[[2025-07-10|25-07-10-08]] - [[matt_cronin]] thinks abstract is well organized. [[2025-07-09|25-07-09-14]] updated emoji of 🎹scale, [[🎹🎼🎶scale_harmony_melody_verse]] - [[🎹scale(🐢🐢promise vendor)]] ## Title: The Promise Vendor: A Rational Choice Model of Entrepreneurial Overpromise ## Abstract: Entrepreneurial ventures often engage in "overpromising," a behavior widely viewed through the lens of cognitive bias. We challenge this view by developing a rational choice model to explain when and by how much an entrepreneur should promise before securing the resources to deliver. We extend the classic newsvendor model in two fundamental ways: (1) we define time-symmetric underage and overage costs (Cu, Co) for decisions made under two-sided commitment uncertainty (from both customers and resource partners); and (2) we introduce a "matching value" (V), representing the unique prize of successfully aligning these commitments. Our model yields a closed-form solution for the optimal promise level (q*), demonstrating that overpromising is a rational strategy when the opportunity cost of a missed sale (Cu) is high relative to the cost of a broken promise (Co). Counter-intuitively, our analysis reveals that the matching value (V) acts as a strategic moderator, not a simple accelerant of ambition. For ventures facing high opportunity costs (Cu > Co), a larger prize (V) dampens the tendency to overpromise, enforcing discipline. Conversely, for ventures facing high failure costs (Co > Cu), V provides the necessary incentive to undertake calculated risks. Theoretically, we contribute a unified framework that reframes apparent entrepreneurial bias as a predictable output of a firm's strategic context. Managerially, we introduce the duality of the proactive "Promise Vendor," who acts to shape the future, and the reactive "News Vendor," who optimizes based on the past. This distinction provides a formal language for allocating resources between opportunity creation and operational efficiency. Keywords: Entrepreneurship, Newsvendor Model, Promise, Overpromise, Decision Theory, Resource Allocation, Strategic Duality. 1. limit to early stage founders to emphasize the tension of being funded but not delivering VS not being funded but can deliver 2. for 🟪Existing theory treats this as irrational bias, yet it persists across contexts.🟪 1. find three existing theory on over-confidence and its rationality, by tracking the literature citing below 1. eric van deen stein: "Rational Overoptimism (and Other Biases)" [[📜vandensteen04_rational_overopt]] 2. thomas aestrobo "Inventor Perseverance after Being Told to Quit: The Role of Cognitive Biases" [[📜aestrobo07_inventor_perseverance]] 3. adding one match and two reward is key contribution i.e. - V p_f * p_d (where p_f is probability of funded and p_d is probability of delivery) ## 🎱 Octave Scale Nodes (16) - Rhythmic Revision | Category | Code | Template Pattern (Following Moran's Consecution) | | :--------------- | :--- | :---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **[[🟣alert]]** | A | **[Introduction]** Entrepreneurs overpromise. Theory calls this bias. Yet the pattern persists—why? | | | A1 | **🟪1:** A promise needs two yeses. Customer says "I want this." Partner says "I can build this." Both must align. | | | A2 | **🟪2:** When both say yes, magic happens. Not just revenue—Series B, network effects, market dominance. Call it V. | | | A12 | **🟪12:** V changes everything. The game shifts from avoiding costs to capturing lightning. | | **[[♻️dig]]** | D | **[Literature Review]** Newsvendor assumes smooth curves. Entrepreneurs face cliffs. We need sharper tools. | | | D1 | **🟩1:** Three states exist. Match: both yes. Failure: sold but can't deliver. Miss: could deliver but didn't sell. | | | D2 | **🟩2:** The equation must capture V. Not just costs—the prize: `argmin [Co*Pc(1-Pr) + Cu(1-Pc)Pr - V*Pc*Pr]`. | | | D12 | **🟩12:** Solve for q*. Find where promise meets possibility. Balance on the knife's edge. | | **🟧 Grow** | G | **[Model/Method]** Newsvendor knows "too much" hurts, "too little" hurts. We add: "just right" rewards. | | | G1 | **🟧1:** Math makes it precise. Overage: Pc(1-Pr). Underage: (1-Pc)Pr. Match: Pc*Pr. | | | G2 | **🟧2:** Build the full equation. Weigh failure's sting against opportunity's regret against success's sweetness. | | | G12 | **🟧12:** The formula emerges: `q* = ln((2Cu + V) / (2Co + V))`. This number decides your fate. | | **🟥 Core** | C | **[Results/Discussion]** Overpromise isn't madness. It's math. When