Chapter 20: Geometric Economics — The Bond Geodesic Equilibrium
RUNNING EXAMPLE — Priya’s Model
Priya discovers that TrialMatch implicitly models patients as rational economic agents who will ‘choose’ to travel for trials if the expected medical benefit is high enough. This is the same error the Bond Geodesic Equilibrium corrects: real agents follow heuristic gradients through bounded decision spaces, not global optimization functions. A rural patient without a car is not ‘choosing’ lower-value care—she is constrained to a different region of the manifold.
This chapter applies the Geometric Ethics framework to economic decision theory, demonstrating that the classical model of Homo economicus — a perfectly rational agent maximizing scalar utility — is not wrong because humans are irrational, but incomplete because it computes on a projected subspace of the actual decision manifold. We construct the Bond Geodesic Equilibrium (BGE), prove it subsumes Nash equilibrium as a special case, and derive prospect-theoretic phenomena as geometric properties of the decision manifold.
20.1 The Failure of Scalar Economics
Classical economics rests on Homo economicus — the perfectly rational agent who maximizes a scalar utility function over all possible actions. This model is mathematically elegant and empirically false. Behavioral economics, following Kahneman and Tversky, has documented systematic deviations from rational choice but lacks a unified mathematical framework that explains why these deviations occur and what structure they share.
Kahneman's dual-process theory — System 1 (fast, automatic, heuristic) and System 2 (slow, deliberate, calculating) — provides the psychological architecture. What it lacks is the mathematical content: What is the space on which System 1 and System 2 operate? What is the formal relationship between them? Why does their interaction produce the specific pattern of "biases" that behavioral economics has catalogued?
The answer is that economic decisions are not made on a one-dimensional space. They are made on a multi-dimensional decision manifold that includes monetary cost, moral constraint, social norms, fairness, autonomy, trust, identity, institutional legitimacy, and epistemic status — the same nine dimensions of the moral manifold M developed in Chapter 5, re-interpreted for economic contexts. Every economic transaction is also a moral event. The classical economist's move of stripping away all dimensions except monetary cost is not a simplification — it is a dimensional collapse that destroys the information needed to predict actual behavior.
20.2 The Economic Decision Complex
Definition 20.1 (Economic Decision Complex). The economic decision complex E is a weighted simplicial complex constructed as follows:
Vertices (0-simplices): Each vertex v_i represents an economic state — a configuration of goods, services, obligations, and relationships. The vertex carries an attribute vector a(v_i) ∈ R^9 scoring the nine dimensions.
Edges (1-simplices): An edge (v_i, v_j) represents an available action — a transaction, decision, or behavioral choice. The edge carries a weight w(v_i, v_j) ≥ 0 representing the total cost on the full manifold.
Higher simplices: A k-simplex [v_0, …, v_k] represents a bundle of mutually available actions.
Definition 20.2 (Multi-Dimensional Edge Weights). The weight of an edge (v_i, v_j) in E is:
w(v_i, v_j) = ΔaT Σ−1 Da + Σk βk * 𝟙[moral boundary k crossed]
where Da = a(v_j) - a(v_i) is the attribute-vector difference, Sigma is the 9x9 dimensional covariance matrix estimated from observed economic behavior, and βk is the penalty for crossing the k-th moral-economic boundary.
The Mahalanobis distance is critical. Economic dimensions are not independent: fairness (d_3) interacts with consequences (d_1); autonomy (d_4) modulates the weight of social impact (d_6); trust (d_5) gates access to higher-consequence transactions (d_1).
20.3 Heuristic Bounded Rationality
The agent's decision on E is A* search (Chapter 11) with evaluation function f(n) = g(n) + h(n), where g(n) is the accumulated economic cost (System 2: slow, deliberate calculation) and h(n) is the moral-heuristic cost (System 1: fast, automatic boundary enforcement).
Theorem 20.1 (Heuristic Truncation). If the moral heuristic h is admissible — i.e., h(n) ≤ h*(n) for all nodes n, where h*(n) is the true remaining cost on the full manifold — then A* search with h finds the optimal path (the Bond geodesic) on E.
