KRITΩN — dsc Strategy Consulting

Ask one question first: how should the criteria reach the axes?

Every axis can be switched over later, so nothing is locked in here.

Choosing a way starts a fresh workspace — “undo” in the workspace brings the previous one back.

Authorship

This tool is a synthesis. It was derived from an analysis of the works named below and combined with development of our own. The derivation of axes from named criteria, the propagation of uncertainty rather than its hiding, the rule that a matrix may feed another but never itself, and the requirement that every partition line be argued, are the work of dsc Strategy Consulting. We claim neither the foundations nor the established techniques built on them — they are named and attributed here. What we claim is the synthesis, and the moves the literature does not contain. This page shows what was inherited from whom, and what was developed here.

A two-dimensional matrix used as the aggregation node of a criteria hierarchy, its result feeding the axis of a higher matrix, applied recursively. Hierarchies aggregate through formulas; here they aggregate through a readable space.
Designation — naming areas — as a formal, general construction step rather than a fixture of one named framework.
The choice of mean presented as an explicit strategic assumption about compensation, with its iso-lines shown.
An override that keeps the computed value and the judgment side by side as a record.
A general grammar for partitioning the space — arbitrary lines, one-pole and two-pole bands, five-area partitions — and for refining one area with a matrix of its own.

The theoretical basis this rests on

九章算术 Nine Chapters on the Mathematical Art — matrix representation: organizing data systematically in rows and columns, and operating on it.
Ἀριστοτέλης, Metaphysics; Boethius, De Divisione — mereology: how a whole divides into parts and parts compose a whole. The two directions the matrix tree travels.
Thomas Aquinas, Expositio super librum Boethii De Trinitate, 13th c. — descending division against ascending composition: the tree read downwards is analysis, read upwards it is synthesis.
Fritz Zwicky, Discovery, Invention, Research Through the Morphological Approach, 1969 — morphological analysis: systematically combining notions and instruments instead of picking a framework off the shelf. The origin of Matrix Genesis.
Jacques Bertin, Sémiologie graphique, 1967 — the grammar of graphics: position, size and shape carry meaning, and carry it better than a number does.
Boston Consulting Group, The Product Portfolio, 1970 — the strategic matrix as a portfolio instrument, and the naming of areas that turns a coordinate into an instruction.
Robert Sokal & Peter Sneath, Principles of Numerical Taxonomy, 1963 — grouping by distance rather than by a summary score, and the complete-linkage rule that keeps clusters compact instead of letting them run into chains.
J. W. Carmichael & P. H. A. Sneath, Taxometric Maps, 1969 — position in a space as the basis for grouping; the ancestor of archetype clustering.
David Krantz, R. Duncan Luce, Patrick Suppes & Amos Tversky, Foundations of Measurement, 1971 — what a scale must satisfy before arithmetic on it means anything. Why the scaling of an axis is a decision, not a formality.
Ralph Keeney & Howard Raiffa, Decisions with Multiple Objectives, 1976 — the value hierarchy: objectives decomposed into attributes and recomposed by weighting. The closest established relative of the matrix tree, and the reason its nodes are formulas rather than pictures.
Bernard Roy, ELECTRE / outranking methods, from 1968 — that aggregation may be non-compensatory: a decisive weakness need not be buyable by strength elsewhere. The reason the choice of mean is a strategic assumption, not a formality.
Michela Nardo, Michaela Saisana, Andrea Saltelli, Stefano Tarantola et al., Handbook on Constructing Composite Indicators, OECD/JRC, 2008 — the institutional standard for normalization, weighting and aggregation, and for reporting uncertainty and sensitivity alongside the result rather than after it.
G. H. Hardy, J. E. Littlewood & George Pólya, Inequalities, 1934 — the family of generalized means and the inequalities between them. The mathematics under the five consolidation modes, and the reason their order is not arbitrary.
Michaela Saisana, Andrea Saltelli & Stefano Tarantola, Uncertainty and Sensitivity Analysis Techniques as Tools for the Quality Assessment of Composite Indicators, Journal of the Royal Statistical Society A, 2005 — that a composite result must be reported together with how far it survives its own assumptions.
Harry Markowitz, Portfolio Selection, 1952 — a portfolio is judged as a whole, not as a list of its parts.