stakes are high, bold beats cautious. | | | C1 | **🟥1:** Use the formula. Input your context. Get your promise level. Transform gut feel into precision. | | | C2 | **🟥2:** Two vendors exist. News Vendor reacts to yesterday. Promise Vendor creates tomorrow. Choose your stance. | | | C12 | **🟥12:** Mindset shapes perception. Perception feeds formula. Formula generates action. Action appears as bias—but it's strategy. Tomorrow, others copy this. New anomalies bloom. | ## 🎼 Chord Progression Edges - Melodic Flow |Line|Theme|Flow|Section|Narrative Beat| |:--|:--|:--|:--|:--| |**1**|**🟪Alert**|🟪A → 🟪A12 → [🟪A1, 🟪A2]|**Intro**|_Entrepreneurs overpromise._ Why? Because promises need two yeses (🟪A1). Because success brings magic (🟪A2). Because magic changes everything (🟪A12).| |**2**||[🟪A1, 🟪A2] → 🟩D12|**→ Lit**|Two yeses? Magic value? Standard models can't compute this.| |**3**||🟩D12 → 🟧G12 → 🟥C|**Arc**|New tools needed (🟩D12). Formula found (🟧G12). Bias explained (🟥C).| |**4**|**🟩Dig**|🟩D → 🟩D12 → [🟩D1, 🟩D2]|**Lit Review**|_Models assume smooth curves._ We need cliffs (🟩D). Three states matter (🟩D1). V matters most (🟩D2).| |**5**||[🟩D1, 🟩D2] → 🟧G12|**→ Method**|States defined. Value captured. Now build.| |**6**|**🟧Grow**|🟧G ← 🟧G12 ← [🟧G1, 🟧G2]|**Method**|_Start with newsvendor wisdom._ Add probabilities (🟧G1). Add full costs (🟧G2). Get formula (🟧G12).| |**7**||[🟧G1, 🟧G2] ← 🟩D12|**Validate**|Check: Does model answer need? Yes.| |**8**|**🟥Core**|🟥C ← 🟥C12 ← [🟥C1, 🟥C2]|**Results**|_Bias is strategy._ Use formula (🟥C1). Choose stance (🟥C2). Understand system (🟥C12).| |**9**||🟥C12 → 🟪A'|**Loop**|Today's insight becomes tomorrow's puzzle. The wheel turns.| ### 🎶 Melody: Here’s a concise breakdown using the screenshot definitions and your lyrics: | Element | Definition | Example | | ---------- | --------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **Motif** | A small number of notes that recur | “V × p_f × p_d — that’s the key!” | | **Tune** | Singable, complete in itself, with a beginning, middle, and end | **Chorus:** “V times p_f times p_d—that’s the key! One match from two yeses sets us free!” | | **Melody** | Any sequence of successive pitches occurring in time | **Verse 1 (Alert):** “Why overpromise? Two yeses multiply. One match magnifies. Prize moderates surprise.”<br>**Verse 2 (Dig):** _Old tools fail. Three states exist. Prize must count. Solve for balance.<br>**Verse 3 (Grow):** _Start simple. Add precision. Build equation. Find the number._<br>**Verse 4 (Core):** _Bold beats cautious. Formula guides. Mindset matters. Circle completes._<br>**Coda:** _Solution breeds problem. Problem needs solution. Forever._ | **Verse 1 (Alert):** _Why overpromise? Two yeses needed. Magic possible. Everything changes._ **Verse 2 (Dig):** _Old tools fail. Three states exist. Prize must count. Solve for balance._ **Verse 3 (Grow):** _Start simple. Add precision. Build equation. Find the number._ **Verse 4 (Core):** _Bold beats cautious. Formula guides. Mindset matters. Circle completes._ **Coda:** _Solution breeds problem. Problem needs solution. Forever._ ### Visual Mapping to Paper Structure: ``` Paper Section ADGC Module Key Output ───────────── ─────────── ────────── 1. Introduction → 🟪 Alert → Problem: Why overpromise? 2. Literature → 🟩 Dig → Gap: Need new model 3. Model/Method → 🟧 Grow → Build: q* formula 4. Results → 🟥 Core → Insight: It's rational! Discussion → 🟥→🟪 → New problems emerge ``` ### Key Dualities from Transcript: - **Promise Vendor** (🟪A side): Proactive, future-shaping, discrete commitments - **News Vendor** (🟧G foundation): Reactive, past-fitting, continuous demand The progression now clearly shows how each paper section maps to the ADGC framework, with the ergodic property creating the endless loop where contributions spawn new anomalies. --- ## 🎼 Chord Progression Edges (22) — _Revised based on new inputs_ This updated narrative flow incorporates the specific model details and the "proactive vs. reactive" duality mentioned in the transcript. |Line|Movement / Theme|Progression Flow|Corresponding Narrative Edge(s)| |:--|:--|:--|:--| |**1**|**1. A-Theme (Exposition)**|A → A12 → [A1, A2]|**The Problem (Alert):** We introduce the puzzle of overpromise (A). This tension is amplified (A12) by the two-sided nature of promises (`Pc`, `Pr`) (A1) and the lure of a unique matching value `V` (A2).| |**2**||[A1, A2] → D12|**The Need (Dig):** The complexities of `Pc`, `Pr`, and `V` (A1, A2) demand an integrated model (D12) that can handle this new form of uncertainty.