Moral heuristics — "do not steal," "keep promises," "reciprocate kindness" — are admissible because they never overestimate the true cost of violating a moral boundary. The penalty for stealing (social, legal, psychological) is always at least as large as the heuristic's estimate. These are not cognitive biases; they are search heuristics that reduce an intractable optimization to a tractable one, at the cost of provably bounded suboptimality.
This is Simon's bounded rationality program, formalized: agents are rational on the manifold they can perceive, using heuristics that provably approximate the optimal solution.
Remark (Marr's Levels of Analysis). The claim that economic decision-making is A* search must be understood at the correct level of David Marr's (1982) tri-level analysis. A* is the computational theory — it specifies what is computed (the minimum-cost path on the decision manifold) and why (optimality under heuristic bounded rationality). The framework makes no claim about the algorithmic level (how the brain implements the computation) or the implementational level (which neural circuits execute it). The brain may use satisficing, fast-and-frugal heuristics (Gigerenzer), accumulator models, or drift-diffusion processes that are algorithmically very different from A* but converge to the same computational-level solution. The claim is that A* correctly describes the function being computed, not the algorithm computing it. This distinction matters: cognitive scientists who object that "the brain does not run A*" are objecting at Marr's algorithmic level, while the framework's claims are at the computational level. The two are compatible. The framework predicts the outcome of the computation (which path the agent selects); it does not predict the neural implementation of the selection process.
20.4 The Bond Geodesic and the Scalar Irrecoverability Theorem
Definition 20.3 (Bond Geodesic). The Bond geodesic gamma* from economic state s to state t on E is the minimum-cost path:
gamma* = arg min_gamma Σ w(e_i)
where the sum is over edges e_i in path gamma. When boundary penalties are absorbed into the metric, this is a geodesic in the sense of Chapter 10.
Theorem 20.2 (Scalar Irrecoverability). No continuous function phi: R^9 -> R is injective. Therefore, any continuous scalar utility function u = phi(a) applied to the nine-dimensional attribute vector a ∈ R^9 destroys information that is mathematically irrecoverable.
Proof. By Brouwer's invariance of dimension, R^9 and R^1 are not homeomorphic. Restricting to the compact cube [0,1]^9, suppose phi: [0,1]^9 -> R were a continuous injection. Then phi maps a compact space injectively and continuously into a Hausdorff space, so phi is a homeomorphism onto its image — an embedding of a 9-dimensional space into R^1. This contradicts invariance of dimension. []
This is the Scalar Irrecoverability Theorem of Chapter 15.6, applied to the economic domain. "Irrational" behavior is rational on the full manifold, irrational only on the projection. Homo economicus computes on the wrong manifold.
20.5 The Bond Geodesic Equilibrium
When multiple agents pathfind simultaneously on the economic decision complex, we enter game theory. The Bond Geodesic Equilibrium (BGE) is the natural equilibrium concept on the manifold.
Definition 20.4 (Bond Geodesic Equilibrium). A strategy profile (gamma_1*, …, gamma_n*) is a Bond Geodesic Equilibrium if for each agent i, the path gamma_i* is a Bond geodesic on agent i's perceived decision complex, given the paths chosen by all other agents.
To establish the relationship between BGE and Nash equilibrium, we construct the augmented game.
Definition 20.5 (Augmented Game). Given a multi-agent decision problem on E, the augmented game is Gamma+ = (N, {S_i}, {u_i}) where:
• N is the set of agents
• S_i is agent i's set of available paths on E
• u_i = -BF_i is agent i's payoff: the negative of the total behavioral friction (edge weight sum) along their chosen path, given others' paths
This construction is canonical: it says that agents in the manifold game are maximizing the negative of their total cost on the full manifold — i.e., they are minimizing behavioral friction, which is exactly what A* search does.
The BGE–Nash Relationship
Theorem 20.3 (BGE–Nash Relationship).
Equivalence: A strategy profile is a BGE of the manifold game if and only if it is a Nash equilibrium of the augmented game Gamma+.
Scalar nesting: If all non-monetary dimensions are zeroed out (i.e., the attribute vector collapses to a(v) = (d_1(v), 0, …, 0)) and each agent selects a single action (not a path), then BGE reduces to Nash equilibrium of the classical game with payoffs u_i = d_1.
