Geometric vs arithmetic mean in a decision score
The essentials in 30 seconds
- The geometric mean and the arithmetic mean agree only when all ratings are equal.
- A profile of five ratings at 0.9 and four at 0.3 beats nine ratings at 0.6 on the average (0.633 against 0.600) and loses on the geometric mean (0.552 against 0.600).
- One rating of 0 brings a geometric score to 0.
- EQOS Asia aggregates its 9 dimensions with a weighted geometric product (EQOS Asia case study pages, as of October 2026).
Two ways of averaging the same ratings can rank two options in opposite order. This guide sets the geometric mean beside the arithmetic mean, using worked profiles, and explains which one a decision score should use. It builds on the geometric mean for decision scores and ends with a way to test both on your own case, as of October 2026.
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What does an arithmetic mean allow in a decision score?
The arithmetic mean adds the ratings and divides by their count. It treats the ratings as interchangeable units of strength, so 0.2 on one dimension can be offset by 0.2 more on another. This is called compensation. A team that wants a total amount of merit, such as a points tally across independent criteria, finds this behaviour natural and easy to explain.
Compensation has a price in a decision engine. A situation with 5 strong dimensions and 4 collapsed ones can show a pleasant average, and the average hides which dimensions fail. The reader sees a comfortable number while the structure underneath is fragile. A score meant to detect fragility needs an aggregation that does not allow strengths to buy off weaknesses.
Which profile wins under a geometric mean and which under an average?
Compare two illustrative profiles. Profile A has five ratings at 0.9 and four at 0.3. Profile B has nine ratings at 0.6. The average of A is 0.633, ahead of B at 0.600. The geometric mean reverses the order: A falls to 0.552, while B stays at 0.600. The ranking of the two options depends on the aggregation chosen.
The reversal tells you what each method values. The average prefers the profile with the higher total, and the geometric mean prefers the profile without a hole. For a decision that fails when any one dimension fails, such as a cross-border launch, B is the safer reading. The table sets the figures side by side. All values are illustrations, not EQOS Asia results.
What does the AM-GM inequality say about a decision score?
For positive numbers, the geometric mean is at most the arithmetic mean, and equality holds only when all the numbers are equal (en.wikipedia.org, Geometric mean). Applied to a decision, this gives a rule you can use immediately: the geometric score of a profile never exceeds its average, and the distance between them measures how uneven the profile is.
The distance becomes a diagnostic. Profile B has a distance of 0, because its ratings are equal. Profile A has a distance of 0.081, from 0.633 down to 0.552. A team can compute both figures and read the gap as an unevenness alert before it reads any single rating. A large gap points to the dimensions that deserve evidence first.
How does a rating of zero affect a geometric decision score?
A product that contains a zero equals zero. In a geometric score, one dimension rated 0 brings the whole result to 0, whatever the other ratings say. Take eight ratings at 0.9 and one at 0. The average is 0.800 and the geometric mean is 0.000. The average describes a strong situation, and the geometric mean describes a situation that cannot proceed as it stands.
This is a feature when the zero is real, for example a missing legal permission or a partner who has withdrawn. It calls for care in rating, because a 0 should mean collapse and not simply a lack of data. Many teams set a small floor above 0 for unknown values, then mark them for review, so that missing evidence triggers a task and not a veto.
When does an arithmetic mean still suit a decision?
An arithmetic mean suits criteria that substitute for each other. A weighted decision matrix that compares three office locations on rent, commute and amenities is a good example: a cheaper rent can reasonably offset a longer commute. The criteria are independent, the stakes are modest, and the sum is easy to audit in a meeting.
A geometric mean suits dimensions that depend on each other, such as trust, transparency and integrity inside one organisation. A gap in one weakens the others, so offsetting is misleading. Before choosing, ask a single question of each pair of dimensions: if one collapses, can the other make up for it? If the answer is no, multiply.
Why do weights matter in a geometric mean scoring model?
Real decisions rarely treat all dimensions as equally important. A weighted geometric mean raises each rating to a power that reflects its importance, so the heaviest dimension moves the score most while every rating keeps its voice. EQOS Asia states that each dimension is raised to its weighting, which makes the score a geometric product and not a simple average (EQOS Asia case study pages, as of October 2026).
The next page covers the method in detail. Read weighted geometric mean for decision weights to see how weights are set, how they change the ranking of options, and how to document them. The EQOS Asia weighting coefficients remain proprietary, and the documentation is available under NDA on request (EQOS Asia method page, as of October 2026).
How can you test both aggregations on a real decision?
Rate your dimensions once, then compute both means in a spreadsheet and compare the rankings. When the two agree, the choice of method does not matter for that decision. When they disagree, the gap points to an uneven profile worth examining before any commitment. The test takes about 10 minutes and gives a team a shared reference for the discussion.
The public Λ simulator applies the EQOS Asia engine to 9 dimensions rated from 0 to 100 (EQOS Asia simulator page, as of October 2026). For a real case, a 30-minute pre-diagnostic by video, scheduled in Singapore time (SGT), applies the equation to your situation at no commitment (EQOS Asia contact page, as of October 2026). The pricing page lists the tiers that follow.
Frequently asked questions
Which is better for a decision score, the geometric or arithmetic mean?
It depends on whether strengths may offset weaknesses. The arithmetic mean allows offsetting and suits independent criteria. The geometric mean limits offsetting and suits interdependent dimensions, where one collapse weakens the others. EQOS Asia chose a weighted geometric product for its 9 dimensions (EQOS Asia case study pages, as of October 2026).
Is the geometric mean always lower than the arithmetic mean?
For positive numbers, the geometric mean is at most the arithmetic mean, and the two match only when all numbers are equal (en.wikipedia.org, Geometric mean). A larger gap signals a more uneven profile, which makes the gap a useful diagnostic for a decision score.
Can ratings of zero be used in a geometric score?
A rating of 0 brings the whole product to 0, so reserve it for a real collapse such as a missing permission. For unknown values, many teams use a small floor above 0 and flag the item for review, so that missing evidence creates a task and not a veto.
Does the choice of mean change the ranking of options?
It can. In the worked example, profile A leads on the average at 0.633 and trails on the geometric mean at 0.552, while profile B scores 0.600 on both. Computing both means on your own ratings shows whether the ranking is stable.
Test your knowledge
1. When do the geometric and arithmetic means give the same value?
- When all ratings are equal
- When ratings are above 0.5
- When there are 9 ratings
Show the answer
When all ratings are equal.
2. Which profile leads on the average in the worked example?
- Profile B
- Profile A
- Neither
Show the answer
Profile A.
3. What is the geometric mean of eight ratings at 0.9 and one at 0?
- 0.800
- 0.900
- 0.000
Show the answer
0.000.
4. What does the gap between the two means measure?
- How uneven the profile is
- The number of dimensions
- The size of the weights
Show the answer
How uneven the profile is.
5. Which criteria suit an arithmetic mean?
- Criteria that depend on each other
- Criteria that substitute for each other
- Criteria rated zero
Show the answer
Criteria that substitute for each other.
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
Sources: EQOS Asia method page (eqos-asia.com/method.html), simulator page (eqos-asia.com/simulator.html), contact page (eqos-asia.com/contact.html), WeWork case study (eqos-asia.com/case-studies/wework.html), en.wikipedia.org/wiki/Geometric_mean, consulted on 22 October 2026. Page updated on 22 October 2026.