| |**3**||D12 → G12 → C|**The Arc:** The need for this specific model (D12) leads directly to the development of our solution, the `q*` formula (G12), which delivers our core contribution (C).| |**4**|**2. D-Theme (Development)**|D → D12 → [D1, D2]|**Structuring the Solution (Dig):** We define the overall modeling gap (D) and break it down (D12) into the necessary components: a shift to discrete uncertainty (D1) and a new objective function including `V` (D2).| |**5**||[D1, D2] → G12|**Building the Model (Grow):** The specific needs for a discrete model (D1) and a new formula (D2) are the exact inputs required to derive the integrated `q*` solution (G12).| |**6**|**3. G-Theme (Recapitulation)**|G ← G12 ← [G1, G2]|**Constructing the Engine (Grow):** Our final formula `q*` (G12) is shown to be a logical extension of the base newsvendor framework (G). We deconstruct it to show its parts: the probability states (G1) and the full cost function (G2).| |**7**||[G1, G2] ← D12|**Meeting the Need:** We demonstrate explicitly how our model's components (G1, G2) perfectly fulfill the diagnostic requirements for a new theory (D12).| |**8**|**4. C-Theme (Resolution)**|C ← C12 ← [C1, C2]|**Delivering the Contribution (Core):** The paper's main insight (C) is delivered via a unified framework (C12) that yields two key outputs: the prescriptive rule for when to overpromise (C1) and the strategic duality of Promise vs. News vendors (C2).| |**9**||C12 ← A|**Closing the Loop (The Möbius Twist):** Our framework (C12) resolves the initial anomaly (A). However, by making the logic of promising explicit, it creates a new, more advanced problem: how do strategic actors behave when they _know_ this model governs their counterparts' decisions? The solution (C) generates the next research anomaly (A').| ### 1. How `V` Fundamentally Alters the `Cu` vs. `Co` Balance The classic Newsvendor model balances two costs: the cost of being short (`Cu`) and the cost of being over (`Co`). The optimal decision is driven by the critical ratio `Cu / (Cu + Co)`, which represents a trade-off. It's a cost-minimization game. Your Promise Vendor model introduces the matching value `V`, which is not a cost to be minimized but a **potential prize to be won**. This fundamentally alters the decision-making logic in two ways: - **From Cost Avoidance to Prize Seeking:** The entrepreneur is no longer just balancing two negative outcomes. They are balancing two negatives (`Cu`, `Co`) against a significant positive (`V`). This `V` acts as a powerful incentive—a "pull" towards making the match happen. It shifts the mindset from purely reactive cost management to proactive opportunity creation. - **Altering the Mathematical Ratio:** The prize `V` is added to _both_ the numerator and the denominator in the core logic: `(2Cu + V) / (2Co + V)`. This means `V` doesn't just add a simple bonus; it changes the _sensitivity_ of the decision. It reframes the importance of the original costs. A large `V` can make a small difference between `Cu` and `Co` seem less significant, focusing the entrepreneur on the grand prize instead of the marginal costs. ### 2. The Surprising Role of the Matching Value `V` You are absolutely correct. My previous statement was an oversimplification. The effect of an increasing `V` on the optimal promise level `q*` is not straightforward; it depends entirely on the underlying relationship between `Cu` and `Co`. Let's analyze the ratio `R = (2Cu + V) / (2Co + V)`. The optimal promise `q*` increases if this ratio increases. The derivative of `R` with respect to `V` is `(2Co - 2Cu) / (2Co + V)^2`. This leads to a much more nuanced and powerful insight: - **Case 1: `Cu > Co` (High Opportunity Cost):** In this classic "overpromise" scenario, the term `(2Co - 2Cu)` is negative. This means that as the prize `V` gets larger, the ratio `R` actually _decreases_. A massive potential prize **dampens the tendency to overpromise**. It introduces a sense of gravity, making the entrepreneur _more_ disciplined because the stakes of getting it right are so high. The prize doesn't encourage wild promises; it encourages making the _right_ promise. - **Case 2: `Co > Cu` (High Failure Cost):** In this "underpromise" scenario, `(2Co - 2Cu)` is positive. As the prize `V` gets larger, the ratio `R` _increases_. Here, a large prize **encourages more risk-taking**. It provides the incentive needed to overcome the fear of the high failure cost (`Co`) and reach for a valuable opportunity that would otherwise be ignored. This is a