Refinement: In games where agents can operate on the full manifold, BGE selects among Nash equilibria by the manifold structure — the equilibrium that minimizes total behavioral friction across all dimensions.
Proof. (1) By construction, gamma_i* is a Bond geodesic if and only if it minimizes BF_i given others' paths, which is exactly the Nash condition on Gamma+. (2) When a = (d_1, 0, …, 0) and paths are single edges, BF_i = d_1 cost, so -BF_i = -d_1 cost = classical payoff (up to sign). (3) Among multiple Nash equilibria of Gamma+, the BGE selects the profile with minimum total BF, since that is what A* search converges to. []
This is the central result: Nash equilibrium is the d_1-only projection of BGE, exactly as Newtonian mechanics is the low-velocity limit of general relativity. The projection is the contraction of Chapter 15 applied to game theory.
Existence and Uniqueness
Theorem 20.4 (Existence of Mixed BGE). Every finite augmented game Gamma+ has at least one mixed BGE.
Proof. By Nash's theorem (1950), every finite game has a mixed-strategy Nash equilibrium. Gamma+ is a finite game (finite agents, finite paths). By Theorem 20.3(1), a mixed Nash equilibrium of Gamma+ is a mixed BGE. []
Definition 20.6 (Mixed BGE). A mixed BGE is a profile of probability distributions (sigma_1, …, sigma_n) over paths, where each sigma_i minimizes agent i's expected behavioral friction given others' mixed strategies.
Remark (Pure BGE Existence). Pure BGE need not exist in general (as with pure Nash). Sufficient conditions include: (a) the augmented game is a potential game; (b) the augmented game has supermodular structure; (c) agents' decision complexes are independent (no cross-agent edge weight dependencies).
The Contraction Lemma
Lemma 20.1 (Contraction Condition for BGE Uniqueness). For each agent i, let alpha_i > 0 measure the self-separation of agent i's best-response mapping (how much i's own behavioral friction changes with i's own path choice) and let kappa_i >= 0 measure the cross-sensitivity (how much i's behavioral friction changes with others' path choices). If
alpha_i > kappa_i for all i in N
then the best-response mapping on Gamma+ is a contraction with Lipschitz constant L = max_i(kappa_i / alpha_i) < 1, and the BGE is unique.
Proof. The best-response mapping T: S -> S maps each profile to the profile of individual best responses. For agent i, ||T_i(s) - T_i(s')||≤ (kappa_i/alpha_i)||s_{-i} - s'_{-i}|| by the ratio of cross-sensitivity to self-separation. Taking the maximum over i, ||T(s) - T(s')||≤ L||s - s'|| with L = max_i(kappa_i/alpha_i) < 1. By Banach's fixed-point theorem, T has a unique fixed point. []
Interpretation: BGE is unique when each agent's decision is dominated by their own manifold structure (high alpha_i) rather than by what others do (low kappa_i). This is the "weak coupling" condition. When coupling is strong (kappa_i ≈ alpha_i), multiple BGE can coexist — as in coordination games, where the equilibrium depends on which manifold region the agents coordinate on.
20.6 Welfare Properties
Theorem 20.5 (BGE Welfare). A BGE is Nash-optimal on the augmented game Gamma+: no agent can unilaterally reduce their behavioral friction by deviating.
However, a BGE is not in general Pareto optimal. Consider the Prisoner's Dilemma on the manifold: if the fairness dimension d_3 is inactive, both agents defect (as in classical Nash); the mutual-cooperation profile has lower total BF but is not individually stable. The Pareto failure of Nash equilibrium persists in BGE for the same structural reason.
Remark. In potential games — where all agents' behavioral friction derives from a common potential function — the BGE does coincide with a Pareto optimum of the augmented game. This is a strong sufficient condition that holds in many economically important settings (congestion games, market entry games).
20.7 Behavioral Game Theory as Manifold Geometry
The BGE framework resolves several longstanding puzzles in behavioral game theory by identifying the active manifold dimensions:
Ultimatum game rejections. In the standard ultimatum game, a proposer offers a split of $10; the responder can accept or reject (destroying both payoffs). Homo economicus predicts the responder accepts any positive offer. Experimentally, offers below ~30% are rejected roughly half the time. The BGE explanation: the responder's decision complex includes d_3 (fairness). Rejecting an unfair offer has high monetary cost (d_1) but avoids a large fairness boundary penalty. The Bond geodesic includes rejection when the fairness penalty exceeds the monetary cost.
