The answer changes depending on who gives it.
\nA decision matrix is a table with the alternatives in rows, the criteria in columns and a weight for each criterion: the winner is the alternative that scores highest on criteria set before looking at the offers [1].
\nIn Italy, 80.9% of companies with at least three employees are controlled by a single person or a family, which in most cases also runs them (2022 data) [2].
\nThe professional choosing software for their practice, the owner of a family business changing suppliers, the leadership of a hundred-person company all need to tell the best choice apart from the one that arrived last.
\n\n\nA decision matrix doesn't calculate the right choice: it fixes criteria and weights before you look at the alternatives, so the decision is argued over the columns and not over who proposed it.
\n
This article shows how to build one, a worked example, the spreadsheet that keeps it standing and when you're better off without it.
\nBetween a choice made on gut feeling by the business owner and one made with a grid of criteria written down beforehand, which one gets it wrong more often?
\nIn most Italian companies, management is in the hands of the business owner or a family member [2]: the gut feeling of whoever is in charge is often the only criterion in play, and not even the business owner can tell afterward whether it was the right one.
\nWithout a grid, companies choose in three ways: on gut feeling, on price, or by picking the supplier who called last.
\nNone of the three is unreasonable, but none leaves a trail you can reread when the choice goes wrong.
\nThe decision matrix puts that trail on paper before the discussion begins: alternatives in rows, criteria in columns, a weight for each criterion.
\nThis section explains what it is, what it differs from and where it fits in the path that runs from the problem found to the choice made.
\nIn mathematics a matrix is a table arranged in rows and columns [6]; here you add a row of weights above the criteria and a column of totals on the right.
\nIt is decision theory reduced to its essentials: choosing the preferable option among several possible ones by looking at the consequences [7].
\nThe Eisenhower matrix and the other priority matrices sort activities that will be done anyway, which is the subject of priority management; the decision matrix establishes which of several alternatives will be done.
\nMulti-criteria analysis is the family of which the weighted matrix is the simplest member [1]; the decision tree follows choices in sequence, and cost-benefit analysis reduces every criterion to money.
\nThe matrix comes after the analysis of causes, which is covered in the guide to business problem solving.
\nOf the two, the one that gets it wrong more often is the choice where, afterward, nobody can say what mattered: the grid is there so you can say it.
\nWeights decided before seeing the alternatives, or weights adjusted after seeing the scores: which of the two matrices tells the truth?
\nThe second only tells you who filled in the table; the first holds up even with rough weights: in 1979 Robyn Dawes showed that a linear model with imperfect weights, even all equal, beats the expert's intuitive judgment in predicting a numerical outcome [3].
\n\n\nThe weights are the decision: whoever writes them down before seeing the alternatives has already established what matters, and the matrix simply makes it visible to everyone.
\n
The same precedence is codified in the decision analysis of the Kepner-Tregoe method, which separates constraints — conditions to be met, not weighed — from wants before looking at the options.
\nThe method comes down to four technical choices: how many criteria, which scale, which weights, which final check.
\nEach has a typical mistake that empties it of meaning, and the fourth — the sensitivity test — is the one that is rarely done.
\nThe lines that follow set them out one by one, so that the example in the next section can be read without going back.
\nThere are three to five criteria, independent of one another (not \"cost\" and \"price\") and written as verifiable questions (\"does it cover orders and inventory?\"); a criterion that gives every alternative the same score is removed.
\nThe scale runs from 1 to 5 in a consistent direction: for every criterion 5 indicates the best condition for the company, and on cost it is the cheapest offer.
\nWeights run from 1 to 3, are set before the scores are known and each carries a one-line rationale; if you want more precision, distribute one hundred points among the criteria.
\nThe weight is the value tradeoff made explicit [1].
\nThe total is the sum of weight times score; the weighted average, the total divided by the sum of the weights, gives a grade from 1 to 5 and does not change the ranking, only its readability.
\nThe sensitivity test has two moves: recalculate with equal weights, then shift one weight at a time by one point, up or down.
\nIf the winner changes, the decision depends on that weight, and that is the point to discuss in the meeting, not the scores; if it doesn't change, the choice is robust.
\nDawes's result comes from prediction tasks, such as selecting candidates [3]: carried over to choosing between alternatives, it says that experience is for choosing the criteria, not for replacing them.
\nThe matrix that tells the truth is the one with weights set beforehand and put to the test; the example that follows shows it with numbers.
\nWith weights or without weights, does the same software win?
