0.3😵‍💫Thesis Scope and Example Case

![[1.3🎞️Thesis Scope and Example Case 2025-05-03-11.svg]] %%[[1.3🎞️Thesis Scope and Example Case 2025-05-03-11|🖋 Edit in Excalidraw]]%% # Three-Part Solution Framework **Section 1: Bottleneck Breaking (Individual-level Internal Optimization)** _Problem:_ Entrepreneurs must sequence actions optimally under resource constraints but cannot estimate uncertainty reduction per cost directly. _Solution:_ At each time t, entrepreneurs minimize residual UC(a)/C(a) by selecting action a∈A, subject to constraint Da(Ae, Se)=S'e. This decomposes the complex metric into estimable components through bottleneck identification. _Mechanism:_ The entrepreneur iteratively selects actions that minimize uncertainty per unit cost, where the state transition follows deterministic dynamics in the short term. _Key Insight:_ Instead of exhaustively searching action sequences, entrepreneurs can make myopic decisions based on current bottlenecks. **Section 2: Proactive Testing (Individual-level External Coordination)** _Problem:_ Multiple stakeholders (investor, customer, operational partner) create circular dependencies with interdependent decisions. _Solution:_ Entrepreneurs minimize residual WBS'e/C(A'e) for action set A'e, subject to D'e(S'e, A'e)=S'e^(t+1). This enables simultaneous multi-stakeholder engagement rather than sequential negotiation. _Mechanism:_ Actions are selected to maximize weighted uncertainty reduction across all stakeholders, recognizing that state transitions affect multiple parties simultaneously. _Key Insight:_ The entrepreneur acts as a central coordinator, choosing actions that create positive spillovers across the stakeholder network. **Section 3: Expectation Propagation (System-level Calibration)** _Problem:_ Individual ventures and social planners have misaligned expectations about state transitions and outcomes. _Solution:_ A two-step calibration process: 1. Social planner proposes state transitions: s's = D̂s(as, ss) 2. Entrepreneur generates state transitions: D̃e ~ N(D̂e, σ²) 3. Entrepreneur updates state: Da(ae, se) = s'e 4. Social planner updates expectations: E[s'e] = s's _Mechanism:_ The system enables bi-directional learning where entrepreneurs' actual transitions inform planners' models, while planners' aggregated knowledge provides better priors for entrepreneurs. _Key Insight:_ This creates a feedback loop that continuously improves both individual decision-making and system-wide resource allocation. --- # Need: Improve Usability of Current Entrepreneurial Decision Models Current entrepreneurial decision models (EDMs) are not realistically tractable by entrepreneurs due to three fundamental problems, each operating at a different level or complexity: ## Individual Level Complexity **Individual Level - Operational Complexity** Entrepreneurs struggle to sequence actions optimally under resource constraints. They must decide which bottlenecks to address first—should they pursue testing facility collaboration or customer segmentation? Traditional approaches either rely on pure theory (lacking real-world applicability) or pure data-driven methods (lacking strategic structure). This complexity manifests in the challenge of estimating uncertainty reduction per unit cost, which we decompose into three parts: uncertainty per state (B), state transitions per action (D), and action cost (C). By breaking down this complex metric into estimable components, entrepreneurs can make systematic decisions about which actions yield the highest uncertainty reduction for their limited resources. **Individual Level - Multi-stakeholder Complexity** Entrepreneurs face circular dependencies among stakeholders with interdependent decisions. Investors wait for customer validation, customers require operational approval, and operators need investment proof. The challenge lies in