🛝propose(thesis) - amoon.world🌙

## Overview On Thursday, I'll analyze three phrases from Joni Mitchell's "Both Sides Now" to compare Bolton et al.'s moral hazard framework with Moon's STRAP model. Using the primal-dual foundation from Moon, we'll explore how entrepreneurs and social planners can navigate uncertainty through three key processes. --- ## Three Perspectives: From Both Sides Now | Bolton et al. | Moon (STRAP) | | ---------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------- | | Binary experiment outcomes False positives/false negatives Private benefit Z | Multiple stakeholder states Entropy-based uncertainty Multi-stakeholder preferences | | Investor-entrepreneur contract Limited to two parties Market failure or inefficient funding | Stakeholder coordination Multiple stakeholders with thresholds Weighted uncertainty reduction | | Moral hazard in experiment design Ventures failing post-experiment University validation, proof-of-failure | Strategic experiment selection Bottleneck uncertainties Dual variable optimization | | Bolton et al. | Moon (STRAP) | Keywords | Section | | ---------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------- | -------------------------------------------------- | ----------------------------------------- | | Binary experiment outcomes False positives/false negatives Private benefit Z | Multiple stakeholder states Entropy-based uncertainty Multi-stakeholder preferences | Perspective Illusion Motivation Tradeoffs | **I. 🧭 Agents Perceive to Act** | | Investor-entrepreneur contract Limited to two parties Market failure or inefficient funding | Stakeholder coordination Multiple stakeholders with thresholds Weighted uncertainty reduction | Exchange Complexity Outcomes | **II. 🗺️ Society Dualize to Distribute** | | Moral hazard in experiment design Ventures failing post-experiment University validation, proof-of-failure | Strategic experiment selection Bottleneck uncertainties Dual variable optimization | Concealment Failure Solutions | **III. 🧬 Agents Act to Perceive** | [[📜Bolton24]] # Variable Mapping Between Papers | Bolton et al. Concept | Bolton Variable | Moon Concept | Moon Variable | | ------------------------------- | --------------- | --------------------------- | ------------------------------------------------------------------------------------------------- | | Venture value if successful | $V$ | Venture value | $f_{js}lt;/span> (stakeholder state values) | | Prior probability of success | $p_0$ | Prior probability | $\vec{p}_j = (p_{j1}(x),\ldots,p_{jS}(x))lt;/span> (choice probabilities) | | Cost of experiment | $C$ | Cost coefficient | $c_jlt;/span> | | Cost of full development | $K$ | Budget constraint | $Rlt;/span> (total budget) | | Experiment specificity | $s_1$ | Venture attributes | $xlt;/span> (affects choice probabilities) | | Experiment sensitivity | $s_2$ | Stakeholder preferences | $\beta_{js}lt;/span> (affects choice probabilities) | | Entrepreneur's private benefit | $Z$ | Not explicitly modeled | N/A | | Investor ownership stake | $\alpha$ | Not explicitly modeled | N/A | | Expected payoff from experiment | $\pi_{s_1,s_2}$ | Uncertainty | $H(\vec{p}_j)lt;/span> | | Proof-of-failure payment | $X$ | Not explicitly modeled | N/A | | Not explicitly modeled | N/A | Actions | $a_jlt;/span> (weeks) | | Not explicitly modeled | N/A | Optimal decision | $a^*_jlt;/span> (weeks) | | Not explicitly modeled | N/A | Threshold targets | $\mu_jlt;/span> | | Not explicitly modeled | N/A | Dual variable for threshold | $\lambda_jlt;/span> | | Not explicitly modeled | N/A | Dual variable for resource | $\gammalt;/span> | Based on the color scheme in the image: - Blue: Choice probabilities and uncertainty metrics - Red: Actions and decisions - Orange: Threshold targets, state values, and threshold dual variables - Cyan: Budget, cost coefficients, and resource dual variables - Gray: Entrepreneur's attributes and stakeholder preferences | Variable group | Variable | Description | Unit | Category | | ------------------------ | ---------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------- | -------------- | --------------------------------------------------------------------------------------- | | **State Variables** | | | | | | | $\vec{p}_j = (p_{j1}(x),\ldots,p_{jS}(x))lt;/span> (choice