 2.1 Theoretical Background #### 2.1.1 Tau Unifies a False Dichotomy Table 2. False Dichotomies Unified by the τ Framework | | | | | |---|---|---|---| |Domain|Low τ (Complex / High i)|High τ (Simple / Low i)|Unifying Principle| |Strategy schools|Action school ("act then think")|Planning school ("think then act")|τ maps action–planning onto a continuum| |Learning schools|Model-free (experience-driven)|Model-based (theory-driven)|τ weights prior knowledge| |DNA tension metaphor|Loose DNA (high variation, flexibility)|Tight DNA (low variation, efficiency)|τ tunes variation vs. replication fidelity| |Sampling|Few samples (fast decisions)|Many samples (precise estimates)|τ ≈ pseudo–sample size| |Firebreak metaphor|Wide firebreak (wide open space)|Narrow firebreak (tight control)|τ sets the width of future possibility| |Founder's response to given uncertainty|Fight with self-imposed uncertainty|Fight with knowledge|τ sets the explore–exploit balance| |Venture cases|Tesla (flexible pivots)|Better Place (rigid strategy)|τ* decreases with higher complexity c and integration cost i| Thus τ is not a binary choice but a continuous variable that should be tuned to environmental conditions (i: information-integration cost, normalized by venture value; c: environmental complexity). As c and i rise, the optimal τ decreases (choose flexibility); as they fall, the optimal τ increases (choose efficiency). Tesla's trajectory (start low τ, then earn precision) and Better Place's failure (rigid high τ amid high complexity) illustrate the point. #### 2.1.2 Beta-Binomial Conjugate Structure The beta-binomial conjugate relationship provides the mathematical foundation for this framework. The success probability φ follows a Beta distribution: φ ~ Beta(μ, τ) where μ represents the aspiration level (mean promise) and τ represents the concentration parameter (precision). This parameterization unifies the action-planning spectrum: - Low τ → Action school: high uncertainty, quick adaptation - High τ → Planning school: high confidence, commitment to plan This mathematical structure enables us to model how founders update their beliefs through Bayesian learning while maintaining analytical tractability.