understanding how actions create spillover effects across stakeholders—for instance, how validation from a testing facility builds customer trust. Traditional sequential negotiation approaches fail to break these feedback loops, leading to prolonged commitment cycles. The key distinction is: - Operational Complexity = How to sequence and prioritize actions given limited resources (internal optimization) - Multi-stakeholder Complexity = How to manage interdependent stakeholder decisions and spillover effects (external coordination) ## Institution Level Complexity At the broader ecosystem level, insufficient modeling education and poor coordination between ventures and public stakeholders create fragmented, non-cumulative learning. This results in system-wide planning failures. # **Solution** To address these interconnected problems, I propose three targeted solutions: **Solution 1: Bottleneck Breaking (🤜🙋‍♀️)** _Problem:_ Entrepreneurs struggle to sequence actions optimally under resource constraints (operational complexity). _Approach:_ We decompose the complex metric of uncertainty reduction per unit cost into three estimable components: uncertainty per state (B), state transitions per action (D), and action cost (C). This enables systematic prioritization of bottleneck-breaking actions. _Example:_ In our cement startup case, instead of directly estimating which action (collaboration vs. segmentation) yields better uncertainty reduction per cost, we: - Estimate B: How much each stakeholder's uncertainty relates to current state - Estimate D: Probability of state transitions for each action (80% for collaboration, 20% for segmentation) - Estimate C: Resource costs (2 years vs. 3 months) - Optimize using ∇w[U/c(a)] = ∇w[BS/c(a)] to find optimal action sequence _Implementation:_ Sections 3.1-3.3 detail theory development, production methods, and evaluation framework. **Solution 2: Proactive Testing (🧐👥)** _Problem:_ Stakeholders create circular dependencies with interdependent decisions (multi-stakeholder complexity). _Approach:_ Instead of sequential negotiations, we use simultaneous hypothesis testing across stakeholders to trigger positive spillover effects. The dynamic transition model D(S,A)=S' captures how actions affect multiple stakeholders simultaneously, while matrix B helps anticipate accept/reject responses. _Example:_ Rather than separately approaching investors (who want customer validation) and customers (who want operational approval), we design experiments that demonstrate value to all stakeholders at once - such as a pilot project that simultaneously validates technical feasibility, customer demand, and financial viability. _Implementation:_ Sections 5.1-5.3 cover theory development, solution production, and evaluation methodology. **Solution 3: Expectation Propagation (🤜👥)** _Problem:_ Institutional-level fragmentation prevents ecosystem-wide learning and coordination. _Approach:_ We develop mechanisms for calibrating expectations between individual ventures and institutional stakeholders, enabling shared learning and coordinated resource allocation across the ecosystem. _Example:_ Instead of each startup independently learning optimal paths, institutions aggregate uncertainty patterns across ventures to provide better priors for new entrants, while startups' experiences update institutional understanding of evolving market dynamics. _Implementation:_ Sections 7.1-7.3 present theoretical foundation, production approach, and evaluation framework. Each solution addresses its corresponding complexity level - operational (internal optimization), multi-stakeholder (external coordination), and institutional (ecosystem alignment) - creating a comprehensive framework for usable entrepreneurial decision-making. ## 🎯 The Entrepreneurial Decision-Making Challenge — *Material Startup Edition* ### Optimization