---
slug: risk_seeking
name: Risk Seeking
one_liner: "Prefer an uncertain prospect to a sure outcome of equal expected value — the convex-utility, variance-favoring dual of risk-averse concavity along the certainty-versus-uncertainty preference axis."
type: prime
schema_version: 2
status: density_v2_draft
categories: [economic, cognitive]
origin_domain: decision_theory
alternate_origin_domains: [economics_finance, cognition_and_psychology, evolutionary_biology]
aliases: [risk_proneness, risk_loving, variance_seeking, gambling_preference, convex_utility]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-01 dualization, sub-flavor 1a) — the structural dual of `risk_aversion` along the certainty-vs-uncertainty preference axis (convex vs concave utility). Discovered in the op-01 full sweep 2026-07-03. Verified absent via search_prime + slug check; exact action_bias/omission_bias polarity precedent for co-equal dual pairs. STATUS: RECOMMENDED ACCEPT."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). Did NOT go through Phase-A triage. SI/SF/similarity grades are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT yet written."
- "Phase-C action: re-similarity check vs risk_aversion / expected_value / loss_aversion / prospect_theory to confirm it does not collapse into the input; draw the co-equal sibling edge to `risk_aversion` and any shared-parent edge (preference-over-uncertain-prospects / utility-curvature) at incorporation. one_liner must be synced to a v1 draft per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 3
  structural_abstraction: 4
  transfer_evidence: 3
  reasoning: 'The rule "prefer a gamble to its certainty-equivalent expected value" is a pure ordering property of preferences over uncertain prospects — a convex utility function, U''(w) > 0 — with no commitment to what the payoffs measure, so structural abstraction is a strong 4 (it is stated over an agent with preferences, which is slightly less medium-free than a pure relational graph). It recurs across substrates: convex utility in decision theory and finance (lottery buyers, convex-payoff trading, low-solvency firms "gambling for resurrection"), risk-prone foraging under the energy-budget rule in behavioral ecology, and sensation-seeking / variance preference in psychology — a domain breadth of 3, real but clustered in agent-bearing fields. Transfer is genuine (the energy-budget rule predicts the same convexity-driven variance preference in animals that Arrow-Pratt predicts in humans) but the sharpest evidence sits in economics and its behavioral cousins rather than spanning the physical sciences, so transfer evidence is 3 and the composite is 4.'
similarity_to_nearest_existing_prime:
  slug: risk_aversion
  similarity: 0.72
structural_framed:
  label: mixed-structural
  aggregate: 0.28
  criteria: {vocab_travels: 0.2, evaluative_weight: 0.3, institutional_origin: 0.1, human_practice_bound: 0.3, import_vs_recognize: 0.4}
  rationale: 'Preferring an uncertain prospect to its equal-expected-value certainty is a formal curvature property of a preference ordering (convex utility), which reads structural; but it is a property of an agent''s preferences rather than a substrate-free relation, so it carries mild human/agent-practice binding (human_practice_bound 0.3) and a faint evaluative tint (evaluative_weight 0.3 — "risk-seeking" is often read as a normatively loaded trait, though the structure itself is value-neutral). The label "risk-seeking" is somewhat a term of art imported from decision theory (import_vs_recognize 0.4), pulling the aggregate to 0.28: mostly structural, lightly framed by its agent-and-preference substrate.'
phase_b_passes_completed: []
---
# Risk Seeking

## Core Idea

Risk seeking is the property of an agent's preferences that makes it *prefer an uncertain prospect to a sure outcome of the same expected value*: offered a certain payoff of E[W] or the random payoff W whose average equals E[W], the risk-seeking agent takes the gamble. It is one pole of a single structural axis — *how an agent trades expected value against uncertainty* — whose opposite pole is `risk_aversion` (prefer the sure thing). Formally the two poles are the two signs of one curvature: risk aversion is a concave utility function (U''(w) < 0), risk seeking is a *convex* one (U''(w) > 0), so that the utility of the expected outcome falls below the expected utility of the outcomes, and the agent will *pay* — accept a negative risk premium — for the privilege of facing variance rather than certainty. The pair is co-equal and exhaustive over an agent that is not risk-neutral: neither pole is the default, and the whole content of each prime is which sign of the curvature it names.