\nIn the example that follows, no: without weights the cheapest offer wins, with weights the one that covers orders and inventory wins, and the offer from the supplier who called last comes third in both versions.
\nA family-owned precision engineering company, fifteen people, a business owner who spends half the day on the shop floor: orders and inventory live on separate spreadsheets and deliveries slip.
\nThree alternatives are on the table, proposed by three different people, and each has a good reason for their own.
\nMore than half of Italian companies with at least ten employees already use a digital management system, and planning applications are the ones with the most room for growth [2]: it is a decision that sooner or later comes.
\nThe matrix below is filled in completely, with the weights set by the business owner before the meeting and the scores given in the meeting.
\nThe example is hypothetical: A is the business owner's proposal after the salesperson's demo, B is the production manager's, C is the finance office's, which would extend the accounting software already in use.
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n| Alternative | C1 coverage (3) | C2 acceptance (3) | C3 cost (1) | C4 rollout (1) | C5 reversibility (1) | Simple sum | Weighted total | Weighted average |
|---|---|---|---|---|---|---|---|---|
| A — full suite, large vendor | 5 | 2 | 1 | 2 | 2 | 12 | 26 | 2.9 |
| B — industry-specific | 4 | 4 | 3 | 3 | 3 | 17 | 33 | 3.7 |
| C — extension of the accounting software | 2 | 3 | 5 | 5 | 5 | 20 | 30 | 3.3 |
scroll the table →
\nWithout weights C wins, 20 to 17: it is the choice on price.
\nWith weights B wins, 33 to 30: it covers the problem and is accepted by those who will use it.
\nA comes last in both versions, and the business owner reads it in columns C2, C3 and C4, not in the tone of whoever is telling them.
\nSensitivity test: with equal weights C wins, as in the simple sum; shifting one weight by one point at a time, B stays first, but by a single point (36 to 35) when cost, rollout or reversibility go up to 2; with cost at 3, C overtakes B by one point (40 to 39).
\nThe decision depends on how much cost matters compared to coverage, the only question the meeting needs to settle; recalculating three times by hand is the reason the table lives in a spreadsheet.
\nA matrix filled in with a pen on a sheet of paper and one filled in on a spreadsheet give the same total: so why the spreadsheet?
\nFor three things paper can't do: lock the weights before the scores, recalculate the sensitivity in a second and keep the version discussed in the meeting.
\nThe spreadsheet doesn't add intelligence to the matrix: it adds discipline.
\nWhoever sets it up once with the right formulas never has to redo the math, and above all can no longer tweak a weight without the control cell flagging it.
\nThis section describes the structure of the spreadsheet column by column, so you can rebuild it in fifteen minutes with any spreadsheet application.
\nThe spreadsheet has five blocks.
\nSUMPRODUCT (MATR.SOMMA.PRODOTTO(pesi; punteggi) in the Italian version), weighted average, rank with RANK (RANGO in Italian) and conditional formatting on the top-ranked row.Suitable spreadsheet applications, as category examples and without endorsement or recommendation: Microsoft Excel, Google Sheets, LibreOffice Calc.
\nThe same total as on paper, but with the weights locked, the sensitivity recalculated and the version preserved: what remains to be settled is who fills it in.
\nA matrix filled in by the business owner alone in the evening, or one filled in at a meeting with the people who will have to carry it out: which of the two still holds three months later?
\nOn a sample of Italian companies with at least twenty employees, the Bank of Italy (2022) observes that a strong overlap between those who own and those who govern the company is associated with lower adoption of structured management practices [5]: the matrix is one of those practices, and filled in alone it goes back to being a gut feeling with numbers next to it.
\nA matrix has four roles, and in a small company they can be held by two or three people: who proposes the alternatives, who sets the weights, who gives the scores, who closes with a written rule.
\nIn Italy's permanent business census, managerial management applies to 1.4% of Italian companies with at least three employees controlled by an individual or a family, and drops to 0.8% in the 3-9 employee bracket [2]: in the others, the second opinion, if there is one, has to be on the spreadsheet.
\nThis section puts the four roles in sequence and links them to the concepts that keep a decision meeting standing.
\nThose who carry out the work gave the scores, the person accountable for the result set the weights: that is the matrix that still holds three months later, if it was worth doing.
\nDeciding in ten seconds with a simple rule or in an hour with a matrix: when is speed the right choice?
\nMore often than you might think: Gigerenzer and Gaissmaier (2011) show that rules that ignore part of the information can decide as accurately as complete models [4], and the method has a cost that for many choices exceeds the benefit.