Trust game cooperation. In trust games, agents cooperate far more than Nash predicts. The BGE explanation: dimension d_5 (trust) is active. Cooperation is the Bond geodesic when the trust dimension's edge weights make defection more costly on the full manifold than on the d_1 projection.
Public goods provision. Agents contribute to public goods even when free-riding is the Nash strategy. The BGE explanation: dimension d_6 (social impact) creates boundary penalties for free-riding that exceed the monetary savings.
Each of these "anomalies" is predicted by BGE, not catalogued post hoc. The framework says: tell me the active dimensions and their weights, and I will tell you the equilibrium. This is a stronger claim than behavioral economics makes, and it is falsifiable.
20.8 Prospect Theory as Manifold Geometry
The major phenomena of Kahneman and Tversky's prospect theory are derived as geometric properties of the decision manifold:
Loss aversion. The edge weights in E are asymmetric: the weight for moving from state a to a worse state b (loss) exceeds the weight for the reverse move (gain), even when |Da| is the same. Formally, w(a -> b) > w(b -> a) when a is the reference point. This is not a "bias" — it is an asymmetry of the manifold metric, analogous to the asymmetry of a Finsler metric.
Framing effects. A framing effect — where logically equivalent descriptions of the same decision produce different choices — is a gauge symmetry violation on the decision manifold. The Bond Invariance Principle (BIP, Chapter 12) requires that evaluations be invariant under meaning-preserving transformations. Framing effects occur when the agent's heuristic function h(n) is not gauge-invariant. This is a miscalibration of the heuristic, not a fundamental feature of the manifold.
Reference dependence. The edge weights depend on the starting vertex — the agent's current state serves as the reference point. This is built into the Mahalanobis distance: Da = a(v_j) - a(v_i) is measured from the current state, not from an absolute origin.
Hyperbolic discounting. The temporal dimension of the manifold has non-constant curvature: near-future and far-future states are not metrically equivalent. The "present bias" is a consequence of higher edge-weight density near the current temporal position.
The endowment effect. Owning a good changes the agent's position on the manifold (the attribute vector shifts). The Mahalanobis distance from "own the good" to "sell the good" differs from the distance from "don't own" to "buy the good" because the reference point has changed. This is not irrationality — it is path-dependence on a curved manifold.
20.9 Attribute Conservation in Bilateral Exchange
Theorem 20.6 (Attribute Conservation). In a closed bilateral exchange between agents A and B, for each transferable dimension k ∈ {d_1 (monetary value), d_2 (rights/entitlements), d_4 (autonomy)}:
Da_k(A) + Da_k(B) = 0
That is, what A gains on dimension k, B loses, and vice versa.
This is the economic specialization of the Conservation of Harm (Chapter 12, Theorem 12.1): in a closed system with re-description invariance, conserved quantities cannot be created or destroyed by relabeling. For transferable dimensions — money, property rights, autonomy — bilateral exchange is zero-sum on each dimension separately.
Remark (Non-Conservation of Evaluative Dimensions). Evaluative dimensions — d_3 (fairness), d_7 (identity/virtue) — are not conserved. Both parties to an exchange can simultaneously perceive increased fairness, or both can perceive unfairness. A fair exchange creates mutual value on d_3 that did not exist before the exchange. This distinction between transferable and evaluative dimensions formalizes the intuition that trade creates value beyond the material transfer.
20.10 Worked Examples
The preceding sections developed the Bond Geodesic Equilibrium as a mathematical structure. This section applies it to three real-world cases, demonstrating that the framework is not merely formal but operationally predictive. Each case study identifies the active manifold dimensions, computes the d_1-only equilibrium (what classical economics predicts), and then computes the full-manifold BGE (what actually happened). The gap between the two is the empirical signature of the missing dimensions.
