Aligned Failure

A formal toy model of modal conflict: each agent's marginal reliability can increase while the reliability of the community majority decreases, because failures become aligned.

ModalConflictModel0_2

Agents

Independent reliability

Single-source reliability

Generated runs/worlds

Grid ordering

1. Summary

Regime	Agent analytic	Majority analytic	Agent empirical	Majority empirical

Independent majority reliability:
P(M correct) = Σ_k=tⁿ C(n,k)p^k(1-p)^n-k =

Hover over the summation, a distribution row, or a grid cell. The distribution table highlights the corresponding columns in the grids.

2. Distribution over number of correct agents

K is the number of correct agents in a run/world. The majority is correct when K ≥ t. Independent evidence spreads probability across many rows; a single source puts nearly all analytic mass at the extremes. Each mini-bar is scaled from 0 to 1.

K	Majority?	Independent analytic	Independent empirical	Single-source analytic	Single-source empirical

3. Modal grids

correct incorrect M = community majority

The canvases always fit the panel width. With many runs, each column becomes thinner rather than overflowing. Switch to raw run order to see that the sample is generated randomly.

Independent evidence: dispersed failures

errors partly cancel

Single source: aligned failures

errors align