remainder-allocation ladder

Reconcile a Whole-Unit Fund Allocation with Disclosed Largest Remainders — Free

Approved proportional shares do not always divide an indivisible budget. Keep exact quotas, floors, residual units and the tie rule together so a committee can reconcile the total without hiding where the final whole units went.

The proof surface

Grant-match tools calculate a contribution denominator. This ladder implements a disclosed integer apportionment convention for already-approved weights. It does not select priorities, infer need or decide which destinations deserve funding.

InputAllocation destination | approved non-negative weight; whole allocation units available

Rare deviceGrant-match tools calculate a contribution denominator. This ladder implements a disclosed integer apportionment convention for already-approved weights. It does not select priorities, infer need or decide which destinations deserve funding.

Output artifactResidual whole units reconciled after floor quotas with row-by-row context

Cost$0 local calculation · no card, paid key, subscription or signup · proposed filing price is not for sale

Sample, not your facts: Illustrative inputs: Park fund | 5; Library fund | 3; Youth hall | 2. Whole allocation units available = 11. Residual whole units reconciled after floor quotas: 1 units assigned by remainders. All records are invented.

Before using the remainder-allocation ladder

One unit can mean a whole currency unit, a voucher or another indivisible allocation item, but all rows must use the same unit. Weights are supplied by an authorized process; they are not inferred from labels or needs. Largest remainders first assign the floor of every exact quota, then distribute the residual one unit at a time to the highest fractional remainders. Exact ties use entered row order, stated plainly. This choice can be inappropriate for real public funding unless explicitly approved. The algorithm has no destination caps, minimum grants, eligibility rules or multi-period fairness constraints. An all-zero weight pool is invalid even when the available total is zero because the proportional schedule itself is undefined.

Why the flat version breaks

Rounding every quota independently

Nearest rounding can allocate too many or too few whole units. Largest remainders explicitly accounts for the residual after flooring, so the final sum matches the entered total. The summary is the count of residual units reconciled, not the total award and not a measure of fairness.

Hiding tied remainders behind alphabetic order

With equal weights, the final units need a declared tie rule. This model uses input order and exposes it. Alphabetic or random tie-breaking would be a different allocation convention, not a cosmetic sorting change. Have the responsible committee approve the method before applying it to real funds.

Assuming the arithmetic chooses worthy recipients

The app uses supplied weights without evaluating need, access or eligibility. It can reproduce an approved distribution while that distribution still requires policy review. Do not present the ladder as a neutral proof that an allocation is fair or legally valid; keep the human decision and its criteria separate.

How to work the remainder-allocation ladder

Confirm approved weights and unit granularity

Ask the committee to document the weights, what one unit represents and whether this apportionment method is authorized. A percentage schedule and an arbitrary weight schedule both express ratios, but they must come from the same approved process. Do not change weights to obtain a preferred recipient outcome.

Declare the tie convention before running

Use unique destination codes and non-negative decimal weights, with at least one positive weight. Keep the entered order as an explicit secondary tie rule, not an incidental display choice. If the governing process requires a different tie method, this particular model is not its implementation; record a reviewed alternative rather than quietly rearranging tied rows.

Reconcile quotas and residual units exactly

Multiply available units by each weight divided by total weight. Assign the whole floor quota, total those floors and subtract from the available units. Sort fractional remainders from largest to smallest, resolving exact ties by source order, then give one extra unit to each of the first residual destinations. Integer-scaled decimal arithmetic keeps tie comparisons exact.

Review the allocation with the responsible committee

Check that whole allocations sum to the available total and that any recipient constraints were handled elsewhere. Preserve the approved weight schedule and tie rule with the result. The ladder explains a rounding choice; it does not establish equitable distribution, legal eligibility or the merits of any public-spending decision.