Example 20.1: Uber Surge Pricing — Why "Efficient" Pricing Fails on the Manifold
Uber's surge pricing algorithm multiplies base fares by a demand factor during peak times. Classical economics says this is efficient — it clears the market by matching supply and demand through the price mechanism. When demand exceeds supply, the price rises until enough passengers drop out and enough drivers enter to restore equilibrium. On d_1 alone, this is textbook welfare maximization. Yet passengers routinely express outrage at surge pricing, regulators have investigated it, and Uber itself has capped surge multipliers. If the pricing is efficient, why does the market reject it?
The 9D analysis reveals that surge pricing optimizes on a single dimension while creating catastrophic costs on several others. On d_1, the price is indeed "efficient" — it matches supply and demand. Classical economics stops here. But d_3 (fairness) tells a different story: a 5x surge during a snowstorm or after a terrorist attack — as happened after the 2014 Sydney hostage crisis, when Uber fares spiked to over $100 for short rides away from the Lindt Cafe siege — violates deeply held fairness norms. The identical ride, described differently ("market-clearing price" versus "price gouging during crisis"), receives radically different evaluations. This is a gauge-invariance violation: the economic content is identical, but the moral evaluation changes under re-description.
The autonomy dimension d_4 exposes a further failure. During emergencies, passengers have no viable alternative — public transit may be shut down, taxis overwhelmed, walking dangerous. Their d_4 is effectively zero: they cannot meaningfully choose to decline the transaction. Surge pricing exploits the curvature increase in d_4 during emergencies, extracting maximum revenue precisely when the passenger's autonomy is at its minimum. On d_5 (trust), passengers who chose Uber as their primary transport trusted the platform to provide affordable, reliable service. Surge pricing during crises shatters that trust, leading to long-term behavioral changes: uninstalling the app, switching to competitors, supporting regulatory intervention. The d_5 cost is not captured in any single transaction but accumulates across the entire user relationship.
The social impact dimension d_6 reveals the class structure of surge pricing during emergencies: the wealthy can afford to escape at any multiplier, while the poor cannot. A 5x surge effectively rations emergency transport by income, a d_6 failure with stark class implications that no amount of "efficiency" language can neutralize.
The BGE analysis makes this precise. Uber's algorithm computes the d_1-only BGE — the surge price IS the d_1 equilibrium. But the full-manifold BGE, incorporating d_3, d_4, d_5, and d_6 with empirically appropriate weights, produces a different equilibrium: one with lower surge multipliers, price freezes during declared emergencies, and caps on maximum surges. This is exactly what Uber eventually implemented after sustained public backlash — capped surges, automatic price freezes during crises, and commitments to "no surge" during natural disasters. Uber empirically discovered the manifold. The framework would have predicted these corrections in advance, because the d_1-only geodesic was visibly far from the full-manifold geodesic from the moment surge pricing was deployed.
Example 20.2: The Dictator Game across Cultures — Metric Variation
In the dictator game, one player (the dictator) receives $10 and can give any portion to another player who has no power to accept or reject — the second player simply receives whatever the dictator allocates. Homo economicus predicts the dictator gives $0, since giving away money reduces d_1 with no strategic consequence. This prediction is spectacularly wrong. In Western undergraduate samples, the modal offer is $2–$3, with a mean around $2.80. But the more revealing data come from Henrich et al. (2005), who ran the dictator game in 15 small-scale societies across 5 continents and found enormous variation: average offers ranged from 15% of the endowment (Machiguenga, Peruvian Amazon) to 58% (Lamelara, Indonesia).
The variation is not random — it correlates systematically with market integration and cooperation norms within each society. The Lamelara are a whale-hunting community on the island of Lembata. Whale hunting requires coordinated crews of 10–15 men in open boats, harpooning sperm whales by hand. Failure to cooperate means failure to eat. This community has evolved extraordinarily high weights on d_5 (trust) and d_6 (social impact). The community's metric tensor Sigma has high off-diagonal terms between d_1 and d_5/d_6, meaning that monetary decisions cannot be separated from their trust and social-impact implications. The dictator game offer of 58% reflects the community's metric, not individual irrationality — in Lamelara, keeping most of a windfall for yourself would be a severe violation of the social contract that sustains cooperative whale hunting.