Objective: $ \arg\min_{\textcolor{red}{a} \in \textcolor{red}{A}} \textcolor{purple}{W_d} \cdot \textcolor{#3399FF}{U_d} + \textcolor{purple}{W_s} \cdot \textcolor{#3399FF}{U_s} + \textcolor{purple}{W_i} \cdot \textcolor{#3399FF}{U_i} $ Subject to: $ \begin{aligned} B \cdot \textcolor{green}{S} &= [\textcolor{#3399FF}{U_d}, \textcolor{#3399FF}{U_s}, \textcolor{#3399FF}{U_i}] \\ C \cdot \textcolor{red}{A} &\leq \textcolor{#8B0000}{R} \\ D(\textcolor{green}{S}, \textcolor{red}{A}) &= \textcolor{green}{S'} \end{aligned} $ | Symbol | Meaning | Example | Mapped Section | | ------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------- | | $\textcolor{red}{A}$ | Action vector: {Segment, Collaborate, Capitalize} | Apply to testing lab, approach eco-builders, pitch to climate-aligned VCs | [[I🤜🙋‍♀️ Bottleneck Breaking to Relax Operational Complexity]] | | $\textcolor{green}{S}$ | Stakeholder acceptance state (binary) | $\textcolor{green}{S} = [0, 1, 0]$: ops partner has said yes, but customer and investor are unconvinced | [[III.⚡Bottleneck-Driven Action Sequencing]] | | $\textcolor{#3399FF}{U_d}, \textcolor{#3399FF}{U_s}, \textcolor{#3399FF}{U_i}$ | Residual uncertainties for each stakeholder | High $\textcolor{#3399FF}{U_s}$ if testing is pending; lower $\textcolor{#3399FF}{U_d}$ if builders are supportive | [[III.⚡Bottleneck-Driven Action Sequencing]] | | $\textcolor{purple}{W_d}, \textcolor{purple}{W_s}, \textcolor{purple}{W_i}$ | Stakeholder weights | Sublime may prioritize $\textcolor{purple}{W_s}$ over $\textcolor{purple}{W_d}$ early on | [[III.⚡Bottleneck-Driven Action Sequencing]] | | $B$ | Maps $\textcolor{green}{S}$ to $\textcolor{#3399FF}{U}$ | Even if customer likes the cement, lack of ASTM validation keeps $\textcolor{#3399FF}{U_s}$ high | [[II.🔄Action given Multi-Stakeholders Value System]] | | $C$ | Maps $\textcolor{red}{A}$ to $\textcolor{#8B0000}{R}$ | Internal test costs $10K; ASTM testing $100K | [[I🤜🙋‍♀️ Bottleneck Breaking to Relax Operational Complexity]] | | $\textcolor{#8B0000}{R}$ | Resource constraint | Capital/time budget per action cycle | [[I🤜🙋‍♀️ Bottleneck Breaking to Relax Operational Complexity]] | | $D$ | Transition function: $\textcolor{green}{S}, \textcolor{red}{A} \rightarrow \textcolor{green}{S'}$ | Applying to testing lab may unlock investor confidence indirectly | [[II.🔄Action given Multi-Stakeholders Value System]] | #### 🧪 Illustrative Use Cases 1. **$C$ (Cost):** Should we run internal tests ($10K) or wait for official testing ($100K)? Matrix $C$ guides uncertainty-reduction per dollar tradeoffs. 2. **$D$ (Dynamics):** Does validating with a third-party testing lab improve customer and investor sentiment? $D(\textcolor{green}{S}, \textcolor{red}{A})$ may show multi-stakeholder transitions from a single action. 3. **$B$ (State-to-Uncertainty):** Why is $\textcolor{#3399FF}{U_i}$ still high after pilot demos? Because the investor’s perceived risk remains until formal validation (as encoded in $B$). ### 🔍 Examples Anchored in Sublime Systems #### **1. Cost Matrix $C$ Example (Operational Constraint):** > “Should we run internal lab tests or pay for external validation?” - $\textcolor{red}{A}_1$ = Internal pilot → $\textcolor{#8B0000}{R}_1$ = $10K - $\textcolor{red}{A}_2$ = ASTM facility → $\textcolor{#8B0000}{R}_2$ = $100K - Use **$C$** to evaluate which action yields more uncertainty reduction per dollar spent. #### **2. Transition Matrix $D$ Example (Stakeholder Dynamics):** > “What happens to customer trust if we succeed with third-party testing?” - $\textcolor{green}{S} = [0, 0, 0]$ - $\textcolor{red}{A} = \text{Collaborate}$ with lab - $D(\textcolor{green}{S}, \textcolor{red}{A}) = \textcolor{green}{S'} = [0.5, 0.9, 0.3]$: High feasibility lift (ops partner says yes), modest investor and customer spillover. #### **3. Uncertainty Mapping $B$ Example (State-to-Uncertainty):** > “Even