Cost heterogeneity and peak prediction in collective actions

Highlights

• This paper focuses on predicting peaks of participants in collective actions.

• Besides of utility heterogeneity, cost heterogeneity is added into the model.

• Heterogeneity facilitates the outbreak, but homogeneity raises the success rate.

• Distribution (mean and standard deviation) of peaks is estimated and predicted.

Abstract

The peak of participants indicates the success probability of collective actions. The mathematical model is built to explore the mechanism and prediction values of peaks. Besides of utility heterogeneity, cost heterogeneity is added into to simulate the situation of multiple heterogeneities in reality. Each simulation is run one hundred times repeatedly to get stable expectations and standard deviations of peaks under each combination of parameter values. Based on results of simulation, effects of related factors on peaks is investigated and estimated statistically, making it possible to predict peaks. In addition to forecasting the mean of peaks, the variability of peaks is estimated as well. Therefore, the distribution of peaks is predicted. Utility heterogeneity, cost heterogeneity and the Jointness of supply (J) exert significant effects on the distribution of peaks. It indicates that both utility heterogeneity and cost heterogeneity reduce the values and increase the variability (standard deviation) of peaks. Facilitating chain actions among individuals, heterogeneity promotes the outbreak of collective actions. However, it reduces the peaks and decreases the success probability of collective actions, while homogeneity increases the peak of participants and enhances the success chance of collective actions.

Introduction

The collective action refers to the social phenomenon that people gather and act together to achieve specific collective goals (Olson, 1965, Willer, 2009), such as strikes, protests, occupying, demonstrating, etc. For societal impacts and political implications (Meyer, 2004, Polletta and Jasper, 2001, Willer, 2009), collective action is the foundation of the society as human beings often cooperate with each other (Meyer, 2004, Olson, 1965). Collective actions are investigated via three clusters of methods: (a) The qualitative approach refers to theoretical analysis based on observations and case study (Benford and Snow, 2000, Chant, 2007, Goldstone, 1980, Hardin, 1968, Jenkins, 1983, Marx and Wood, 1975, McCarthy and Zald, 1977, Semann, 2009, Tarrow, 1988, Voss and Williams, 2012, Wright, 2009, Zhou, 1993, Zomeren and Spears, 2009); (b) the empirical approach refers to statistically evaluating empirical data (Bennett and Segerberg, 2011, Eisinger, 1973, Ellmers and Barreto, 2009, Hornsey et al., 2006, Mannarini and Talo, 2011, Qiu et al., 2015, Stroebe, 2013, Willer, 2009, Yu and Zhao, 2006, Zaal et al., 2012, Fernandez and McAdam, 1988); and (c) the mathematical approach refers to mathematical models and simulations to discover features and properties of collective action (Centola, 2010, Centola, 2013, Granovetter, 1978, Hu et al., 2014, Myatt and Wallace, 2009, Oliver, 1993, Ostrom, 2003, Siegal, 2009, Sigmund et al., 2010, Jin et al., 2014). Although the mechanisms and processes are heavily investigated, the distribution of participants is paid less attention, especially the phenomenon of peaks. The collective action follows a common regularity that it owns the peak of participants that can be mobilized. The peak varies depending on different cases.

The number of mobilized participants measures the success of collective actions like strikes, protests, and revolutions (Centola, 2013, Granovetter, 1978, Polletta and Jasper, 2001). The peak number of participants reflects the maximum power, influence, and impact of collective actions and therefore becomes a key indicator to predict the success rate. Despite the importance and potential applications, little attention has been paid to the peaks. Fortunately, related mathematical models or formal models of collective actions indirectly pave the way for the exploration and even prediction of the peak, such as the threshold model (Granovetter, 1978, Granovetter, 1986), standing ovation model (Miller & Page, 2004), network model (Alba, 1981, Gould R, 1993, Snow et al., 1980, Fernandez and McAdam, 1988), stochastic learning model (Macy, 1991a, Macy, 1991b, Macy and Flache, 1998, Macy and Flache, 2002, Mannarini and Talo, 2011, Flache and Macy, 2002), critical mass model (Marwell et al., 1988, Oliver et al., 1985, Pamela et al., 1988) or freezing period model (Wang, Liu, Wang, Zhang, & Wang, 2014), and game theory model (Heckathorn, 1988, Heckathorn, 1990, Wang et al., 2014b, Wang et al., 2015, Jin et al., 2014). It suggests in these researches that there are two factors influencing the peak: (a) The Jointness of supply (J) measuring how the size of group affects the individual payoffs. In general, the growing of J facilitates the payoff of individuals. Zero jointness of supply (J = 0) reduces participants and results into the group size paradox in large groups (Hardin, 1988, Olson, 1965). The paradox can be fixed by the “pure jointness of supply” (J = 1) where the size does not reduce individual payoffs and will not undermine participations (Pamela et al., 1988). Binary values of J (0 or 1) cannot capture features of all collective actions. Macy, 1990, Macy, 1991a, Macy, 1991b) expands J to the unit interval [0,1] and makes it continuous. It shows that J raises the number of participants and therefore facilitates the emergence of critical mass (Macy, 1990, Oliver et al., 1985); (b) the heterogeneity (Centola, 2013, Granovetter, 1986, Miller and Page, 2004, Oliver et al., 1985, Yu and Zhao, 2006) among members makes it harder to organize collective actions, playing a negative role in mobilizing individuals to participate (Centola, 2013, Schelling, 2005). However, the homogeneity increases participations of collective actions (Centola, 2011, Centola, 2013).

Following the mathematical approach, this paper focuses on the dynamic process and therefore prediction of peak, constructing a formal model based on the existing finding that both J and heterogeneity have negative effects on participations. Besides of the utility heterogeneity (Marwell et al., 1988, Oliver et al., 1985, Pamela et al., 1988), the cost heterogeneity should be considered as well because cost varies across different people. Therefore, this paper includes three factors such as cost heterogeneity, utility heterogeneity, and Jointness of supply to explore and predict the peaks. The cost heterogeneity refers to that participants have different costs to take part in the same collective action, and the cost homogeneity means that they share the same cost; Similarly, the utility heterogeneity refers to that agents have different subject scorings or feelings of their incomes, and the utility homogeneity means the same score of them. Under the joint homogeneity of cost and utility, ideal peaks can be obtained. Real peaks will be evaluated under cost heterogeneity or utility heterogeneity. Why we study the peak in collective actions? As more participants raise the success probability (Centola, 2011, Centola, 2013, Granovetter, 1978, Pamela et al., 1988), the dynamics and success rate of a certain collective action can be forecasted in advance, which is meaningful for both the organizers and opponents of the collective action. Our target is to estimate and predict the distribution traits (mean and SD) of real peaks. Via comparison effects of utility and cost heterogeneity, a higher fitness of estimation is achieved.