What was developed for this synthesis — dsc Strategy Consulting's own contribution:

A two-dimensional matrix used as the aggregation node of a criteria hierarchy, its result feeding the axis of a higher matrix, applied recursively. Hierarchies aggregate through formulas; here they aggregate through a readable space.
Designation — naming areas — as a formal, general construction step rather than a fixture of one named framework.
The choice of mean presented as an explicit strategic assumption about compensation, with its iso-lines shown.
An override that keeps the computed value and the judgment side by side as a record.
A general grammar for partitioning the space — arbitrary lines, one-pole and two-pole bands, five-area partitions — and for refining one area with a matrix of its own.

Rights

Provision and liability

Whether provision is charged or free of charge depends on the engagement; where an individual agreement exists, it prevails.
It computes and displays on the basis of the data entered. It does not give advice and it does not make decisions.
No warranty is given as to correctness, completeness or fitness for a particular purpose; use is at your own risk.
Decisions and their consequences remain with the user.

Copyright and use

© 2026 dsc Strategy Consulting. The frameworks, the wording and this application are our work.
Clients may use it for their own work, commercially included.
Reusing it, passing it on, publishing it, reselling it or reworking it into a competing offering is prohibited.
If you want to do more with it, ask us — usually we are glad to agree.

Portfolio decisions fail on axes that were asserted rather than derived, and on differences nobody can defend. It builds strategic matrices whose axes come from named criteria, and carries them through to areas, archetypes and a portfolio view.

Criteria are weighted and consolidated by a mean you choose; uncertainty is propagated rather than hidden; a matrix may feed another but never itself; and every partition line is an argument you have to name.

Teleology - Purpose: Why?

KRITΩN — from διακριτήριον, the instrument for discernment. It divides — to enable decision and action. It does so on grounds that are transparent and align with the objective, and not superficially — to avoid prae-iudicium: the habitual conclusion unaligned with the specific problem and objective. Division also involves grouping; each resulting group is an archetype with specific properties — for example objectives, strategy, allocation of resources.

What it is for

To differentiate — only clear and defensible differentiation enables consequent action.

The near end is comprehension with clarity — you cannot treat differently what you cannot tell apart.
The end is consequence — resources, attention and strategy applied where the difference actually is.
Comprehension sits on the border of this tool. Consequence is already outside it, and so is everything that follows from it.
Clarifying the issue and the criteria is not a step this tool can take. It belongs to whoever owns the decision, and it decides whether anything after it is worth having.

What it provides

Comprehension — at three levels, each read against the next.
- The individual: where each entity stands relative to the others.
- The group: which of them belong together, and what therefore holds for all of them.
- The whole: balance and tilt, what is missing, what is over-served, whether the mass carries itself.
Structuring to enable differentiation and valid generalization — one act with two effects.
- Division: segment and hierarchize, along boundaries drawn in advance.
- Grouping: cluster and lump, along groups that emerge from the data.
- Generalization without division is prejudice; the division is what makes it valid.

What you can get out of it

Depending on the approach — not every path yields every one of these.

A position per entity in a space whose axes you defined: entered directly, consolidated from weighted sub-scores, or handed down as the result of a matrix below. A third variable can ride along as bubble size, and may be signed.
A stated assumption wherever several criteria became one — which of the five means consolidated them, with what weights, and therefore how far a strength was allowed to cover a weakness.
A divided space: quadrants with as many lines as you need, distance bands around one pole or two, or the five-area partition — every boundary movable.
Named areas, each carrying the implication for whatever sits in it.
One overall position per entity, so a matrix result can become an axis of the matrix above it instead of a dead end.
Archetypes — entities grouped by weighted distance across every criterion at once, when the question is kinds rather than positions.
A portfolio reading of the whole set: share per area, centre of gravity, spread, net size and coverage ratio where sizes are signed, and the balance against the distribution you are aiming at.
A verdict on your own conclusion: what the picture looks like under each of the five means, and which entities could belong elsewhere within their stated ±.
A record of judgment — any computed value may be overridden, and the computed one stays visible beside it.

What it reflects

What is available: data, often plenty of it; specialists who know their part best; a room that has to be convinced.
What inhibits: too many entities to hold in view; too diverse to compare at sight; a grouping that depends on several properties at once; a total score by averaging that destroys what it was meant to summarize.
Each of these arrives dressed as a technical difficulty and is a judgement problem underneath: which dimensions may stand for the rest, how abstract the axes must be, what may compensate for what. The tool does not repair the arithmetic — it exposes the judgement inside it.