At the other extreme, the Machiguenga are relatively isolated slash-and-burn horticulturalists with low market integration and limited economic cooperation beyond the household. Their metric tensor places more weight on d_1 relative to d_5 and d_6 — not because they are "selfish" in any morally loaded sense, but because their economic ecology does not require the intense cooperation that the Lamelara's does. The off-diagonal terms between d_1 and d_5/d_6 are smaller. Their dictator game offers (15%) reflect this metric faithfully. The Orma, Kenyan pastoralists undergoing rapid market integration at the time of the study, showed an intermediate and informative pattern: offers correlated with individual income, suggesting that d_3 (fairness norms tied to wealth) is activated differently at different d_1 levels — wealthier Orma gave more, consistent with a metric where the d_1–d_3 cross-term increases with absolute d_1 level.
The framework generates a specific, testable prediction (Prediction 3 from Section 20.11): cross-cultural variation in economic games should be predictable from the community's estimated covariance matrix Sigma, which can be independently measured through ethnographic observation of cooperation patterns, punishment norms, and resource-sharing customs. The Henrich et al. data constitute the strongest existing evidence that Sigma varies systematically across cultures exactly as the framework requires. A classical model that treats all humans as optimizing on d_1 alone cannot explain the Machiguenga–Lamelara gap without invoking ad hoc "cultural preferences"; the manifold framework predicts it from the metric.
Example 20.3: Pharmaceutical Price Gouging — Turing Pharmaceuticals and Daraprim (2015)
In September 2015, Turing Pharmaceuticals, led by CEO Martin Shkreli, acquired the U.S. marketing rights to Daraprim (pyrimethamine), a drug used to treat toxoplasmosis — a parasitic infection that is life-threatening in AIDS patients and others with compromised immune systems. Turing immediately raised the price from $13.50 to $750.00 per tablet, a 5,455% increase overnight. The drug had been off-patent since 1953. Production cost was approximately $1 per tablet. Turing had conducted no new research on the compound. The price increase was pure rent extraction enabled by regulatory barriers to generic entry (the drug's small market made generic production unprofitable at the old price, and Turing implemented a closed distribution system that prevented generic manufacturers from obtaining samples for bioequivalence testing).
On d_1 (monetary value) alone, Shkreli's decision was economically "rational" in the classical sense. Daraprim had inelastic demand — patients with toxoplasmosis had no therapeutic alternative, so the price increase would be absorbed by insurers and patients rather than reducing volume. The d_1-only geodesic pointed directly at maximum extraction: charge whatever the market will bear, and the market will bear nearly anything when the alternative is death. On d_1 alone, Shkreli's geodesic was optimal.
But the full manifold tells a catastrophically different story. On d_2 (obligations), pharmaceutical companies operate under implicit obligations to patients — a downstream duty rooted in the Hippocratic tradition. The price made Daraprim inaccessible to uninsured patients and created insurance authorization barriers for others, directly violating d_2. On d_3 (fairness), the price bore no relationship to production cost ($1/tablet) or to R&D investment ($0 — Turing did no new research on pyrimethamine). The d_3 boundary penalty is enormous: the price was disconnected from any value-creating activity and represented pure rent extraction from captive patients.
On d_5 (trust), trust in the pharmaceutical industry — already fragile after decades of pricing controversies — was catastrophically damaged. The Daraprim case became the single most-cited example of pharmaceutical greed in public discourse, contributing to regulatory backlash that affected the entire industry. The d_5 cost was not borne by Turing alone but was externalized across all pharmaceutical companies. On d_6 (social impact), AIDS patients who could not afford the drug or navigate insurance barriers faced serious health consequences or death. The d_6 cost was borne entirely by the most vulnerable population — immunocompromised patients, disproportionately from lower-income communities. On d_7 (identity/virtue), Shkreli's public persona — smirking, unapologetic, taunting critics on social media — activated d_7 revulsion. The case violated the pharmaceutical industry's self-image as a healing profession, triggering identity-level rejection from physicians, pharmacists, and even other pharmaceutical executives. On d_8 (institutional legitimacy), the case exposed regulatory gaps — no existing mechanism prevented price gouging on off-patent essential medicines with small markets — undermining public confidence in the institutions that are supposed to protect patients from exploitation.
