Ups and downs: A dynamical systems model of human affective fluctuations

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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

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A definition of subjective well being

• Subjective well-being can be simply defined as
  the individuals 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.

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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).

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• 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).

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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.

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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, d2x/dt2 (i.e., acceleration).

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• 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.

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A general linear expression including all such
effects isd2x/dt2 pdx/dt qx f(t)

• d2x/dt2 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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Winning the Lottery
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Intermittent Reinforcement
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Random Events
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Real Life
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This is a simple, linear, ordinary differential
equation

• If the individuals 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.

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• 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.

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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.

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Hypothesis 1

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

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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.

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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.

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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.

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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) 181-185.
• 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) 341-346.
• Keely, L. (2000). Why Isn't Growth Making Us
  Happier? Working paper posted at
  http//www.ssc.wisc.edu/7Elkeely/

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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)
340-346.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.