Critical positivity ratio

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The critical positivity ratio (also known as the Losada ratio, the Losada zone, or the Losada line), is a controversial concept in positive psychology. Named after its proposer, Marcial Losada, it refers to a critical range for an individual's ratio of positive to negative emotions, outside of which the individual will tend to have poorer life and occupational outcomes.[1][2][3] The paper introducing the concept of the critical positivity ratio was highly cited, and the concept has since been applied to human relationships,[4] and has been described in popular books.[5] However, a 2013 paper provided a strong critique[6] of the concept, arguing that it was based on misapplication of complex mathematical modelling. This led to its abandonment by at least one former proponent.[7] The modeling element of the paper establishing the positivity ratio has been formally withdrawn as invalid;[8] Nick Brown and Alan Sokal have commented that issues remain with the rest of the paper.[9]


Building on research by Barbara Fredrickson indicating that individuals with a higher ratio of positive to negative emotions tend to have more successful life outcomes,[10] and on studies by Marcial Losada applying differential equations from fluid dynamics to human emotions,[1][2] Fredrickson and Losada[3] used nonlinear dynamics modelling (based on Lorenz systems) to argue that the ideal positivity/negativity ratio lies between 2.9013 and 11.6346. They argued that those with ratios within this range will "flourish", whereas those with values outside it will "languish". They claimed that their model predicted cut-off points for the maximum and minimum positivity ratios within which one should observe qualitative changes in an individual's level of flourishing.


Losada's article [1] was critiqued by Andrés Navas in a Note to the French website of the CNRS "Images des Mathématiques". [11] The whole theory of the critical positivity ratio was strongly critiqued by Nicholas Brown, Alan Sokal, and Harris Friedman, in a 2013 article published in American Psychologist.[6] Brown et al. argue that Losada's conclusions in previous papers using modelling from fluid dynamics, and those in his paper co-authored with Fredrickson,[12] are not only based on poorly reported experiments – they argue that it is difficult to draw any conclusions from some previous studies by Losada (e.g.[2]) because critical details are omitted, and "interpretations of results are made with little or no justification" (p. 5) – but are based on elementary errors in the use of differential equations.

Among the severe flaws described by Brown et al. in the positivity-ratio theory and its presentation were:

  • That the data used by Losada in several analyses do not meet the basic criteria for the use of differential equations (such as the use of continuous variables that evolve smoothly and deterministically over time).
  • That the differential equations used by Losada to calculate the critical positivity ratio use parameters taken directly from Lorenz's simplified, illustrative, and most importantly, arbitrary models for fluid dynamics. Losada gives no rationale for his choice of parameters. Using different arbitrary parameters gives different positivity ratios, and thus the precise values for the ratio given by Fredrickson and Losada[3] (2.9013 to 11.6346) are meaningless.
  • That the butterfly-like Figure 1 provided by Fredrickson and Losada[12] is not a model of the data taken from their human participants, but "the results of computer simulations of the Lorenz equations, nothing more" (p. 11).
  • That even if one takes the idea of the precise positivity/negativity ratio numbers seriously, there should exist not just a single ratio band in which "flourishing" should occur, but several "windows" of desirable and undesirable positivity/negativity ratios above a certain value. That is, it is likely that Fredrickson and Losada did not fully grasp the implications of applying nonlinear dynamics to their data.

Brown et al. state that one can "only marvel at the astonishing coincidence that human emotions should turn out to be governed by exactly the same set of equations that were derived in a celebrated article several decades ago as a deliberately simplified model of convection in fluids, and whose solutions happen to have visually appealing properties. An alternative explanation – and, frankly, the one that appears most plausible to us – is that the entire process of “derivation” of the Lorenz equations has been contrived to demonstrate an imagined fit between some rather limited empirical data and the scientifically impressive world of nonlinear dynamics."(p. 8). They "urge future researchers to exercise caution in the use of advanced mathematical tools, such as nonlinear dynamics" (p. 1).

Fredrickson[7] responded to the critique by agreeing that Losada's mathematical modelling is "questionable" and does not show that there are precise values of the ratio, but also arguing that the evidence for the benefits of a high positivity/negativity ratio is solid. Fredrickson noted that Losada declined to respond to the criticism.


  1. ^ a b c Losada, M. (1999). The complex dynamics of high performance teams. Mathematical and Computer Modelling, 30(9–10), 179–192.
  2. ^ a b c Losada, M. & Heaphy, E. (2004). The role of positivity and connectivity in the performance of business teams: A nonlinear dynamics model. American Behavioral Scientist, 47(6), 740–765.
  3. ^ a b c Fredrickson, B.L. & Losada, M. (2005). Positive affect and the complex dynamics of human flourishing. American Psychologist, 60(7), 678–686.
  4. ^ Waugh, C.E. & Fredrickson, B.L. (2006). Nice to know you: Positive emotions, self-other overlap, and complex understanding in the formation of a new relationship. The Journal of Positive Psychology, 1(2), 93–106.
  5. ^ Fredrickson, B.L. (2009). Positivity: Top-notch research reveals the 3-to-1 ratio that will change your life. New York, NY: Crown.
  6. ^ a b Brown, N. J. L., Sokal, A. D., & Friedman, H. L. (2013). The Complex Dynamics of Wishful Thinking: The Critical Positivity Ratio. American Psychologist. Electronic publication ahead of print.
  7. ^ a b Fredrickson, B. L. (2013) Updated thinking on positivity ratios. American Psychologist. Electronic publication ahead of print.
  8. ^
  9. ^
  10. ^ Fredrickson, B. L. (2004). The broaden-and-build theory of positive emotions. Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, 359, 1367-1377.
  11. ^ Navas, A. (2011). Un cas d'inconscience (?). Images des Mathématiques. [1])
  12. ^ a b Fredrickson, B.L. & Losada, M. (2005). Positive affect and the complex dynamics of human flourishing. American Psychologist, 60(7), 678–686.

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