Why it works

Clarity earns comprehension, defensibility earns consequence. Every demand below serves one of the two.

Effectiveness — how much comprehension is actually reached: the mean stated instead of assumed, the ± carried through, the difference kept instead of averaged away, the area named rather than numbered.
Efficiency — how easily it is reached: values, axes, areas and portfolio follow by themselves; tables in and out; the whole workspace in one file.
Coherence by construction — the format enforces what a sound concept must satisfy anyway: a criterion enters once, areas are disjoint and exhaustive, a result re-enters only one level up, and few enough items stay in view at once.
No premature concretion — it has no vocabulary for measures. The result stays a criterion, never a plan.

Method and instrument

The method divides; the instrument makes dividing workable. A stack of matrices cannot be held by hand — move one sub-score and every node above it has to be done again. What this tool adds is practicability, visibility and discipline, never a concept.

Enchiridion - Manual: How?

Two ways to use it

As a working tool, in the hands of a trained strategist — the senior strategist of the entity, say — who knows the method and drives it alone or with a small team.

Or, and this is where it is worth most, in a workshop moderated by such a specialist, or by us. Because the tool runs online, that workshop works over a collaboration platform (e.g. Teams®) as well as it does in a room.

The operating steps of each page stand on the page itself, under What this does and how to use it — what the page produces, in how many steps, and the rule that governs it. What follows here is what those pages cannot say for themselves.

Which approach to choose

Exactly 2 criteria → enter them directly as the two axes of one matrix.
3 or more criteria → either way. Averaging consolidates them into the two axes as weighted sub-scores on the averaging page: values, weights and method per axis. The tree pairs them in matrices whose results become axes further up — a matrix may combine a criterion with the result of another matrix, so three criteria already make a chain: A × B, then that result × C.
The way is the entry point, not a cage: in “Criteria of this matrix” an axis can later be switched between entered and derived from another matrix. Sub-score averaging stays out of the tree — there a consolidation gets its own matrix — and switching an axis of a single matrix to sub-scores simply opens the averaging page for it.
Archetype clustering stands apart from the three matrix approaches: it needs no matrix, uses every criterion at once rather than two, and answers which entities are of one kind. It opens as its own instrument.

Why matrices as inputs, not aggregation

A matrix result is itself a criterion — which lets a decision rest on many criteria without averaging any of them away.

One matrix takes two criteria. Real decisions rest on more — and forcing them into two axes means averaging them, which destroys exactly the difference the matrix was built to show.
So a matrix's result becomes a criterion in its own right: its overall position feeds an axis of the matrix above it. From the criteria you can actually observe, up to the single statement the decision needs.
Every step stays readable. You can walk back down the tree and challenge one node without discarding the rest. A formula cannot be argued with; a named space can.

Why a matrix, not a score

A strategic matrix condenses many findings into one two-dimensional picture — positions become statements, statements become consequences.

The matrix enforces two things a list never does: condensation and abstraction — many findings compressed into two dimensions that can be held in view at once — and discussion, because a position can be disputed where a number is merely accepted. Comprehension and consequence are what come out of that, not what goes in.
A single score hides how an entity got there. Two businesses with the same average can sit in opposite corners of the space and need opposite decisions — one is strong where it counts and weak where it does not, the other the reverse. The average erases exactly the difference you are being paid to see.
Every step from evidence to conclusion stays visible: which two criteria were paired, where the boundaries run, what each area is called. A scoring model asks to be believed; a matrix can be audited — and argued with.
A table compares numbers, a matrix compares situations. The moment an area carries a name — harvest, develop, restructure — a coordinate turns into a decision that a room full of people can argue about.
Two dimensions are what a human being can hold in view at once. That is the reason for the format, and the reason to consolidate deliberately rather than to average everything into one number.

Why grouping by distance, not by average

Averaging groups entities along its own iso-lines; distance groups them by likeness — and the two disagree systematically, not occasionally.

