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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Critical positivity ratio | 1/3 | https://en.wikipedia.org/wiki/Critical_positivity_ratio | reference | science, encyclopedia | 2026-05-05T09:18:23.760203+00:00 | kb-cron |
The critical positivity ratio (also known as the "Losada ratio" or the "Losada line") is a largely discredited concept in positive psychology positing an exact ratio of positive to negative emotions which distinguishes "flourishing" people from "languishing" people. The ratio was proposed by psychologists Barbara Fredrickson and Marcial Losada, who believed that they had identified an experimental measure of affect whose model-derived positive-to-negative ratio of 2.9013 defined a critical separation between flourishing and languishing individuals, as reported in their 2005 paper in American Psychologist. This concept of a critical positivity ratio was widely embraced by academic psychologists and the lay public; Fredrickson and Losada's paper had been cited more than 320 times by January 2014, and Fredrickson wrote a popular book expounding the concept of "the 3-to-1 ratio that will change your life". In it she wrote, "just as zero degrees Celsius is a special number in thermodynamics, the 3-to-1 positivity ratio may well be a magic number in human psychology." The first consequential re-evaluation of the mathematical modeling behind the critical positivity ratio was published in 2008 by a group of Finnish researchers from the Systems Analysis Laboratory at Aalto University (Jukka Luoma, Raimo Hämäläinen, and Esa Saarinen). The authors noted that "only very limited explanations are given about the modeling process and the meaning and interpretation of its parameters... [so that] the reasoning behind the model equations remains unclear to the reader"; moreover, they noted that "the model also produces strange and previously unreported behavior under certain conditions... [so that] the predictive validity of the model also becomes problematic." Losada's 1999 modeling article was also critiqued by Andrés Navas in a French language publication, a note in the CNRS publication, Images des Mathématiques. Neither of these articles received broad attention at the times of their publication. Later, but of critical importance, the Fredrickson and Losada work on modeling the positivity ratio aroused the skepticism of Nick Brown, a graduate student in applied positive psychology, who questioned whether such work could reliably make such broad claims, and perceived that the paper's mathematical claims underlying the critical positivity ratio were suspect. Brown contacted and ultimately collaborated with physics and maths professor Alan Sokal and psychology professor Harris Friedman on a re-analysis of the paper's data (hereafter the Brown-Sokal-Friedman rebuttal). They argued that Losada's earlier work on positive psychology and Fredrickson and Losada's 2005 critical positivity ratio paper contained "numerous fundamental conceptual and mathematical errors", errors of a magnitude that completely invalidated their claims. Fredrickson wrote a response in which she conceded that the mathematical aspects of the critical positivity ratio were "questionable" and that she had "neither the expertise nor the insight" to defend them, but she maintained that the empirical evidence for the existence of a critical positivity ratio was solid. Brown, Sokal, and Friedman, the rebuttal authors, published their response to Fredrickson's "Update" the next year, maintaining that there was no evidence for a critical positivity ratio. Losada declined to respond to the criticism (indicating to the Chronicle of Higher Education that he was too busy running his consulting business). Hämäläinen and colleagues responded later, passing over the Brown-Sokal-Friedman rebuttal claim of failed criteria for use of differential equations in modeling, instead arguing that there were no fundamental errors in the mathematics itself, only problems related to the model's justification and interpretation. A formal retraction for the mathematical modeling elements of the Losada and Fredrickson (2005) paper was issued by the journal, American Psychologist, concluding that both the specific critical positivity ratio of 2.9013 and its upper limit were invalid. The fact that the problems with the paper went unnoticed for years despite the widespread adulatory publicity surrounding the critical positivity ratio concept contributed to a perception of social psychology as a field lacking scientific soundness and rigorous critical thinking. Sokal later stated, "The main claim made by Fredrickson and Losada is so implausible on its face that some red flags ought to have been raised", as would only happen broadly in graduate student Brown's initiating the collaboration that resulted in the Brown-Sokal-Friedman rebuttal.
== Background == Building on research by Barbara Fredrickson suggesting that individuals with a higher ratio of positive to negative emotions tend to have more successful life outcomes, and on studies by Marcial Losada applying differential equations from fluid dynamics to human emotions, Fredrickson and Losada proposed as informative a ratio of positive to negative affect derived from nonlinear dynamics modelling (based on Lorenz systems), which appeared in 2005 in a paper in American Psychologist. The derived combination of expressions and default parameters led them to conclude that a critical ratio of positive to negative affect of exactly 2.9013 separated flourishing from languishing individuals, and to argue that the ideal positivity/negativity ratio lies between 2.9013 and an upper limit ratio of 11.6346. Hence, they claimed that their model predicted cut-off points for the minimum and maximum positivity ratios within which one should observe qualitative changes in an individual's level of flourishing, specifically, that those within this range of ratios would "flourish", and those outside would "languish". As of January 2014, the 2005 Fredrickson and Losada's paper had been cited more than 320 times in the psychology literature.
== Criticism ==