Geometric mean for decision scores: why one weak dimension drags the whole decision

What is a geometric mean in a decision score?

The geometric mean of n positive numbers is the nth root of their product (en.wikipedia.org, Geometric mean). Take 2 and 8. Their product is 16, and the square root of 16 is 4. A decision score uses the same operation on ratings between 0 and 1, one rating for each dimension of the situation. The result stays between 0 and 1, so a committee reads it on the same scale as every input.

The operation is simple, and its consequence is useful. Because ratings are multiplied, each one scales the final number directly. A rating of 0.5 halves the product at that point, and a rating of 0.9 trims it by a tenth. Every dimension therefore leaves a visible mark on the score, which gives a team a reason to look at all of them.

How do you compute a geometric mean for a decision, step by step?

Four steps produce the result. List the ratings on one scale from 0 to 1. Multiply them together. Count the ratings, which gives n. Take the nth root of the product. With 3 ratings, you take a cube root, and with 9 ratings you take a ninth root. A spreadsheet handles this in one formula, and a calculator with a power key does it by hand.

A short check keeps the result honest. The geometric mean always lands between the lowest and the highest rating. If the answer falls outside that range, a multiplication slipped. Writing the ratings next to their sources, as in a decision matrix, lets a reviewer repeat the computation and obtain the same figure. The figure below shows the four steps in order.

Why does one weak dimension drag a geometric mean down so far?

Consider four illustrative ratings: 0.9, 0.8, 0.7 and 0.1. Their product is 0.0504, and the fourth root of that product is 0.474. The ordinary average of the same four ratings is 0.625. The single rating of 0.1 pulls the geometric mean 0.151 below the average, because the product keeps the full effect of the low value.

This is the behaviour that makes the method useful for decisions. A project with strong finance, strong talent and strong demand, but a collapsed permit position, should not look comfortable. The geometric mean lets the permit rating drag the score down, and the committee sees the weak spot in the number itself. The values are illustrations, not EQOS Asia results.

How does a geometric mean differ from an average in a decision score?

An arithmetic average lets a strong rating cover for a weak one. A geometric mean gives the weak rating a larger say. The two agree only when all ratings are equal, as with nine ratings of 0.6 that give 0.600 on both measures, and the gap widens as the ratings spread apart. For a decision, this means the geometric mean rewards balance across dimensions, while the average rewards the total amount of strength.

The comparison has its own page, with worked profiles and a rule for choosing between the two. Read geometric vs arithmetic mean in a decision score when you need to decide which aggregation fits a given situation, and what each choice says about how much one dimension may be traded against another.

How does EQOS Asia use a geometric product across 9 dimensions?

EQOS Asia states that its score aggregates the 9 dimensions through a weighted geometric product, not an average, so the lowest score drags the whole system down (EQOS Asia case study pages, as of October 2026). The 9 dimensions are coherence, integrity, resonance, care, trust, transparency, clarity, stability and energy (EQOS Asia method page, as of October 2026).

The published retrospectives show the effect. In the WeWork back-test, the lowest rating, integrity at 0.08, weighs as much as the highest, energy at 0.72, and φ(S) lands at 0.189 (EQOS Asia WeWork case study, as of October 2026). The expanded form and the weighting coefficients remain proprietary, while the result is public and the core is deterministic.

Which decisions suit a geometric mean score?

A geometric mean suits decisions where every dimension must hold for the whole to work. A market entry needs regulatory ease, funding and a local partner at the same time. A merger needs cultural fit and financial fit together. In such cases, a very low rating on one dimension signals that the plan as a whole needs attention before the other ratings can matter.

It suits decisions that repeat, too. A team that rates the same dimensions each quarter sees the geometric mean move when a single rating improves or slips, and the reason for the movement is easy to trace. The United Nations Human Development Index also switched to a geometric mean for combining its dimensions (en.wikipedia.org, Geometric mean).

How can you try a geometric mean score on your own decision?

Start with the public Λ simulator. Choose an analysis mode, drag the 9 sliders from 0 to 100, and watch the live result move. Lower one slider and observe how far the result falls. The ratings are relative, so the demo works for any Asian market or currency (EQOS Asia simulator page, as of October 2026). The calibration coefficients remain proprietary and computed server-side.

For a real choice, the method page describes the full workflow, from a signed NDA to an interactive report with a 30/60/90 day lever plan (EQOS Asia method page, as of October 2026). A 30-minute pre-diagnostic by video, scheduled in Singapore time (SGT), applies the equation to your case at no commitment (EQOS Asia contact page, as of October 2026).

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About the author

Stéphane Jambu

President, EQOS Forecast Asia

Stéphane Jambu leads EQOS Forecast Asia and works as a consultant in e-commerce, search visibility, and AI. LinkedIn profile