An average projects the space onto a line. Every entity on the same iso-average line receives the same score, although they may sit at opposite ends of the picture.
The groups that matter cut across those lines. Averaging makes an unlike pair look identical, and hides precisely the difference that defines an archetype.
So archetypes are found by distance — weighted, across every criterion at once — and clusters are kept compact by complete linkage instead of being allowed to run into chains.
Which average is meant matters. Averaging inside an entity, across its criteria, destroys the profile — grouping by that number is the error. Averaging inside a cluster, across its members, one criterion at a time, is the cluster’s profile: a result, not a selector.
A good cluster therefore does show similar values per criterion, which can make clusters look like bands of low, medium and high. They are not: two entities with the same overall average land in different clusters whenever their profiles differ — high–low and low–high are equally far from the middle and nowhere near each other.

What is method, and what is this tool

Everything above is the method, and it holds with paper and a whiteboard. What the tool adds: it recomputes the whole chain on every change, draws the iso-lines of the mean you chose, carries the uncertainty upward, keeps an override beside its computed value, and refuses to compute a claim that needs evidence.

Ontology - Structure: Parts & relations?

Why not simply average everything

A weighted average projects two dimensions onto one line. Everything on that line collapses to the same number, although the entities on it can be as different as it gets — and the groupings that matter usually cut straight across those lines.
An average also compensates without asking: enough strength anywhere buys off any weakness. Real strategy is rarely that generous — thresholds, knock-outs and outright contradictions are the normal case.
So dimensions are kept apart, paired deliberately, and consolidated through a named space rather than through a formula. What is lost in convenience is gained in traceability: every consolidation step stays visible and can be discussed.

How the layers fit together

One matrix takes two criteria and returns one: its linearized result. That result is a criterion like any other, so it can become the axis of a matrix above it.
Repeating that builds a tree — from criteria you can actually observe, up to the single statement the decision needs. A matrix may pair a raw criterion with the result of another matrix, so the tree need not be symmetric.
Each node stays readable on its own. That is the whole point: the chain from evidence to conclusion can be walked backwards, and any step in it can be challenged without discarding the rest.
Averaging and the tree are two ways of consolidating, not rivals. Sub-scores compress detail that nobody wants to discuss; a matrix is for the pairs that deserve a picture.

Known objection — “Portfolio matrices oversimplify and diagnose poorly.” That is an argument against a fixed matrix. Here a matrix is one node: where two criteria would blur into each other, they get a matrix of their own instead of an average.

The moves the method makes

Abstract the axes. Endogenic against exogenic rather than product against market — the same matrix then serves businesses, sites, services or ventures instead of one of them. Abstraction is what makes a matrix travel.
Bifurcate a dimension. One axis may split into two — novelty level against reference frame, the view at the firm against the view at the sector — turning a 2×2 into a nested 4×4. The inverse of consolidation, and available here through several lines per axis.
Refine one area. Where a single region deserves its own analysis, it gets its own matrix: the adverse-context, weak-position corner is a different problem from the rest of the portfolio.
Gate on a third dimension. Strategic fit used as a precondition before the two-dimensional analysis rather than as a third axis — first ask whether the entity belongs at all, then ask where it stands.
Carry the area into a decision. An area name implies a strategic role, a role implies a funding requirement and a resource allocation. The designation is not the end of the chain; it is where the chain turns into money.

Building a matrix — Matrix Genesis

1 · Define the strategic problem and what the matrix is meant to decide — that becomes its name.
2 · Explore the relevant notions and instruments (morphological analysis) — the raw material of the axes.
3 · Synthesize two dimensions from them. If one dimension needs several notions, give it a matrix of its own in the tree, or sub-scores in the averaging way.
4 · Scale each axis with a scoring protocol — %, −100…+100, a free unit, or auto anchors in the Scales panel.
5 · Construct the matrix by positioning the entities from their scores.
6 · Validate the positions, name the areas, and read the implications — the linearized score and the portfolio panel.

Where the data comes from, and where this begins

The spreadsheet stops at the number. This starts there.

Large organisations already hold the data: KPI systems, controlling reports, spreadsheets by the hundred, much of it proprietary. This tool neither collects nor cleans it. Gathering and preparing figures is controlling's craft, closer to accounting than to strategy, and it is done better where it is done today.
It begins one step later, where figures have become scores. Sub-scores, weights and the consolidating mean live here; the raw KPI systems stay where they are.
That step is the one routinely skipped in large organisations — turning many KPIs into a few criteria that mean something, and those into two dimensions people can argue about. Enormous effort goes into producing numbers, and almost none into deciding what pair of dimensions the decision actually turns on.
From there the analytical work is this tool's: consolidate, place, divide, name, condense — or distribute the criteria across several matrices, analyse each on its own, and let their results meet in the final one.

