Running on the Hedonic Treadmill: A Dynamical Model of Happiness Based on an Approach–Avoidance Framework

Abstract

Describing the dynamical nature of happiness is crucial for understanding why individuals are constantly running on a hedonic treadmill around set levels of well-being. Based on the self-centeredness branch of the ’self-centeredness/selflessness happiness model’, we present a dynamical model that focuses on unfolding the hedonic dimension of happiness dynamics through the use of the approach–avoidance framework. This numerical model enables us to understand and analyze emerging hedonic cycles caused by hedonic motivation and hedonic adaptation. In particular, hedonic motivation leads people to experience hedonic activities, which result in successes or failures and experiences of pleasure and afflictive affects; whereas hedonic adaptation causes individuals to return to a baseline level of pleasure and afflictive affects, more quickly for the former than the latter. The proposed dynamical model is based on the approach–avoidance framework that considers human behavior in two separate regulatory processes that contribute to homeostasis of individuals’ happiness. We analyze these two processes independently and conjointly in order to highlight their effect on happiness levels. The analysis shows how individual characteristics and their combination may result in hedonic cycles, afflictive affects, (dis-)pleasure, and particular happiness dynamics. We also discuss how such a numerical model enables us to perform a multifactorial analysis which is hardly feasible outside the context of a simulation and how it may help us to narrow and design relevant experimental surveys from these preliminary numerical results.

Appendices

Appendix A Proof of Eqs. (4) and (5)

We start by rewriting Eqs. (2) and (3),

$$\begin{aligned} P(t)=\sum _{\tau =0}^{t} P_s(\tau ) \,e^{-\gamma _P (t-\tau )} \,,\\ A(t)=\sum _{\tau =0}^{t} A_s(\tau ) \,e^{-\gamma _A (t-\tau )}\,, \end{aligned}$$

and noticing that isolating the last term of these sums leads to the following equations

$$\begin{aligned} P(t)=\sum _{\tau =0}^{t-1} P_s(\tau ) \,e^{-\gamma _P (t-\tau )}+P_s(t)\,, \end{aligned}$$

(A1)

$$\begin{aligned} A(t)=\sum _{\tau =0}^{t-1} A_s(\tau ) \,e^{-\gamma _A (t-\tau )}+ A_s(t)\,. \end{aligned}$$

(A2)

Taking out $e^{-\gamma _P}$ and $e^{-\gamma _A}$ as common factors of the summation terms in Eqs. (A1) and (A2), respectively, we obtain

$$\begin{aligned} P(t)&=e^{-\gamma _P} \sum _{\tau =0}^{t-1} P_s(\tau ) \,e^{-\gamma _P (t-1-\tau )}+P_s(t)\,, \end{aligned}$$

(A3)

$$\begin{aligned} A(t)&=e^{-\gamma _A} \sum _{\tau =0}^{t-1} A_s(\tau ) \,e^{-\gamma _A (t-1-\tau )}+ A_s(t)\,. \end{aligned}$$

(A4)

Note that the factorization required to add $e^{\gamma _P}$ and $e^{\gamma _A}$ in the summation terms, which correspond, respectively, to $P(t-1)$ and $A(t-1)$. Thus, we can rewrite Eqs. (A3) and (A4) as

$$\begin{aligned} P(t)&=e^{-\gamma _P}P(t-1)+P_s(t)\,, \\ A(t)&=e^{-\gamma _A} A(t-1)+ A_s(t)\,, \end{aligned}$$

which are precisely Eqs. (4) and (5).

Appendix B: List of Variables and Parameters of the Model

The list and description of variables and parameters of the model is reported in Table 2. Note that the third column contains both variables and parameters, and the fourth column contains their value ranges and/or the values used for the numerical simulations.

Table 2 State variables and parameters of the mathematical model