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The critical positivity ratio of 2.9013
Fredrickson and Losada (2005) reported a tipping-point ratio of 2.9013 positive to negative emotions. Brown, Sokal and Friedman (2013) said the mathematics behind it was unfounded. Fredrickson and Losada then withdrew the modeling, while Fredrickson argued other evidence still linked higher ratios to flourishing.
- Where it sits
- Academic psychologyResearch published for other researchers and students.
- Evidence level
- ContestedThe evidence conflicts or is disputed, for example after failed replications.
- Sources inspected
- 5 of 52 with the relevant text, company document or archive item checked, 3 as an abstract or reference article, 0 not verified.
What happened
In 2005 Barbara Fredrickson and Marcial Losada published a paper in American Psychologist predicting that a ratio of positive to negative emotions of at least 2.9 would characterise flourishing mental health. In 2013 Nicholas Brown, Alan Sokal and Harris Friedman published a critique in the same journal. Fredrickson replied in the same issue, and a correction notice to the 2005 paper appeared on page 822.
The psychological idea
The empirical part used two samples of university students, 87 and 101 people, who rated 20 emotions each evening for 28 days. Flourishing was classified with a separate questionnaire. The 2.9013 figure was not measured. The paper derives it from the Lorenz control parameter at which chaos begins, equated with a parameter from Losada's earlier model of 60 management teams.
In practice
Mean ratios were 3.2 for flourishing students and 2.3 for the others in the first sample, and 3.4 and 2.1 in the second. The paper reports p = .01 for the first sample and p = .05, one-tailed, for the second. It classed 36 and 9 participants as flourishing. The sources opened document no business or therapy use of the ratio.
Why it mattered
The 2013 exchange documents a mathematical model borrowed from fluid dynamics being challenged in the journal that published it, and the original authors withdrawing the modeling element. The critics and Fredrickson disagreed about what remained.
Limits and qualifications
Brown, Sokal and Friedman's abstract says the fluid-dynamics equations lack theoretical or empirical justification for modeling emotion, that their application contains conceptual and mathematical errors, and that the 2.9013 value is unfounded. Fredrickson's abstract says evidence still supports seeking higher ratios, within limits. In a 2014 response the critics report that the correction formally withdrew the modeling element and model-based predictions, and they find no evidence for tipping points. The correction text itself was not readable.
Evidence behind the claims
Fredrickson and Losada (2005) predicted that a positive-to-negative emotion ratio of at least 2.9 would characterise flourishing mental health, using two samples of university students (87 and 101 people) who rated 20 emotions each evening for 28 days.
Mean ratios were 3.2 versus 2.3 in the first sample (p = .01, one-tailed) and 3.4 versus 2.1 in the second (p = .05, one-tailed), with 36 and 9 participants classed as flourishing.
The 2.9013 value was derived mathematically from the Lorenz control parameter at which chaos begins (24.7368), which Losada's earlier model, built on observations of 60 management teams, equated with a connectivity parameter. The authors describe it as a mathematically derived ideal, not a measured ratio.
Brown, Sokal and Friedman (2013) argue the fluid-dynamics equations lack theoretical or empirical justification for modeling emotion, that their application contains conceptual and mathematical errors, and that the 2.9013 ratio is unfounded.
Fredrickson (2013) replied that empirical evidence still supports computing and seeking higher positivity ratios, especially for flourishing and mental health, within limits.
A correction notice to the 2005 paper appeared in American Psychologist volume 68, issue 9, on page 822 in December 2013, and the PMC copy of the paper says it has been corrected.
Brown, Sokal and Friedman (2014) state that Fredrickson and Losada (2013) withdrew their nonlinear-dynamics model, that the correction formally withdrew the modeling element and model-based predictions, and that they find no evidence whatsoever for tipping points and only weak evidence for nonlinearity.
People involved
- Barbara L. Fredrickson. Lead author of the 2005 paper and author of the 2013 reply
- Marcial Losada. Co-author of the 2005 paper, source of the mathematical model
- Nicholas J. L. Brown. Co-author of the 2013 critique
- Alan D. Sokal. Co-author of the 2013 critique
- Harris L. Friedman. Co-author of the 2013 critique
In the Psy101 course
- OpenStax Psychology 2e, section 14.5: The Pursuit of HappinessChapter 14, Stress, Lifestyle, and Health. Context. Nearest related section; it does not discuss this topic by name.Nearest related section: it covers positive affect and well-being, but it does not mention the positivity ratio or its critique.
This is course relevance only. It is not evidence for the historical or corporate claims on this page.See the full course map.
Sources and inspection
5 of 5 sources were opened and read at the level shown. A source marked as not verified supports no claim on this page by itself.
- [1]Positive Affect and the Complex Dynamics of Human FlourishingFredrickson, B; Losada, M. American Psychologist, 60(7), 678-686 (PubMed Central copy), 2005. Journal article. Primary source.Relevant text checkedRead the PMC page of the paper as returned by the fetch tool: abstract, Method (measures, samples), Results and the derivation of 2.9013, plus the correction note. Not every section was read.
- [2]The complex dynamics of wishful thinking: The critical positivity ratioBrown, N; Sokal, A; Friedman, H. arXiv:1307.7006, author version of American Psychologist, 68(9), 801-813, 2013. Preprint. Critique or replication.Abstract or publisher record onlyRead the abstract on the arXiv page for the author version. The full critique and the journal version were not read.
- [3]Updated thinking on positivity ratiosFredrickson, B. American Psychologist, 68(9), 814-822 (record via Europe PMC), 2013. Journal article. Critique or replication.Abstract or publisher record onlyRead the abstract in a Europe PMC record. The article is not open access.
- [4]Positive affect and the complex dynamics of human flourishing: Correction to Fredrickson and Losada (2005)Fredrickson, B; Losada, M. American Psychologist, 68(9), 822 (record via Crossref), 2013. Journal article. Critique or replication.Reference article readRead bibliographic metadata only. The record has no text and does not say what was corrected.
- [5]The persistence of wishful thinking: Response to Updated thinking on positivity ratiosBrown, N; Sokal, A; Friedman, H. arXiv:1409.4837, author version of American Psychologist, 69, 629-632, 2014. Preprint. Critique or replication.Relevant text checkedRead the abstract and the first two pages of text of the arXiv PDF, which says it is not the copy of record. The pages describe the 2013 correction as the critics read it; the correction notice itself was not read.
Access note: The correction notice's own text was not readable. What it withdrew is reported here only as the critics describe it in their 2014 response.
Independent source review: Claude review agent, independent of the research agent, 2026-10-21. Verdict: pass-with-edits.