Fair Division Generator
Dividing an estate, a flatshare's furniture or a set of shifts runs into the same wall: the items cannot be cut, and the people value them differently. Fairness then has several meanings that do not coincide. This generates private valuations, allocates the items, and then measures the result honestly — asking each person, from their own valuations, whether they would rather have somebody else's share.
What this generator does
Gives every person a private valuation of each item, normalised so each values the whole set at 100, then allocates items to reduce envy, and where that leaves envy tries every other way of handing them out. Every person is afterwards asked, from their own valuations, whether they prefer another share to their own.
How to use this tool
- Choose how many items and how many people.
- Generate, and read who gets what.
- Check each person's own valuation of their share.
- Read the fairness verdict: envy-free and proportional are different things.
Understanding the controls
- How many items
- Between 2 and 8 indivisible items. Fewer items than people guarantees somebody gets nothing, so at least as many items as people are required.
- How many people
- Between 2 and 4. Envy-freeness gets rapidly harder as this rises.
- Seed
- Reproduces the same valuations, so a worked example stays stable.
Worked examples
- Four items, two people
- Blake gets the piano alone, worth 58 to them; Alex gets the car, paintings and cottage, worth 52 to Alex — both above the fair share of 50, and the tool reports no envy.
Common use cases
- Working through a fair division problem with real numbers
- Teaching the difference between proportional and envy-free
- Producing worked examples for a negotiation or mediation class
- Showing why indivisible items make perfect fairness impossible
- Generating allocation exercises with a measurable outcome
How this generator works
Each person's valuations are normalised to sum to exactly 100 by largest-remainder rounding, so the totals really are comparable rather than approximately so. Items are then allocated most-contested first, each going to whoever values it most among the people currently holding least. Where that leaves somebody envious, every way of handing the items out is tried (65,536 at most): a way with no envy, or failing that one that gives everybody a proportional share, replaces the rule's division, and where there is none the notes say that none exists. The result is judged by two separate standards: proportionality, where everyone gets at least their fair share by their own numbers, and envy-freeness, where nobody prefers another person's bundle — and the second is measured by having each person value every other bundle, not assumed from the procedure.
Randomness and fairness
Uses your browser's cryptographic random source for the valuations by default. A seed switches to a reproducible sequence, which is deterministic and not cryptographically secure.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Items are indivisible and no money changes hands, so the compensating side-payments that make real settlements work are not available.
- Envy-freeness is often impossible with indivisible items — one person valuing a single item at more than their fair share can make it unachievable for anyone.
- Where envy is left, every way of handing the items out has been tried and none removes it; among divisions that all leave envy the one shown is the rule's own, and another may leave less of it.
- Valuations are generated rather than entered, so this demonstrates the mathematics rather than settling your particular case.
Privacy and your data
Valuations and allocations are generated in your browser and never transmitted, stored or included in analytics.
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