\nA matrix costs between thirty minutes and an hour of work, plus a meeting: for a choice that can be reversed within a week, that cost doesn't pay off.
\nThe opposite risk is just as real: using it to sort your to-do list, which is a different skill with different tools.
\nThis section gives a four-question test to tell beforehand, not afterward, whether the grid is useful.
\nWith four yeses the matrix is useful; with two or fewer a simple rule is enough.
\nTranslated to the workplace, a simple rule is a threshold (\"under 1,000 euros, whoever carries out the work decides\"), an order rule (\"the first criterion that distinguishes the alternatives decides\") or a decision scope already written down.
\nIt is the wrong tool when the rows are activities to be put in order, the subject of priority management and the Eisenhower matrix, and when there is only one criterion.
\nFor a decision that repeats itself unchanged, an unweighted grid on two variables fixed in advance is enough, like the decision matrix for choosing a training format.
\nWhen the four yeses are missing, speed is the right choice; when they are there, the hour spent costs less than the mistake it prevents.
\nA matrix that always proves its author right, and one that occasionally proves them wrong: which of the two is built properly?
\nThe second, as a rule: Dawes (1979) showed that a linear model holds up even with imperfect weights, as long as they are set beforehand [3]; a table that confirms its author every time most likely has weights tweaked afterward, or alternatives chosen to lose.
\nThe mistakes in a matrix are not in the math: they are in what was decided before doing it.
\nSeven recur, and each has a check of a few seconds that brings it to the surface.
\nIt pays to go through them with the example table in front of you, because most of them show up there.
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n| Mistake | How to spot it | Fix |
|---|---|---|
| Weights tweaked after seeing the scores | the sum of the weights or the date in the header change after the meeting | go back to the weights set beforehand; if they're not convincing, redo the matrix from scratch with new declared weights [3] |
| Overlapping criteria (cost and price; rollout and training counted twice) | two columns have the same scores on every row | merge them into a single criterion and redistribute the weight |
| Inconsistent scale direction | in the cost column the 5 ends up on the most expensive offer | for every criterion 5 indicates the best condition; reread the columns one by one |
| Straw-man alternatives added to make the favorite win | the \"current state / do nothing\" row beats two alternatives out of three | look for real alternatives before the meeting; a single real alternative is not a choice |
| Scores from one person only | a single handwriting, no gap noted | at least two scorers, one of whom will use what is chosen (see the section on the process) |
| Rows that are tasks to do, not alternatives to choose between | the rows would be done anyway, in one order or another | it calls for a different tool: priority management |
| Stopping at the total without a sensitivity test | a single total, no recalculation | recalculate with equal weights and with one weight shifted by one point; if the winner changes, the meeting isn't over (see the section on weights) [3] |
Mistakes 1, 4 and 7 are the same mistake: deciding beforehand on gut feeling and using the table to confirm it.
\nA well-built matrix is one that occasionally proves its author wrong: weights set beforehand and put to the test are what set it apart from a gut feeling laid out in columns.
\nDawes's result [3] comes from prediction tasks with measurable criteria, such as selection and diagnosis: extending it to choosing between business alternatives is an inference by the editorial team, stated as such, and it carries no percentages with it.
\nThe same applies to Gigerenzer and Gaissmaier's principle [4] on simple rules: a general finding about decision making, not data collected on companies.
\nThe Bank of Italy figure comes from the 1,667 observations in the regressions on Italian companies with at least twenty employees from the 2019 wave of the Invind survey — 2022 is the year the paper was published, not the year of the survey [5]: the association between overlapping ownership and governance and lower adoption of structured management practices is descriptive, not causal, and nothing can be said about micro-businesses.
\nThe business software example is hypothetical and the numbers are constructed for teaching purposes: a real case has its own criteria, weights and scores, and the outcome may be different.
\nThe 1-to-5 scale and the 1-to-3 weights are a convention, not a standard: other scales work, as long as the direction is consistent and the weights are set before the scores.
\nThe method assumes real alternatives and criteria that distinguish them: if either condition is missing, the matrix returns a ranking, not a choice.
\nIt is a table with the alternatives in rows, the weighted criteria in columns and the totals on the right, like the one for choosing business software in this article: three alternatives, five criteria with weights 3-3-1-1-1 and a different winner depending on whether the weights are there or not.
\nWithout weights the cheapest offer wins; with weights, the one that covers orders and inventory.