fantastic, non-obvious result and a core part of your paper's contribution. `V` is not a simple accelerator; it is a **strategic moderator** whose effect depends on the context. ### 3. The "New Lens" of Proactive vs. Reactive Strategy The duality between the Promise Vendor (proactive) and the News Vendor (reactive) provides a new lens by giving managers a formal language to describe and quantify a fundamental strategic tension. - **Reactive (News Vendor Lens):** Views the world as a set of historical data and probabilities. The goal is to optimize operations to _react_ to a predicted future. Strategy is about **efficiency, forecasting, and adaptation**. - **Proactive (Promise Vendor Lens):** Views the world as a set of stakeholders (customers, partners) who can be enrolled to _create_ a desired future. The goal is to make commitments that shape the environment. Strategy is about **vision, persuasion, and co-creation**. **Implications of this "New Lens":** 1. **Resource Allocation:** It helps a CEO decide whether the next dollar should be spent on hiring a data scientist (a reactive, News Vendor investment) or a business development lead (a proactive, Promise Vendor investment). 2. **Valuing Intangibles:** It allows the firm to formally incorporate the value of narrative, vision, and stakeholder commitments (`V`) into its capital allocation models, justifying investments that traditional ROI models might reject. 3. **Dynamic Strategy:** It suggests that the optimal strategic posture is not static. An early-stage venture might be 90% proactive. After finding product-market fit, it might shift to 60% reactive to scale efficiently. Your model provides the `q*` metric to track and guide this evolution. ### 4. Explicitly Stating the Two Innovations (with Examples) Here is a clear breakdown of the two core innovations, as requested. **Innovation 1: Cost Definitions with Time Gap** The model re-frames the classic newsvendor costs for a world where decisions are made _before_ capacity is fully secured. - **Underage Cost (`Cu`):** The opportunity cost of caution. It is the "cost to the organization when a promise, which _would have been_ deliverable by time t, is not sold at time 0." This represents a missed match—a customer you could have served but didn't dare to promise. - **Overage Cost (`Co`):** The failure cost of ambition. It is the "cost to the organization when a promise sold at time 0 is _not_ deliverable by time t." This represents a broken promise—a customer you committed to but failed to serve. **Innovation 2: Defining Optimal Promise Regimes** Your model predicts when different promise strategies are rational. - **Overpromise is Optimal (`q* > 0` when `Cu > Co`):** - **Example 1 (Market Seizure):** A startup launching a revolutionary AI service. The `Cu` is immense: losing a key anchor client like Google or Netflix to a competitor means forfeiting market leadership. The `Co` (failing to deliver on the promised timeline) is a manageable cost (refunds, reputational hit) compared to the existential threat of being second-to-market. - **Example 2 (Network Effects):** A platform business (e.g., a new marketplace) needs to build a critical mass of users. `Cu` is the failure to achieve the network effect, rendering the entire platform worthless. `Co` is the cost of disappointing some early adopters, which is a smaller price to pay for a chance at creating a billion-dollar ecosystem. - **Underpromise is Optimal (`q* < 0` when `Co > Cu`):** - **Example (High-Stakes Reliability):** A company supplying critical components for a SpaceX rocket launch. The `Co` of failure is catastrophic: mission failure, loss of life, and the end of the company. The `Cu` of not winning the contract is merely a lost sale. The rational strategy is to promise only what can be delivered with near-absolute certainty. - **Balanced/Moderated Promise is Optimal (when `V` is Predominant):** - **Example (Transformative Projects):** A consortium bidding to build a city's first high-speed rail system. The matching value `V` (economic transformation, political legacy) is colossal. Both `Cu` (losing the bid to a rival city) and `Co` (a failed, multi-billion-dollar public works project) are also enormous. Here, the sheer magnitude of `V` forces extreme diligence. It moderates the decision away from a simple `Cu` vs. `Co` gamble, pushing the promise level (`q*`) towards a highly calibrated, carefully calculated optimum. The goal is no longer just to win, but to ensure the valuable match is successfully realized. ---