The load-bearing invariant is *convexity of the valuation over outcomes*, and it generates the characteristic behaviors directly. Because a convex function rewards spread, the agent's certainty-equivalent for a gamble lies *above* its expected value: it would decline a fair sure payment in order to keep the gamble, and it demands no insurance — it would sell insurance, not buy it. The Arrow–Pratt measure that quantifies aversion simply flips sign and quantifies the intensity of seeking. The trade-off is the mirror image of aversion's: risk seeking accepts a *lower expected outcome* (or equal expected value at higher variance) in exchange for exposure to the upside tail. That exposure is the payoff when the outcome distribution has a fat or unbounded upper tail, a threshold that only a large draw can clear, or a floor that caps the downside so that variance is nearly free on the losing side; it is a pure cost when outcomes are symmetric and the downside bites, since the agent is then paying for variance that carries no compensating asymmetry.

Read as convexity-of-valuation, the pattern recurs wherever an agent chooses among uncertain prospects. In **decision theory and finance** it is the buyer of a lottery ticket, the holder of a convex (option-like) payoff, and — sharply — the near-insolvent firm "gambling for resurrection," where limited liability truncates the downside at zero and makes the value function locally convex, so the rational move is to *increase* variance. In **behavioral ecology** the energy-budget rule predicts risk-prone foraging exactly when an animal's expected intake falls below its survival requirement: the survival function is convex in that region (only a lucky large find clears the threshold), so a starving forager should prefer the variable food patch over the steady one — the same structure that drives the failing firm. In **psychology** it appears as sensation-seeking and as the convex segment of the prospect-theory value function in the domain of losses, where decision-makers turn risk-seeking to avoid a sure loss. Across all of these the recognizable move is identical: value the spread, prefer the gamble to its average, and accept a worse expectation for access to the tail.

## Notes

**Provenance.** Produced by the op-01 dualization operator (sub-flavor 1a) as the structural dual of `risk_aversion` — flipping the sign of utility curvature (concave → convex) along the certainty-versus-uncertainty preference axis. Discovered in the op-01 full sweep 2026-07-03. It is the paradigm co-equal-dual case: the input's own Core Idea explicitly names concavity and the Arrow–Pratt measures, and the seeking pole is the other sign of the same object.

**For owner evaluation (keep/cut).** The case FOR: this is a co-equal, mutually-exhaustive structural dual of an existing prime, with an *established* name in decision theory and a clean formal signature (convex utility, U'' > 0). The corpus already carries the `action_bias` / `omission_bias` co-equal-dual precedent, so accepting the second pole of a preference-curvature axis is consistent with prior curation. Verified absent via search_prime + slug check. The manifest rated it ACCEPT. The specific risks Kurt should weigh: (1) **overlap/collapse risk** — similarity to `risk_aversion` is high (est. 0.72) because the two are literally sign-flips of one function; the question is whether the encyclopedia wants both poles as separate primes or a single "risk_attitude / utility_curvature" prime that names the axis and treats aversion and seeking as its two values. The `action_bias`/`omission_bias` precedent argues for two separate primes; a "one axis, one prime" convention would argue for a merge. (2) **framed-tint risk** — "risk-seeking" carries a mild evaluative/agent-practice framing (SF aggregate est. 0.28, higher than eager_evaluation's 0.1) because it is a property *of an agent's preferences*, not a substrate-free relation; it is still predominantly structural but less purely so than a scheduling relation. (3) **possible missing-parent signal** — if both aversion and seeking are kept, they may want a shared parent prime naming the certainty-vs-uncertainty preference axis / utility-curvature itself, which does not yet exist; this is a lattice-gap worth flagging rather than a reason to cut.

**At incorporation.** Re-similarity-check against `risk_aversion` (collapse test), `expected_value`, `loss_aversion`, and `prospect_theory` to confirm it stands as its own prime rather than folding in. If kept, draw the co-equal-sibling edge to `risk_aversion` and consider proposing a shared parent (preference-over-uncertain-prospects / utility-curvature) to close the possible lattice gap. Confirm the aliases do not collide with an existing slug. Sync the `one_liner` to a v1 draft per CLAUDE.md before merge, and mirror it across v1/v2 in the same commit.
