FA-12771 / Voting rule computation / Open access

Sequential divisor allocation reuses initial priorities · case 01

Sequential divisor allocation reuses initial priorities.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

All seat priorities are frozen at the initial vote totals.

THE FAILURE

All seat priorities are frozen at the initial vote totals.

Unsuccessful approach: Using an odd divisor progression silently switches to a different allocation rule.

Case contract

Allocate nonnegative seats sequentially by highest exact votes/(awarded+1), resolving equal priorities by earlier index. Votes are nonnegative with positive total.

Why this case matters

A deterministic toy ballot model makes the stated counting convention executable.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(votes, seats):
    out=[0]*len(votes)
    out[max(range(len(votes)),key=lambda i:votes[i])]=seats
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('update seat priority', solve([5*N,2*N],2), [2,0])
check('minority eventually receives seat', solve([5*N,2*N],3), [2,1])
check('equal priorities stable', solve([N,N],3), [2,1])
check('zero seats', solve([N,N],0), [0,0])
check('zero votes', solve([0,N],3), [0,3])
check('single group', solve([N],4), [4])
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
update seat priority	`[2, 0]`	`[2, 0]`	Passed
minority eventually receives seat	`[3, 0]`	`[2, 1]`	Failed
equal priorities stable	`[3, 0]`	`[2, 1]`	Failed
zero seats	`[0, 0]`	`[0, 0]`	Passed
zero votes	`[0, 3]`	`[0, 3]`	Passed
single group	`[4]`	`[4]`	Passed

SHA-256 / 3cc944b0068cca6d7c1a61233d90f4bfc41f0d0e115732c43530f86024b2290e

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(votes, seats):
    out=[0]*len(votes)
    for _ in range(seats):
        i=max(range(len(votes)),key=lambda i:Fraction(votes[i],2*out[i]+1))
        out[i]+=1
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('update seat priority', solve([5*N,2*N],2), [2,0])
check('minority eventually receives seat', solve([5*N,2*N],3), [2,1])
check('equal priorities stable', solve([N,N],3), [2,1])
check('zero seats', solve([N,N],0), [0,0])
check('zero votes', solve([0,N],3), [0,3])
check('single group', solve([N],4), [4])
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
update seat priority	`[1, 1]`	`[2, 0]`	Failed
minority eventually receives seat	`[2, 1]`	`[2, 1]`	Passed
equal priorities stable	`[2, 1]`	`[2, 1]`	Passed
zero seats	`[0, 0]`	`[0, 0]`	Passed
zero votes	`[0, 3]`	`[0, 3]`	Passed
single group	`[4]`	`[4]`	Passed

SHA-256 / df080fed9f1ab55ebedad1b380c16cf8b3f9fef076107fc56434b05846880d8e

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

Abstract counting rules only; excludes jurisdictional law, ballot authentication and election operations. 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 2026-09-29T14:39:00.079913+00:00.

Case digest / 4e43691edc0eb53591ff259cf760ca2e08d588da9611800b0766ed6f3ad25471