if we’ve done internal testing, why is investor uncertainty still high?” - $\textcolor{green}{S} = [1, 0, 0]$ - $B \cdot \textcolor{green}{S} = \textcolor{#3399FF}{U} = [0.5, 0.9, 0.8]$: Customer is cautiously optimistic, but lack of ops partner validation keeps $\textcolor{#3399FF}{U_s}$ high. --- ### 📊 Summary: Model Components Mapped to Material Startup Logic |Component|Type|Color|Description in Practice| |---|---|---|---| |**$\textcolor{red}{A}$**|Input|🔴 Red|Action chosen (e.g., apply to demo, call investor)| |**$\textcolor{green}{S}$**|Input/State|🟢 Green|Binary indicator of stakeholder buy-in| |**$\textcolor{#3399FF}{U}$**|Output|🔵 Blue|Remaining uncertainty (per stakeholder)| |**$\textcolor{purple}{W}$**|Input|🟣 Purple|Importance weights per stakeholder| |**$B$**|Matrix|—|Translates current state into uncertainty profile| |**$C$**|Matrix|—|Encodes action costs (financial/resource/time)| |**$D$**|Matrix|—|Encodes dynamics of state change per action| |**$\textcolor{#8B0000}{R}$**|Constraint|🟤 Dark Red|Available resource budget| --- Let me know if you’d like this chunk packaged as an Overleaf section or adapted for slide decks. ---- | Solution | Symbols | Complexity Addressed | As-is → To-be | How | Why | | ---------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------- | ---------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------ | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **Phase-based learning by Entrepreneur** | ![wavy red line] D(a,s)=s' | Time | Too complex/too simple strategy only, one stakeholder model → Modularized, not too simple but not too complex, containing multiple operational variables with multiple stakeholders | Sub-path based formulation with simplex algorithm | Entrepreneurs need phases to learn and change operational modes (experiment first); mobility ventures show D-shape differs between phases (from innovation/idea/value creation to value capturing with precision/operational efficiency) | | **Proactive hypothesis proposal by Entrepreneur** | UC/Cost = UC/State × State/Act × Act/Cost (B,D,C) | Space | Causal inference (inferring preference, initial state, and stakeholders' perception) → Synthesizing probabilistic programs (aligning explainability, participatory modeling of value creation/capture) | Multi-model probabilistic program and simplex algorithm | Entrepreneurs need to understand boundaries of acceptable regions and find the fastest path toward those regions | | **Calibrated federated learning by Entrepreneur & Social Planner** | D mapped to D-bar interconnected equations, s'=E[s\|a], D-MDP | Time & Space | City without vision or strategy → Bounded probability distribution on width and height of S-curve; dynamic consistency leading to tighter solution set | D-bar sharing through milestones (time and performance metrics in form of test quantities) | Need coordinated vision with milestones (e.g., "2030: 50% EV for California"); shift in performance measures (mile per intervention to cost per mile, range-based to efficiency-based) | Table 1.3 A three-solution framework addressing temporal (red), spatial (green), and spatio-temporal (violet) complexities in entrepreneurial decision models through phase-based learning, proactive hypothesis testing, and calibrated federated learning approaches. This table presents a comprehensive framework for addressing key complexities in entrepreneurial decision models through three integrated solutions. The red-coded phase-based learning approach tackles temporal complexity by transforming overly simplistic or overly complex strategies into modularized operational models with sub-path formulations. The green-coded proactive hypothesis proposal methodology addresses spatial complexity by evolving causal inference into participatory value modeling through probabilistic programming techniques. Finally, the