Where this tool stops

The method knows two more moves that this tool does not make for you: grouping entities into archetype clusters by their distance in the matrix, and laying several portfolios over one another as a multi-portfolio. Both are done by eye here — the areas and the portfolio figures give you the material for it.
Boundaries are lines, circles around a pole, or the 5-area curves. Divisions along ratio rays through the origin (x % of y) are not available.

Terminology - Glossary: Meaning?

Term	Meaning
Entity	What you assess: a business, product, project, market, supplier, candidate. Entities are the same in every matrix of a workspace; their positions are not.
Criterion	A dimension you assess entities on. Two criteria become the axes of one matrix.
Axis	A criterion placed on a matrix. It is entered directly, consolidated from sub-scores, or derived from another matrix's result.
Score	An entity's value on one axis.
Sub-score	A component of a criterion. Several sub-scores are consolidated into one axis by a weighted mean.
Mean	How sub-scores are consolidated: arithmetic, harmonic, geometric, quadratic or cubic. They differ in how much a weakness is allowed to drag the result down.
Size	A third variable, shown as the bubble's area. It may be signed — negative entities are drawn hollow.
Space	The whole spanned by the two axes. A partition divides it into areas.
Partition	How a matrix is divided: quadrants, distances from 0/0, two-poles distances, or the 5 area matrix. One choice per matrix.
Area	A named part of the space, made by the partition. The name is the point: it states what being there means.
Quadrant	An area of a two-by-two partition. Quadrants are a special case; areas is the general word.
Designation	Giving an area a name that states what being there means — the step that turns a coordinate into an instruction.
Pole	A reference corner for the distance partitions — 0/0 is low on both criteria, 100/100 is the ideal.
Overall position (linearized score)	Turning a position (x, y) into one score from 0 to 100 — the entity's overall standing in that matrix, and what allows the result to serve as the axis of the matrix above it.
Uncertainty (±)	A percentage attached to a criterion or sub-score, relative to each entered value. Drawn as whiskers around the entity, propagated through the consolidation.
Override	A value you set by hand where a computed one exists. It wins, stays marked, and can be released again — the difference between the two is the record of a judgment.
Matrix tree	Matrices whose results feed the axes of matrices above them, from the criteria you can observe up to the one statement you need.
Final matrix	The matrix whose result no other matrix uses. It is the answer, not a place to edit the tree.
Portfolio	All entities of one matrix seen together: size-weighted share per area, center of gravity, spread, and balance against target shares.
Archetype	A kind rather than a position: a group of entities that resemble each other across all criteria, not merely on one axis pair.
Clustering	Forming archetypes by weighted Euclidean distance over every criterion. An entity joins the cluster to whose farthest member it is still closest — complete linkage, which keeps clusters compact instead of letting them run into chains.
Robustness	How far a conclusion survives its own assumptions: the same picture under each of the five means, and whether an entity's stated ± reaches across a boundary.

Mechanics - Operation: Which control?

Nothing leaves this machine

No server, no account, no transmission. The tool runs in your browser and your case stays there — which is why it can be used on material a client would never put in a cloud.

It follows that a private window forgets everything when it closes, and that clearing your browser data clears the case with it. Save file keeps a copy; the exports take the result out.

Design the matrix tree

Drag a criterion onto an axis to assign it. Drag a matrix’s result chip onto another matrix’s axis to connect them — circular connections are refused. Rename matrices directly on the cards; axis details (scales, units, sub-scores) live in the workspace panels afterwards.

These are outputs of the method, not illustrations of it. Each was constructed with the same moves the tool offers, and each can be opened, inspected and taken apart.

Example matrices

Classic single matrices. A click loads one — your entities stay, and “undo” brings your own structure back.

Several matrices feeding one another are on the next page —

Consolidate criteria by weighted averaging

Define the sub-scores for each axis, set their weights and the averaging method, then enter or import the values below — one table per axis, the axis values are calculated live. Sub-scores are 0–100 %. The little pictures are the iso-lines of each mean: every pair of two sub-scores on one line gives the same result — click one to choose it.