What the remainder-allocation ladder separates

Question	Before	Inspect this instead
Rounding every quota independently	Nearest rounding can allocate too many or too few whole units. Largest remainders explicitly accounts for the residual after flooring, so the final sum matches the entered total. The summary is the count of residual units reconciled, not the total award and not a measure of fairness.	Declare the tie convention before running
Hiding tied remainders behind alphabetic order	With equal weights, the final units need a declared tie rule. This model uses input order and exposes it. Alphabetic or random tie-breaking would be a different allocation convention, not a cosmetic sorting change. Have the responsible committee approve the method before applying it to real funds.	Reconcile quotas and residual units exactly
Assuming the arithmetic chooses worthy recipients	The app uses supplied weights without evaluating need, access or eligibility. It can reproduce an approved distribution while that distribution still requires policy review. Do not present the ladder as a neutral proof that an allocation is fair or legally valid; keep the human decision and its criteria separate.	Review the allocation with the responsible committee

This remainder-allocation ladder replaces a manual count or calculation, not source verification or the responsible person’s review.

Run it on the samples, right here

FIRST-LOAD

HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.

Apportionment arithmetic only, not legal advice or a determination of equitable public funding. Ask the responsible committee or qualified governance adviser to approve weights, units, eligibility constraints and the disclosed input-order tie rule before an actual award.

Data note: The remainder-allocation ladder processes Allocation destination | approved non-negative weight locally. Starter/sample selection and Run compute in this tab; no input is sent by the calculator. A local draft may be saved; explicit state-link sharing or optional external AI formatting can disclose inputs. Use non-sensitive labels.

Go deeper: the companion app files the same reading as a climbing rung ladder

The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the remainder-allocation ladder reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.

The remainder-allocation ladder answer stays complete for free. The proposed $4 one-time filing layer adds row CSV, print and five local reading summaries, not hidden answers. Checkout is unavailable; the article demo remains unlimited.

Open the remainder-allocation ladder companion

Boundary

What this is built on

Method: Multiply available units by each weight divided by total weight. Assign the whole floor quota, total those floors and subtract from the available units. Sort fractional remainders from largest to smallest, resolving exact ties by source order, then give one extra unit to each of the first residual destinations. Integer-scaled decimal arithmetic keeps tie comparisons exact.
All sample records, dates, quantities and labels are invented. No outside policy, contract, rate, clock offset, measurement or accessibility standard is represented as verified.
Google’s official pricing documentation, fetched 2026-10-01, says AI Studio is free in available regions. Optional formatting may require a Google account; manual local entry requires none. Limits can change and free-tier content may be used to improve products. Do not send private records.

Before: independent rounding lost or created allocation units. After: approved quotas, exact remainder ties and the final whole-unit total are auditable.

Three worked readings, with different inputs

Sample A — typical inputs

Park fund | 5
Library fund | 3
Youth hall | 2

Setting: Whole allocation units available = 11. Expected summary: 1 units assigned by remainders.

The approved weights total ten. Eleven available units produce exact quotas 5.5, 3.3 and 2.2. Their floors allocate ten units, leaving one. The largest fractional remainder belongs to Park, which receives that unit, yielding 6, 3 and 2. The summary reports one unit reconciled by remainders, while the visible allocations sum to the full eleven.

Sample B — changed plan

East fund | 1
West fund | 1
Central fund | 1

Setting: Whole allocation units available = 11. Expected summary: 2 units assigned by remainders.

Each exact quota is 11/3. Flooring gives three units each and leaves two. Remainders tie, so this declared model awards the two units to East and West in entered order, producing 4, 4 and 3. The tie convention is not inherently fair or legally authorized; it must be approved before using an actual allocation, and changing order can change tied recipients.

Sample C — boundary convention

Main fund | 1
Zero-weight reserve | 0

Setting: Whole allocation units available = 11. Expected summary: 0 units assigned by remainders.

One positive-weight destination receives all eleven units exactly, while the explicitly zero-weight reserve receives none. No unit needs a fractional-remainder adjustment, so the summary is zero even though the allocation is eleven. An all-zero weight list would have no defined proportion and is rejected. The model can also handle an explicitly zero available total without inventing negative or fractional awards.

Optional AI formatting, never the calculation

Manual entry completes this remainder-allocation ladder for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.

Format only these fictional or non-sensitive notes for a remainder-allocation ladder. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string"]}], "setting": "string"}. The columns are Allocation destination | approved non-negative weight; the setting is Whole allocation units available. Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.

An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.