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As a shift from traditional diffusion research to diffusion networks studies, threshold models supplies important intellectual resources for diffusion research. Threshold has been used to study interpersonal effects of collective behavior, e.g., residential segregation (Granovetter & Soong, 1988; Schelling, 1971), spiral of silence (Glynn & Park, 1997; Granovetter & Soong, 1988; Krassa, 1988), consumer demand (Granovetter & Soong, 1986), and diffusion of innovations (Valente, 1996).

One illustration of threshold could be easily given with a simple case of collective

behavior. Suppose that one social system consists 10 people, and their individual thresholds are 0, 1, 1, 4, 4, 4, 5, 7, 8, and 9, respectively. The first one whose threshold is 0 initiates in engaging in the collective behavior without being influenced by others. Following the first actor, the second and third people whose thresholds are 1 spontaneously engage in the activity following the first people. Thus, so far there are three people engaging in the collective behavior. Given the smallest individual threshold of the other people is 4, nobody will engage in this activity. Thus, the diffusion stops with “infects” 3 people in the social system.

The significance of threshold lies in its determination of the diffusion curves. The threshold for different individuals in a social system varies. The innovators usually have very low thresholds, which makes them engage in the diffusion as soon as it is initiated. Later diffusers who are strongly against the innovation usually have very high thresholds. Their adoptions are only possible after many other individuals who have adopted the innovation in

their personal network. If the distribution is left-skewed, it means that the average threshold of the system is relatively small, thus the diffusion curve could take off relatively earlier and the diffusion can reach more people; if the distribution is right-skewed, it means that the average threshold is relatively big, and the diffusion stops earlier with a smaller diffusion size. If the distribution of the threshold is normally distributed, it is expected that the cumulative diffusion curve should be S-shaped.

Threshold models presume that individual behavior is based on the fraction of people in a social system who have already engaged in the behavior (Granovetter, 1978; Granovetter & Soong, 1983, 1986, 1988). Thus, one person’s threshold is the proportion of a community to engage in a behavior before the individual makes up his/her mind to do so. Individuals of lower thresholds tend to engage relatively earlier than those who have higher thresholds. The numeric value of threshold should be in the range of zero and one.

Threshold can be used to capture the impact of interpersonal effect. Based on the assumption of maximizing utility of cost and benefit from binary decision-making, threshold concerns the extent to which an individual’s behavior is contingent upon that of others. The first diffusion investigation to gauge the nature of diffusion networks is the study of new drug’s diffusion among medical doctors by Coleman et al. (1966). Valente (Valente, 1993, 1995) employed threshold models to reanalyzed the diffusion data of drug collected by Coleman et al. (1966). Each doctor has an individual threshold as the resistance to the medical innovation, which was gradually overcome by interpersonal effect. According to the utility-cost assumption of threshold models of human behavior, when the driving force equals the resistance of cost, individual starts to engage in the behavior. Based on the relationship between threshold and adoption of innovations, scholars of diffusion of innovations generalize that an individual is

more likely to adopt an innovation if more of the other individuals in his or her personal network have adopted previously (Rogers & Kincaid, 1981; Valente, 1995).

There is one extreme situation of threshold – the “zero threshold” (Valente, 1995, p. 64) , whose value is zero. Zero threshold implies that the people of zero threshold will engage in the collective behavior without being influenced by the other people in a social system. Thus, zero threshold itself implies the important of alternative influence in addition to interpersonal effect. Therefore, it could be used to capture the non-interpersonal effects in the diffusion process, for example, how many people have engaged in the diffusion without being influenced by their interpersonal networks.

Based on the mechanisms of diffusion, two basic types of diffusion are recognized: the chain-reaction snowballing of diffusion, and the diffusions among disconnected nodes. The chain-reaction contagion occurs because the members of a social system are closely linked by interpersonal networks. Prior research (Coleman, et al., 1966) shows that “the network

interconnectedness of an individual in a social system is positively related to the individual’s innovativeness” (Rogers, 2003, p. 330). In addition to interpersonal effect, external impacts also play an important role in diffusion process. For example, Burt (1987) argues that structural equivalence (e.g., two individual occupy the same position in the structure of the interpersonal network) shapes the adoption of new innovations, rather than social influence. Valente (1995) found that a combination of external influences (e.g., media influence) and the interpersonal effects can best explain the adoption of new drugs.

It’s necessary to note the difference and connection between threshold and critical mass. Threshold concerns the tipping point for individuals, and critical mass is about the tipping point for the social system, groups and sub-groups. Critical mass occurs at the point at which enough

individuals in a system have adopted an innovation so that the innovation’s further rate of adoption becomes self-sustaining. Another assumption of threshold models is the

interdependence among individuals in social system. Interdependence is a situation in which an individual’s behavior affects those of the others. According to the point of cost and benefit, there is a risk and uncertainty for people to engage in certain behaviors. Thus, if a group of people make decisions collectively, the interdependence of them help them reducing the uncertainty by making decisions based on the choices of others who they refer to, which implies that

interdependence change individual threshold (Valente, 1995). Sequential interdependence happens when earlier diffusers’ behavior influence later diffusers, and reciprocal

interdependence exists when later diffusers provide benefits to earlier diffusers, especially in the context of interactive media. For example, reciprocal interdependence tends to spread

telecommunication services by prevent preexisting adopters from stopping using them (Markus, 1987).

There are two ways to measure threshold (Granovetter, 1978; Granovetter & Soong, 1983, 1986, 1988). First, to observe how an individual’s behavior shifts with the other’s decisions in terms of revealed preference (Granovetter & Soong, 1988), e.g., following this approach, Valente (1996) studied the diffusion of innovations. The second method to measure the threshold is by asking the respondents directly, e.g., Noelle-Neumann uses this method to measure the

willingness to express (Noelle-Neumann, 1974, 1993). This second method is suspect, since its validity can’t be tested. In this study, I adopt the first method and incorporate the ego-network information to unobtrusively gauge the collective behavior in news diffusion.