violet-coded calibrated federated learning system combines both temporal and spatial dimensions by replacing unstructured approaches with bounded probability distributions that enable dynamic consistency through milestone-based coordination between entrepreneurs and social planners. Together, these color-coded solutions form a robust toolkit for enhancing model usability across the different complexity dimensions of entrepreneurial decision-making. ## NEED # Markovian Entrepreneurial Decision Framework: Structured Database Table |Concept|Mathematical Formulation|Phase Transition Bottleneck|Stakeholder Acceptance Bottleneck|Application to Sublime Systems| |---|---|---|---|---| |**State Vector (S)**|$S = [S_1, S_2, S_3]$ where $S_i \in {0,1}$|$S_{NAIL} \rightarrow S_{SCALE}$ transition occurs when $\sum_{i=1}^{3} S_i \geq 2$|Full acceptance requires $S = [1,1,1]$|$S_1$: Testing facility approval $S_2$: Eco-builder adoption $S_3$: Investor commitment| |**Uncertainty Matrix (B)**|$B \cdot S = U$ where $B \in \mathbb{R}^{3 \times 3}$|Critical values of $B$ determine phase transition threshold: $\frac{\partial U}{\partial S}\big\vert_{S_{NAIL} \rightarrow S_{SCALE}}$|$B_{ij}$ coefficients reveal cross-stakeholder dependencies|$B = \begin{bmatrix} 0.8 & 0.6 & 0.4 \ 0.7 & 0.9 & 0.5 \ 0.3 & 0.6 & 0.8 \end{bmatrix}$ where $B_{21} = 0.7$ means testing approval reduces builder uncertainty by 70%| |**Resource Constraints (C)**|$C \cdot A \leq R$ where $C \in \mathbb{R}^{3 \times 3}$|Resource allocation shifts at transition: $\frac{R_{SCALE}}{R_{NAIL}} > 1$|Resources must be strategically allocated to reach $S = [1,1,1]$|$C = \begin{bmatrix} 0.4 & 0.3 & 0.7 \ 0.5 & 0.6 & 0.4 \ 0.7 & 0.5 & 0.3 \end{bmatrix}$ mapping segment/collaborate/capitalize actions to resources| |**State Transition (D)**|$D(S,A) = S'$|Transition rates increase exponentially after inflection: $\frac{dS}{dt}\big\vert_{SCALE} > \frac{dS}{dt}\big\vert_{NAIL}$|Optimal path to $[1,1,1]$ given by $\arg\max_A P(S' = [1,1,1] \| S,A)$|$D(S,A) = S + \begin{bmatrix} A_1 \cdot (1-S_1) \ A_2 \cdot (1-S_2) \ A_3 \cdot (1-S_3) \end{bmatrix} \cdot P_A$| |**Optimization Objective**|$\min (W_1 \cdot U_1 + W_2 \cdot U_2 + W_3 \cdot U_3)$|At transition: $\frac{\Delta U}{\Delta C} = \frac{W_1 \cdot \Delta U_1 + W_2 \cdot \Delta U_2 + W_3 \cdot \Delta U_3}{\Delta C}$|Minimizing stakeholder-weighted uncertainty|For Sublime: $W = [0.3, 0.4, 0.3]$ balancing testing, builder, and investor concerns| |**Proactive Testing**|$D_{proactive}(S, A_{multi}) = D(S, A_1) \cup D(S, A_2) \cup D(S, A_3)$|Accelerates transition by parallelizing validation: $T_{NAIL-SCALE}^{proactive} < T_{NAIL-SCALE}^{sequential}$|Enables simultaneous state changes across multiple stakeholders|Sublime can simultaneously validate with testing facilities while demonstrating to builders and investors| |**Value Creation**|$V(S) = V_{innovation}(S) + V_{operation}(S)$|Phase transition occurs when $\frac{dV_{innovation}}{dS} = \frac{dV_{operation}}{dS}$|Total value maximized at $S = [1,1,1]$: $V([1,1,1]) > V(S)$ for all $S \neq [1,1,1]$|Sublime's value creation shifts from innovation (CO₂ reduction) to operational efficiency (cost parity)| |**Decision Sequencing**|$\pi^*(S) = \arg\max_A \sum_{S'} P(S'|S,A) \cdot V(S')$|Optimal policy switches at transition: $\pi^__{NAIL} \neq \pi^__{SCALE}$|Sequence that maximizes probability of reaching $[1,1,1]$| ## SOL ## FULFILLMENT from [[moshe_benAkiva]] - you mentioned "1.Experimental (proactive)" is impractical or infeasible, but this is very usual in entrepreneurship where previous collected data hints the next experiment. I believe ultimate outcome of every model should be an action that triggers data based on which next action is chosen. Incidentally I don't trust any data collected by others (measurement issues) so my preference is experimental > hypothetical > observational