FA-066 / Distributed coordination / Open access

Duplicate or foreign ballots manufacture a quorum · case 01

A coordinator declares a decision after counting retries or ballots from outside the membership.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The quorum predicate counts received messages instead of distinct eligible voters.

VERIFIED REPAIR

Intersect unique voter IDs with the current membership before testing a strict majority.

Unsuccessful approach: Deduplicating ballot IDs still counts votes from removed or unknown members.

Case contract

Members define a fixed nonempty voting configuration. Return whether distinct eligible voter IDs number at least floor(member count/2)+1; an empty configuration cannot reach quorum.

Why this case matters

Models quorum accounting independently of transport delivery multiplicity. It deliberately omits cryptographic authentication and joint-consensus membership changes.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(members, votes):
    return bool(members) and len(votes) > len(set(members))//2
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
members = list(range(2*N+1))
check('retransmitted single ballot', solve(members, [0]*(N+1)), False)
check('only foreign voters', solve(members, list(range(100, 101+N))), False)
check('exact eligible majority', solve(members, list(range(N+1))), True)
check('one below majority', solve(members, list(range(N))), False)
check('noise cannot complete minority', solve(members, list(range(N))+[999]), False)
check('repeats do not destroy real majority', solve(members, list(range(N+1))*N), True)
check('empty configuration', solve([], [0]), False)
check('single eligible member', solve(['only'], ['only']), True)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
retransmitted single ballot	`True`	`False`	Failed
only foreign voters	`True`	`False`	Failed
exact eligible majority	`True`	`True`	Passed
one below majority	`False`	`False`	Passed
noise cannot complete minority	`True`	`False`	Failed
repeats do not destroy real majority	`True`	`True`	Passed
empty configuration	`False`	`False`	Passed
single eligible member	`True`	`True`	Passed

SHA-256 / e86c1b3374ff6c76424d3a6136bfafa6280fe59c7970e97fd5495079b4b3a744

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(members, votes):
    return bool(members) and len(set(votes)) > len(set(members))//2
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
members = list(range(2*N+1))
check('retransmitted single ballot', solve(members, [0]*(N+1)), False)
check('only foreign voters', solve(members, list(range(100, 101+N))), False)
check('exact eligible majority', solve(members, list(range(N+1))), True)
check('one below majority', solve(members, list(range(N))), False)
check('noise cannot complete minority', solve(members, list(range(N))+[999]), False)
check('repeats do not destroy real majority', solve(members, list(range(N+1))*N), True)
check('empty configuration', solve([], [0]), False)
check('single eligible member', solve(['only'], ['only']), True)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
retransmitted single ballot	`False`	`False`	Passed
only foreign voters	`True`	`False`	Failed
exact eligible majority	`True`	`True`	Passed
one below majority	`False`	`False`	Passed
noise cannot complete minority	`True`	`False`	Failed
repeats do not destroy real majority	`True`	`True`	Passed
empty configuration	`False`	`False`	Passed
single eligible member	`True`	`True`	Passed

SHA-256 / f993907cd45a9eb7d066fa2c64250a3a87a21e2a7fd75f3cb3d1426a21fa6251

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(members, votes):
    eligible = set(members)
    return bool(eligible) and len(eligible & set(votes)) > len(eligible)//2
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
members = list(range(2*N+1))
check('retransmitted single ballot', solve(members, [0]*(N+1)), False)
check('only foreign voters', solve(members, list(range(100, 101+N))), False)
check('exact eligible majority', solve(members, list(range(N+1))), True)
check('one below majority', solve(members, list(range(N))), False)
check('noise cannot complete minority', solve(members, list(range(N))+[999]), False)
check('repeats do not destroy real majority', solve(members, list(range(N+1))*N), True)
check('empty configuration', solve([], [0]), False)
check('single eligible member', solve(['only'], ['only']), True)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
retransmitted single ballot	`False`	`False`	Passed
only foreign voters	`False`	`False`	Passed
exact eligible majority	`True`	`True`	Passed
one below majority	`False`	`False`	Passed
noise cannot complete minority	`False`	`False`	Passed
repeats do not destroy real majority	`True`	`True`	Passed
empty configuration	`False`	`False`	Passed
single eligible member	`True`	`True`	Passed

SHA-256 / a92bc43dfc2ff5b9258ae219a7c2b05700759f4877f181f155e3ca55693db6ea

Verification & scope

This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:36:49.896520+00:00.

Case digest / a259764003798ac762f6eeb69c38adbdf4be596b3dd6c4f52a01aa988715c27f