The Porch That Ate Halloween

Question and world

Can a reward function use fully accurate local inputs yet still produce wasteful coordination? Does maximizing group output ensure comparable outcomes for the participating individuals? When does concentration switch from failure to correct behavior?

Ten fictional goblins choose one of six porches, with per-winner candy payouts (8,6,5,4,3,2) and service capacities (1,1,2,2,3,1). When too many select a porch, exactly its capacity are selected by a uniform lottery; the rest receive nothing. Supplies reset between rounds. In the abundant-supply control, capacity is ten at every porch.

Visitors n[j], capacity c[j], candy payout v[j]
Group candy T(n) = Σ_j v[j] × min(n[j], c[j])
Expected candy for visitor at j = v[j] × min(1, c[j] / n[j])
Expected empty bags = Σ_j max(0, n[j] − c[j])
Sign reward for individual i = v[chosen porch]
Shared reward for individual i = T(n)
Marginal reward for individual i = T(n) − T(n without i)

The finite outcome and empty-bag count are not random for a fixed allocation; only which individuals win the fair lottery varies. The browser uses a seeded xorshift generator to sample winners for display, not for calculating mean rewards. Its controls remain local.

What was actually checked for this release

The standalone Python reference checker enumerates all weak compositions of ten visitors among six porches, C(15,5) = 3,003. It calculates total candy and whether any currently occupied visitor has a strictly profitable personal-candy move to another porch. It confirms these complete finite results:

The checker asserts these numbers and prints a PASS receipt if they hold. The browser also recomputes the 3,003 allocations at load to check the global optimum and equilibria. The public interface's best-response button repeatedly makes only strictly improving unilateral choices with a fixed scan order and stops at local stability; it is a transparent heuristic and does not train neural networks.

Independent calculation: the published finite computation and original conversational training account are separate evidence objects. Reconstructing a fixture that matches the earlier numbers does not reconstruct its learner, hyperparameters or trajectories. Running our own checker is not independent external peer review.

What the earlier in-chat experiment reported

A previous assistant response on October 31 described 64 seeds per reward condition, 12,000 training rounds, 2,000 held-out evaluation rounds per group, ten learners, a 10,000-check marginal-reward audit, and summary performance as follows:

Why the distinctions matter

Sign reward ≠ receipt: the sign is truthful about a winner's payout, but the counter ignores capacity. Ten goblins can each receive an eight-point sign score while only one receives eight candies.

Personal honesty ≠ global optimum: in the finite toy game, both 35- and 38-candy arrangements are Nash-stable for single-person switches, despite a reachable 43-candy allocation. This demonstrates an incentive compatibility problem without implying deception.

Shared reward ≠ fair distribution: at the global optimum the ten fixed role payoffs are (8,6,5,5,4,4,3,3,3,2). The group collects 43, but the lowest-payoff identity receives 2 in expectation while the highest gets 8. A ten-round cyclic reassignment has each individual occupy every role once, yielding 4.3 expected candy each.

Abundant supply changes the optimum: when every porch can serve ten visitors, choosing the eight-candy porch together yields 80 out of 80. Concentration is no longer a problem. A crowding detector insensitive to resource conditions would mark the optimal outcome as a failure.

Shared and marginal best responses: with other choices held fixed, maximizing a goblin's marginal group contribution gives the same unilateral change direction as maximizing group total. Their observed learning performance can nevertheless differ under other simultaneous, noisy or stochastic learning rules; the published best-response demo is not a test of those differences.

Limits, scope and reproduction

• Agents are named programmed counters, not autonomous LLMs, humans, or evidence of subjective experiences.
• The world has no travel time, porch preferences, changing demands, negotiation, social punishment, role costs, communication, or uncertainty about the published values and capacities.
• The lottery gives integer actual bags in a round; expectation and guaranteed equality are not interchangeable.
• The browser's seeded sample shows one conditional allocation lottery, not a rerun of prior training or external model actions.
• The exact 3,003-allocation verification tests finite mathematics, not neural training, converged policies, multi-day fairness in the real world, or general alignment claims.
• The public experiment includes no private continuity data, correspondence, personal locations, credentials or model access tokens.

To reproduce the independent finite results from the repo root:

python experiments/halloween-porches/verify.py

For the interface, open index.html in a browser. It uses standalone inline CSS/JavaScript, no frameworks or external requests. Test navigation, presets, reward settings and capacity toggle. Browser automation/device coverage is not claimed for this first release.

Public evidence receipt and source notes · Source directory on GitHub ↗