How it works, precisely
Each person ranks the options. A first choice costs 1, a second costs 2, and so on: that builds the cost matrix.
The algorithm finds the assignment minimising the TOTAL cost, exploring every possible combination intelligently — never one by one, which would be out of reach.
An important consequence: the computation may sacrifice one person to relieve several. The optimum is collective, and that is exactly what it is asked to be.
A worked example
Three people, three assignments. Each cell gives the rank of the wish.
| Audit | Redesign | Support | |
|---|---|---|---|
| Chloé | 1 | 2 | 3 |
| Ali | 1 | 3 | 2 |
| Bruno | 2 | 1 | 3 |
- Serving everyone their first wish is impossible: Chloé and Ali both want Audit.
- Chloé→Audit, Bruno→Redesign, Ali→Support: total cost 1 + 1 + 2 = 4.
- Ali→Audit, Bruno→Redesign, Chloé→Support: total cost 1 + 1 + 3 = 5.
The first combination wins: for comparable wishes, it costs the group less. No other arrangement beats 4.
Where it comes from
This is the « assignment problem », a classic of operations research. Harold Kuhn published an efficient solution in 1955 and named it the « Hungarian algorithm », in tribute to the Hungarian mathematicians Dénes Kőnig and Jenő Egerváry whose work it drew on.
It later emerged that Carl Gustav Jacobi had solved the problem in the nineteenth century, in work published posthumously in 1890 — sixty-five years before its rediscovery.
The algorithm is now an ordinary industrial tool: assigning crews to flights, tasks to machines, vehicles to journeys. Every application that pairs two sets while optimising a total cost descends from it.
Where it is used
- Sharing assignments or case files across a team while maximising overall satisfaction.
- Allocating pupils to workshops, options or projects.
- Assigning on-call or duty slots.
- Scheduling crews, rounds or machines — the historic industrial use.
Limits and pitfalls
- The best possible total satisfaction
- No draw involved
- Exact result, not approximate
- Can sacrifice one person for the common good
- Tactical rankings are possible
- Less intuitive to explain
Frequently asked questions
How is this better than serial dictatorship?
On average the group is more satisfied: the algorithm sees every combination at once, where serial dictatorship is at the mercy of the running order. The price is readability — and the possibility of lying.
What happens if two assignments tie?
Several solutions can reach the same minimal cost; one is picked. If the stakes are high, announce the tie-break rule in advance, or switch to serial dictatorship, whose mechanics are reproducible.
Do I need as many places as people?
No, but the gap has a price: too few places and someone goes unassigned; too many and some stay empty. The computation remains valid either way.