\nMultiply each score by the weight of its criterion, add up the products and divide the total by the sum of the weights.
\nThe result is a grade from 1 to 5 that doesn't change the ranking, but makes it readable at a glance.
\nThe decision matrix chooses which of several alternatives to pursue, with weighted criteria; the Eisenhower matrix sorts your own activities by urgency and importance, that is, it decides in what order to do things that will be done anyway.
\nYes, with any spreadsheet application: as category examples, without endorsement or recommendation, Microsoft Excel, Google Sheets or LibreOffice Calc.
\nYou need a sum-of-products function for the weighted total, a division for the weighted average and a control cell that flags any change in the sum of the weights.
\nThree to five, independent of one another and written as verifiable questions.
\nA criterion that gives every alternative the same score is useless and is removed; two criteria that measure the same thing are merged into one.
\nStart from the real alternatives, at least three, proposed also by those who carry out the work.
\nWrite three to five criteria as verifiable questions and set weights from 1 to 3 before knowing the scores, with a one-line rationale for each.
\nGive scores from 1 to 5 in the meeting, with at least two people, where 5 indicates the best condition for the company on every criterion.
\nCalculate the weighted total and the weighted average, then redo the math with equal weights and with one weight shifted by one point: if the winner changes, the meeting discusses that weight, not the scores.
\nClose with the rule written in the header and keep the version discussed, which is what you reread three months later.
\nA decision matrix is not a calculator of the right choice: it is a way of writing down beforehand what matters, so that the choice is argued over the columns and not over the people.
\nIn the business software example, the offer that arrived last lost in both versions of the table, and whoever had proposed it could read the reason column by column.
\nThe matrix closes problem solving, it doesn't open it: finding the causes and choosing the analysis method are covered in the guide to business problem solving, while putting tasks in order is a different skill, covered in priority management.
\nThe steps that come before the grid — the gap put in writing, the alternatives kept open, the mandate of whoever closes the decision — are described in the guide to decision making.
\nWhat distorts judgment while those steps are being taken is the subject of the page on cognitive biases.
\nA company in which important choices go through a grid written beforehand has shorter meetings, suppliers chosen for reasons you can reread and team members who propose alternatives because they know by which criteria they will be evaluated.
\nThree months later, the decision can be reopened by reading the table, not by reconstructing who had pushed hardest.
\n\n[1] Keeney, R. L. and Raiffa, H., \"Decisions with Multiple Objectives: Preferences and Value Tradeoffs\", Cambridge University Press, 1993 (1st ed. Wiley, 1976). Available at: https://www.cambridge.org/core/books/decisions-with-multiple-objectives/DEF338459C327778C3F8C4C4A682032F
\n[2] ISTAT, \"Censimento permanente delle imprese 2023: primi risultati\", press release, November 14, 2023 (reference year 2022; sample of about 280,000 companies with 3 or more employees). Available at: https://www.istat.it/comunicato-stampa/censimento-permanente-delle-imprese-2023-primi-risultati/ — PDF: https://www.istat.it/it/files/2023/11/REPORTCensimprese.pdf
\n[3] Dawes, R. M., \"The robust beauty of improper linear models in decision making\", American Psychologist, 34(7), 571-582, 1979. DOI 10.1037/0003-066X.34.7.571. Available at: https://psycnet.apa.org/record/1979-30170-001
\n[4] Gigerenzer, G. and Gaissmaier, W., \"Heuristic Decision Making\", Annual Review of Psychology, 62, 451-482, 2011. DOI 10.1146/annurev-psych-120709-145346. Available at: https://www.annualreviews.org/doi/10.1146/annurev-psych-120709-145346
\n[5] Baltrunaite, A., Formai, S., Linarello, A. and Mocetti, S., \"Ownership, governance, management and firm performance: evidence from Italian firms\", Banca d'Italia, Questioni di Economia e Finanza (Occasional Papers) no. 678, March 2022. DOI 10.32057/0.QEF.2022.0678. Available at: https://www.bancaditalia.it/pubblicazioni/qef/2022-0678/index.html
\n[6] Treccani, entry \"Matrice\", Vocabolario on line, Istituto della Enciclopedia Italiana. Available at: https://www.treccani.it/vocabolario/matrice/
\n[7] Treccani, entry \"Decisioni, teoria delle\", Enciclopedia on line, Istituto della Enciclopedia Italiana. Available at: https://www.treccani.it/enciclopedia/teoria-delle-decisioni/
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