Group Decision Making with Affective Features

Abstract

Affective elements have been shown to have impact on how individuals and groups make decisions. In this paper, we consider how emotions and mood impact the degree of competitiveness and cooperativeness in groups. We provide a parametric model to regulate its evolution and introduce a negotiation scheme to facilitate group formation, depending on such affective elements. We simulate a virtual platform for the proposed model and conduct experiments showing that our proposal is effective: agents which cooperate affectively with others through negotiation tend to attain higher utilities and outperform non-cooperative and/or emotionless agents.

Appendices

Appendix

This appendix briefly summarises concepts used from earlier work.

Computational Model of Emotions

We briefly sketch the emotion computational model in Liu and Ríos Insua (2020), through the example of immediate emotions. These include joy and sadness. The agent experiences them after making its decision $a_t^*$, evaluating the utility $u_t^*$ finally attained and computing a surprise factor $s_t^*$ based on a distance between the distribution of actual decision outcome and the forecast one. We use Kullback and Leibler (1951) divergence to define distances between prior and posterior distributions as a measure of surprise. The agent considers its immediate emotion to be joy, if the attained utility exceeds a threshold $th_{imm_t}$; on the other hand, if it is too low, it will feel sad (utilities are scaled in [0,1]). Specifically, we use

• If $u_t^* > th_{imm_t}$,

  $$\begin{aligned} joy_t=\alpha _{imm}\ \left( \left( \frac{u_t^*-th_{imm_t}}{1-th_{imm_t}}\right) \times s_t^*\right) +(1-\alpha _{imm})\ immEm_{t-1}, \quad sad_t=0, \end{aligned}$$

  Else if $u_t^* \le 1- th_{imm_t}$,

  $$\begin{aligned} sad_t=-\left( \alpha _{imm}\ \left( \left( \frac{th_{imm_t}-u_t^*}{th_{imm_t}}\right) \times s_t^*\right) +(1-\alpha _{imm})\ immEm_{t-1}\right) , \quad joy_t=0. \end{aligned}$$

$\alpha _{imm}$ is a smoothing factor controlling emotional evolution over time, and $immEm_{t-1}$ is the value of immediate emotion (joy or sad) at time $t-1$.

Expected emotions, including hope and fear, are computed in a similar manner. To assess expected emotions, we correspondingly substitute the two terms we use in computing immediate emotions (utility attained $u_t^*$ and surprise $s_t^*$) to the expected utility obtained $\psi _t^{*}$ and its variance $var_t$, which assesses the uncertainty about that event happening.

Weights Update

Based on the basic preference model in Sect. 4.1, utility weights are updated after each iteration taking into account earlier weights and the agent’s mood, impacting consequently over the agent’s decision making. The weight update that we introduce is

$$\begin{aligned} w_t^i= \max \{w_t^{i+1}, \min \{w_t^{i-1},w_{t-1}^i - \beta \times a \times mood_t\}\}, \end{aligned}$$

where a is a component measuring the impact of mood over the weights and $\beta$ describes the rate of weight variation, normalizing mood between $-1$ and 1. We then re-normalize the weights through

$$\begin{aligned} w_t^i* =\frac{w_t^i}{\sum _i w_t^i}. \end{aligned}$$

Further details are in Liu and Ríos Insua (2020).