Journal on Policy and Complex Systems
volatility of beliefs across the network as a whole . In some cases , in some networks , a changed percentage of nodes may have little more impact than that change itself , giving the pattern of a random walk in small steps illustrated in Figure 7a . In other cases , in other networks , the impact of a small changed percentage may be much greater , with wider swings and reversals of dominance , as in 7b . Given some initial patterns of belief and some network structures , a small percentage may produce repeated cascades of changed opinion amounting to the wide swing of dominant opinion shown in 7c .
How does network structure correlate with opinion volatility in this sense ? We measure changes in the configuration of belief on a network that are greater than 150 % of the change artificially introduced as background noise . We track both the frequency with which changes of that size occur in different networks — the percentage of cases in which the introduction of a random change in beliefs of 5 % of the population change leads to a greater than 7.5 % swing in over-all beliefs — and the amplitude of change when it does occur . We measure amplitude as the difference in the number of agents holding p at the point of noise introduction and the number holding p in the next time interval . At points of volatility in a network , what percentage of the network changes beliefs ?
The radical simplifications involved in the model should again be emphasized . We are dealing with a single binary issue and an extremely simplified concept of belief change . The dynamics involved , however , are not entirely out of range as an idealization of important aspects of opinion change across a community . There are indeed issues that can be phrased as binary choices , and attitudes are indeed subject to the kind of conformity pressure modeled here in terms of deference to the majority of contacts ( Asch , 1952 , 1955 ; Bond & Smith , 1996 ; Cialdini & Goldstein , 2004 ).
Just as we would not claim our measures of democratic networks to be exhaustive , we would not claim our measures of instability to be exhaustive , even with regard to opinion instability . Within the constraints of those measures , however , we can ask a very simple question of our simple models :
In terms of both frequency and amplitude , how does the volatility or stability of opinion correlate with the democracy or anti-democracy of a communication network ?
Opinion Volatility in Democratic and Anti- Democratic Regimes
In the graphs that follow , we map
our two dimensions of network “ democracy ” on two axes , as outlined above . The x-axis shows a decreasing mean degree in sample networks — decreasingly democratic networks in that sense — from left to right . The y-axis shows increasing preferential exponent — decreasing democratic networks in that sense — from bottom to top . Networks most democratic in both regards
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