How the calculator works
Each option gets one number: the average of its scores, with every criterion counted in proportion to how important you said it is.
Weighted score = (importance × score, added up over every criterion) ÷ (all the importance values added up)
Dividing by the total means only the ratios between importance values matter, and the result stays on the same 1 to 10 scale as your scores. A criterion with an importance of 0 drops out entirely.
This is the weighted sum model, also called simple additive weighting, the most common method in multi-criteria decision analysis. Its one requirement is that every number in the sum is in the same unit. Adding a salary in dollars to a commute in minutes would mean nothing, which is why every criterion here is scored on the same 1 to 10 scale instead of entered as a raw figure.
In the job example that opens the calculator, the importance values add up to 45. Growth and learning has an importance of 8, so it carries 8 ÷ 45 = 18% of the total. The offer scores 8 on it and staying scores 4, which is worth 0.71 points to the offer. Do the same for every row and the offer finishes on 6.62 against 6.16 for staying. The "Where the lead comes from" panel shows that breakdown for whatever you enter.
The idea is old. In September 1772 Joseph Priestley asked Benjamin Franklin whether to take a job as Lord Shelburne's librarian. Franklin answered with what he called "moral or prudential algebra": list the reasons on each side, estimate their weights, and strike out reasons of equal weight until you can see which side is heavier. He mentions the method in a letter to Richard Price the same month, and the editors' notes there explain the Priestley exchange. A weighted matrix does the same arithmetic in a table, for as many options as you have.
Setting up a useful matrix
Rule out dealbreakers before you score. A weighted average lets a high score in one place make up for a low one somewhere else. That is the point of it, but it also means an option that fails something you can't live with, like a commute you won't do or rent you can't cover, can still come out on top. Cross those options off first.
Use criteria that differ between your options. If both jobs have the same pension, a pension row only dilutes the rows that matter. And don't count one thing twice: "Salary" and "Money" in the same table quietly give pay double the importance you meant.
Set importance before you score. Once the scores are in, it's tempting to nudge weights until your favourite wins. If you catch yourself doing that, it's worth noticing; the reflection questions under the result ask about it directly.
Score how good each option is for you. A cheaper flat gets the higher score for rent. Every criterion runs the same way, 10 best and 1 worst, so there's no hidden flip to remember. Half points are fine.
Keep it to five to eight criteria. With twenty, each carries so little weight that none of them can move the result, and the table starts measuring how many rows you wrote.
Reading the stability check
A ranking on its own hides how close it is. The calculator answers two questions about every result once all the scores are in.
What's the smallest score change that ties it? Changing one score moves that option's total by the criterion's share of the importance times the change. In the job example the offer leads by 0.47 points, so the smallest single change that would tie it is 2.6 points on one score. If you're less sure than that about some of your scores, the ranking is softer than it looks.
How far could each importance move? For every criterion the table shows the range of importance over which the current leader stays first, with everything else left as it is. The chart shows the same thing as lines: each option's total as one criterion's share goes from 0% to 100%. Because the total is a weighted average, each line is straight, and the leader changes exactly where two lines cross. The calculator works those crossing points out exactly rather than testing a few values. Finding the smallest change in a weight that reverses a ranking is the approach set out by Triantaphyllou and Sánchez for the weighted sum model and similar methods.
The label at the top of the result summarises both. Clear lead means no single score change of 1 point or less and no importance change of 2 steps or less would change the leader. Leaning one way means one of those small changes would.Too close to call means the lead is under 0.25 points. Those cut-offs are judgement calls rather than statistics, there to tell you when to look harder.
When a matrix is the wrong tool
A matrix treats each option as a fixed set of scores. It has no idea how reversible a choice is, how much guesswork sits behind a score, or what you'd regret most. If one option can be undone in a month and the other can't, make that a criterion or decide it outside the table.
And if the result keeps disagreeing with your gut, take that seriously rather than overruling either one. Most of the time a criterion is missing or an importance is off, and finding which is more useful than the number. The first reflection question, whether you felt relieved or disappointed at the result, is there for that.
Further reading
- Even Swaps: A Rational Method for Making Trade-offs, John S. Hammond, Ralph L. Keeney, and Howard Raiffa, Harvard Business Review, March–April 1998. A way to compare options without assigning weights at all: trade one criterion for another until a criterion stops mattering or an option is clearly worse. Useful when weighting feels arbitrary.
- Multi-criteria analysis: a manual, UK Department for Communities and Local Government (first published 2000, updated 2009). Guidance for government officials on appraising options against several criteria at once, written for policy decisions but readable as a general introduction.
- A sensitivity analysis approach for some deterministic multi-criteria decision-making methods, E. Triantaphyllou and A. Sánchez, Decision Sciences 28(1), 1997. The idea behind the stability check: the smallest change to a weight or a score that changes the ranking.
- Weighted sum model, Wikipedia. A short summary of the formula and its main limitation.
Your decision stays in your browser
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