Ups and downs: A dynamical systems model of human affective fluctuations Keith Warren, Ph.D. The Ohio State University Julien C. Sprott, Ph.D. University of Wisconsin-Madison

A definition of subjective well being Subjective well-being can be simply defined as the individual’s current evaluation of her happiness. Such an evaluation is often expressed in affective terms; when asked about subjective well-being, participants will often say, “I feel good” (Schwartz & Strack, 1999). Subjective well-being is thus, at least in part, a proxy for a global affective evaluation.

Some odd things about subjective well being Increase in income does not lead to increase in subjective well being (Keely, 2000) Most people define themselves as being happy, regardless of their material wealth (Diener & Diener, 1996). Extremely minor incidents, influence estimates of SWB (Schwartz & Strack, 1999).

Most people assume that the external circumstances of others are powerful determinants of subjective well being, in spite of the fact that such circumstances would have little effect on their own SWB (Schkade & Kahneman, 1999).

The beginnings of an explanation Several authors have suggested that human affect is largely determined by the rate of progress toward a goal (Carver & Scheier, 1998; Hsee & Abelson, 1991). Carver & Scheier, 1998, have suggested that an increase or decrease in the rate of progress will be experienced as a surprise.

This suggests an equation In mathematics, the rate of change of a function over time is given by the first derivative, dx/dt (i.e., velocity). The change in the rate of change is given by the second derivative, d 2 x/dt 2 (i.e., acceleration).

We focus on the rate at which we move toward our goals. We focus on the position of others vis-à-vis their (presumed) goals.

A general linear expression including all such effects is: d 2 x/dt 2 + pdx/dt + qx = f(t) d 2 x/dt 2 gives the acceleration toward goal. dx/dt gives the velocity of movement toward the goal--leads to SWB aka happiness (H). x gives our current state vis-à-vis the goal. f(t) is an external disturbance term that will push us toward or away from the goal.

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This is a simple, linear, ordinary differential equation If the individual’s focus is on dx/dt, this explains why successive increases in income do not lead to increasing subjective well-being; each increase, being similar, would lead to the same level of SWB. Similarly, focus on dx/dt would tend to obscure differences in SWB that arise from x.

Since even weak influences can lead to a change in dx/dt, a focus on this will lead to a comparatively large effect of those influences on SWB. Finally, when others focus on x, they will overestimate the importance of external factors to your subjective well-being.

A disadvantage and two advantages Obviously, this model is too simple to solely explain subjective well being. It does, however, explain some surprising facts about SWB. And it suggests some further hypotheses, developed from the fact that the derivative of a function is generally “rougher” than the function itself.

Hypothesis 1 Clinicians will tend to underestimate the volatility of clients’ perceived subjective well being, aka happiness.

Hypothesis 2 Clinicians will tend to underestimate the life satisfaction or dissatisfaction of their clients. This, incidentally, has significant implications for motivating people to change. Like the first hypothesis, this falls straight out of the idea that outsiders see our integral, while we see our derivative.

Hypothesis 3 Clients are likely to overestimate an improvement in their well being in the short run, while underestimating it in the long run. This occurs because they will see the increasing derivative first, then see the decreasing side of the derivative. One might actually argue that they are likely to see themselves as losing ground after any initial increase.

A Plausible Empirical Test Newhill, Mulvey & Pilkonis (2001) have proposed a measure of emotional dysregulation. Includes measures of sensitivity/ vulnerability to emotional stimuli and return to baseline. This theory would imply that clinicians will underestimate sensitivity and overestimate time to return to baseline.

Bibliography Carver, C. S. & Scheier, M. F. (1998). On the self-regulation of behavior. New York: Cambridge University Press. Diener, E. & Diener, C. (1996). Most people are happy. Psychological Science, 7(3) Hsee, C. K. & Abelson, R. P. (1991). Velocity relation: Satisfaction as a function of the first derivative of outcome over time. Journal of Personality and Social Psychology, 60(3) Keely, L. (2000). Why Isn't Growth Making Us Happier? Working paper posted at:

Schkade, D. A. & Kahneman, D. (1999). Does living in California make people happy? A focusing illusion in judgments of life satisfaction. Psychological Science, 9(5) Schwartz, N. & Strack, F. (1999). Reports of subjective well-being: Judgmental processes and their methodological implications. In Kahneman, D., Diener, E. & Schwarz, N. (eds.) Well-being: The foundations of hedonic psychology. New York: Russell Sage.