probabilities) | Probability that stakeholder j assigns to outcome state s | Unitless (0-1) | Effective | | | $f_{js}lt;/span> (stakeholder state values) | Value associated with stakeholder j choosing state s | $ | Effective | | | $\mu_jlt;/span> | Threshold target value for stakeholder j | $ | Satisfactory | | | $c_jlt;/span> | Cost of action j | $ | Efficient | | | $Rlt;/span> (total budget) | Budget/resources available | $ | Efficient | | **Action Variables** | | | | | | | $a_jlt;/span> | Binary decision variable indicating whether action j is taken | Unitless (0/1) | Efficient | | **Diagnostic Variables** | | | | | | | $H(p_j)$ | Entropy measuring uncertainty in stakeholder j's choice distribution | bits | Effective | | | $\lambda_jlt;/span> | Dual variable for threshold constraint - shadow price of relaxing threshold | bits/$ | Satisfactory | | | $\gammalt;/span> | Dual variable for resource constraint - shadow price of additional resource | bits/$ | Efficient | | | Primal-dual gap | Convergence measure quantifying distance from optimality | bits | Satisfactory | | **Key Trends** | | | | | | | $H(p_j)$ | Decreases as ventures mature | bits ↓ | Effective | | | Dual variable | Decrease as ventures gains feasibility | bits/$ ↓ | Efficient/Satisfactory | | | Primal-dual gap | Converges to zero indicating stakeholder alignment | bits → 0 | Satisfactory | Note: Colors represent categories from the framework: - Red: Efficient (resource utilization) - Green: Effective (goal achievement) - Purple: Satisfactory (convergence diagnostics) - --- ## I. 🧭 Agents Perceive to Act: "Cloud Illusions" > _"I've looked at clouds from both sides now From up and down and still somehow It's cloud illusions I recall"_ ### Bolton et al.: - **Perspective**: Binary experiment outcomes (Pass/Fail) - **Illusion**: Experiments with false positives create illusion of progress - **Key Equation**: $P(s = P|v = V) = s_1$ (specificity) --- ### Moon (STRAP): - **Perspective**: Multiple stakeholder states (Reject, Consider, Accept) - **Illusion**: Entropy as measure of true uncertainty - **Key Equation**: $H(\vec{p}_j) = -\sum_s p_{js} \log p_{js}$ --- ### Action Proposal 1: Entrepreneurs should quantify uncertainty as entropy rather than probability, acknowledging the multi-state nature of stakeholder decisions to avoid the illusion of binary outcomes. --- ## II. 🗺️ Society Dualize to Distribute: "Something's Lost, Something's Gained" > _"Well, something's lost, but something's gained In living every day"_ --- ### Bolton et al.: - **Exchange**: Investor-entrepreneur contract (α) - **Complexity**: Limited to two stakeholders - **Outcomes**: Market failure or inefficient funding --- ### Moon (STRAP): - **Exchange**: Coordination across multiple stakeholders - **Complexity**: Multiple thresholds μⱼ with dual variables λⱼ - **Outcomes**: Optimized uncertainty reduction across stakeholders --- ### Action Proposal 2: Social planners should adopt dual-variable frameworks to identify which stakeholder constraints are truly binding (highest λⱼ), as these may not be the ones that appear unsatisfied in a binary framework. --- ## III. 🧬 Agents Act to Perceive: "From Give and Take" > _"I've looked at love from both sides now From give and take and still somehow"_ --- ### Bolton et al.: - **Concealment**: Moral hazard in experiment design - **Failure**: Failed ventures after passing misleading experiments - **Solutions**: Paying for proof of failure (X ≥ Z) --- ### Moon (STRAP): - **Concealment**: Strategic selection of which uncertainty to reduce first - **Failure**: Unidentified bottleneck uncertainties - **Solutions**: Primal-dual optimization of experiment selection --- ### Action Proposal 3: Entrepreneurs should design experiments that explicitly target the highest-weighted uncertainties (by λⱼ) rather than maximizing pass probability, while investors should reward information gain rather than just success. --- ## Synthesis: Both Sides Now The STRAP framework helps mitigate moral hazard by: 1. **Quantifying the true value of uncertainty reduction** rather than binary success/failure 2. **Identifying non-obvious bottlenecks** through dual variables 3. **Aligning incentives around information gain** rather than experiment outcomes --- By integrating insights from both models, we can create a more robust approach to entrepreneurial decision-making under uncertainty. _"I've looked at life from both sides now From win and lose and still somehow It's life's illusions I recall I really don't know life at all"_ --- I'm reaching out to introduce my favorite english song: from both sides now On thursday, I will sample three phrases from this song and use these to scaffold comparing the assigned paper (Bolton) with mine (Moon25). using the primal dual model from moon25, i will walk you though how [[I.