The Daraprim case is a canonical demonstration that d_1-optimal geodesics can be catastrophically wrong on the full manifold. The market eventually "punished" the deviation from the manifold geodesic, though more slowly than the framework's real-time calculation would have predicted: Shkreli was eventually imprisoned (for securities fraud, not pricing, though the pricing notoriety clearly influenced prosecutorial attention), Turing's reputation was destroyed, the company was restructured, and the case catalyzed Congressional hearings and state-level drug pricing legislation. Competing manufacturers eventually entered the market with generic pyrimethamine at a fraction of the price. Every prediction of the manifold framework was confirmed: the d_1-only geodesic was unstable, the manifold exerted corrective forces on every non-monetary dimension, and the system converged — slowly, expensively, with unnecessary suffering — toward the full-manifold BGE that the framework would have identified from the start.
20.11 Falsifiable Predictions
The framework generates six predictions that distinguish it from both classical and behavioral economics:
Prediction 1 (Dimensional Activation): Ultimatum game rejection rates should vary with the salience of specific manifold dimensions. Making fairness (d_3) more salient (e.g., by framing the game explicitly as a fairness test) should increase rejections; making it less salient (anonymous, one-shot, large stakes) should decrease them. What would falsify: if rejection rates are invariant to dimensional salience manipulations.
Prediction 2 (Bond Index Correlates): Agents with higher Bond Index scores should (a) reject more unfair ultimatum offers, (b) contribute more in public goods games, (c) show higher WTP for fair-trade goods, and (d) exhibit smaller framing effects. What would falsify: if Bond Index is uncorrelated with these measures.
Prediction 3 (Cross-Cultural Metric Variation): The covariance matrix Sigma should vary systematically across cultures in ways predicted by known cultural dimensions. What would falsify: if Sigma is invariant across cultures, or varies unsystematically.
Prediction 4 (Boundary Penalty Measurement): Sacred-value boundaries (βk = infinity) should produce qualitatively different response patterns from high-but-finite boundaries. What would falsify: if all boundary effects are graded.
Prediction 5 (Heuristic Admissibility): Moral heuristics should satisfy admissibility: h(n) ≤ h*(n). Agents using cultural heuristics should find paths that are suboptimal but within epsilon of optimal. What would falsify: if moral heuristics systematically overestimate costs.
Prediction 6 (Manifold Dimensionality): Factor analysis of economic behavioral data should recover approximately nine independent dimensions. What would falsify: if the factor structure is consistently lower-rank (fewer than seven) or higher-rank (more than eleven).
20.12 Connection to the Framework
The Bond Geodesic Equilibrium completes the multi-agent story that began in Chapter 14 (Collective Moral Agency):
• Chapter 11 solved single-agent pathfinding: f(n) = g(n) + h(n) on the moral manifold.
• Chapter 14 built the collective agency tensor: how multi-agent moral structure is represented.
• This chapter answers: what is the equilibrium when multiple agents pathfind simultaneously?
• Chapter 15 asks: how does this equilibrium get contracted to a scalar decision?
The BGE is the game-theoretic completion of the geometric ethics program. Nash equilibrium — the foundation of modern economics — is the d_1-only contraction of BGE, exactly as scalar utility is the rank-0 contraction of the moral tensor (Chapter 6.7). The same mathematical operation (contraction, Chapter 15) that explains why scalar ethics loses information also explains why scalar economics loses information.
20.13 Summary
This chapter has shown that the geometric ethics framework, when applied to economic decision theory, yields:
A formal construction of the economic decision complex E as a domain-specific instantiation of the moral manifold M.
Heuristic bounded rationality: Simon's program formalized via A* search.
The Bond Geodesic Equilibrium: a generalization of Nash equilibrium with existence via Nash's theorem on the augmented game, uniqueness via the contraction lemma, and a formal nesting of Nash as the scalar special case.
Geometric behavioral economics: prospect-theoretic phenomena derived as properties of the manifold metric.
Attribute conservation: transferable dimensions are conserved in bilateral exchange; evaluative dimensions permit mutual value creation.
Six falsifiable predictions distinguishing the framework from classical and behavioral economics.
The next eight chapters extend this pattern to clinical medicine, law, financial markets, theology, environmental policy, artificial intelligence, bioethics, and military ethics.