🧭Agents Perceive to Act]], [[II.🗺️Society Dualize to Distribute]], [[III.🧬Agents Act to Perceive]] to suggest three action proposals for entrepreneurs and social planners. # entreperneur To be specific, entrepreneurs should model their value system by choosing $w_{j}, f_{jk}, c$, ## social planner ![[🗄️table_of_contents]] ## social planner and social planner should lower $c, \mu, $ from [[2.2📐Produce solution(🗺️)]]framing (rows of Society should report $\bar{p},$ f, mu, c so i'll solve posed questions by contrasting bolton's research with mine. - binary vs K-bucket - single stakeholder (entrepreneur and investor) vs multi stakeholder - investor-centered vs founder-centered (bumble) cause of moral hazard (dating app)? information asymmetry (unavoidable) implemented as , judged by god who can see both side only woman can choose [[Both sides now]] solving four questions on introduce research on # 4. # 5. future work JK value system cld | Section | fig./interactive. | | ----------------------------------------------- | ----------------- | | [[I.🧭Agents Perceive to Act]] | | | [[II.🗺️Society Dualize to Distribute]] | | | [[III.🧬Agents Act to Perceive]] | | | Section | fig./interactive. | Decision Variable | | ----------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | | [[I.🧭Agents Perceive to Act]] | Bayesian decision tool for entrepreneurs to model stakeholder uncertainties and generate actionable strategies from abstracted representations | ~a_j = perception decisions to process stakeholder uncertainties through entropy H(~p_j) and Bayesian logit models mapping venture attributes to stakeholder choice probabilities | | [[II.🗺️Society Dualize to Distribute]] | Optimization mechanism using dual variables to dynamically distribute resources across stakeholders with competing needs while satisfying thresholds | λ_j, γ = threshold and resource dual variables representing shadow prices that guide fair resource allocation by balancing threshold satisfaction (λ_j) with resource efficiency (γ) | | [[III.🧬Agents Act to Perceive]] | Sequential learning framework where individual entrepreneurial experiments provide data to update global strategies and improve collective ecosystem outcomes | a__j = optimal action selection that maximizes information gain per resource unit by solving the primal-dual optimization: a__j = arg max_aj (ΔH + Σ_j λ_j Δ(f_j·p_j))/c_j | ### 2.1 Perception | Inputs | Outputs | | ----------------------------------------------- | ------------------------------------------------------------------ | | Entrepreneur's Attributes: $x \in \mathbb{R}^n$ | Choice probabilities: $\vec{p}_j = (p_{j1}(x), \ldots, p_{jS}(x))$ | | Stakeholder preferences: $\beta_{js}$ | Uncertainty: $H(\vec{p}_j) = -\sum_s p_{js} \log_2 p_{js}$ | | | | ### 2.2 Action | Inputs | Outputs | |--------|---------| | Actions: $a_j \in \{0,1\}$ (weeks) | Decision: $a_j^* = \arg\max_{a_j} \frac{\Delta H_j + \sum_j \lambda_j \Delta(f_j \cdot p_j)}{c_j}$ (weeks) | | Threshold targets, State values: $\mu_j, f_{js}$ | Dual variable for threshold: $\lambda_j = \max\{0, w_j(µ_j - \sum_s f_{js}p_{js})/µ_j\}$ | | Budget & cost coefficient: $R, c_j$ | Dual variable for resource: $\gamma = S(a^*)$ | $\simeq$ attributes, preferences coefficient (various); $\simeq$ probabilities (unitless) $\simeq$ uncertainty (bits); $\simeq$ actions (weeks); $\simeq$ thresholds (\$), values(\$), dual var. (bits/$); $\simeq$ budget (\$), cost coefficient (\$/week), resource dual var. (bits/$); The STRAP framework integrates these three components through: 1. Perception (Agents Abstract) - Models stakeholder uncertainties using Bayesian methods 2. Distribution (Society Dualizes) - Uses dual variables to coordinate resource allocation 3. Optimization (Agent Samples) - Selects experiments that maximize information gain per resource unit