Journal on Policy and Complex Systems
show low volatility amplitude across all node degrees . With an average degree in the democratic range above 5 , the amplitude of volatility remains low despite increases in the preferential attachment . Once the preferential attachment exponent rises above 2 and average node degree falls below 5 , anti-democratic networks show a steady and significant increase in volatility amplitude , approaching network changes of 75 % on the right edge of the graph . Measured in terms of amplitude , anti-democratic networks prove far more volatile than do democratic networks .
Within the constraints of our model assumptions , the results seem importantly suggestive . What they suggest is that anti-democratic communication networks can be expected to be significantly less opinion-stable than democratic networks . What our models suggest , for example , is that the destabilizing influence of wide swings of opinion can be expected to occur with both greater frequency and greater depth across decreases in the two dimensions outlined for democratic networks .
We can further underscore these suggestions by combining our two measures of volatility . We simply multiply frequency of opinion volatility — the percentage of cases in which opinion change exceeds 150 % of randomly introduced change — times the amplitude of volatility — the percentage of the population that shifts opinion . The result , shown in Figure 10 , is something like a hazard map for opinion instability in the designing of social institutions .
What the results indicate is that the communication networks most vulnerable to volatility overall — considering both frequency and amplitude — are those that are least democratic on both of our measures : the networks with a low mean degree and high preferential attachment at the upper right . Those least affected by volatility overall are networks democratic on both our measures .
Shifting Networks , Democratic and Anti-Democratic
Opinion volatility is a plausible
measure of instability in a network of political actors .
If an individual finds himself repeatedly torn between radically opposed opinions based on shifting opinions among his pattern of contacts , he seems likely to change his pattern of contacts . The result will be a change in the structure of the communication network : the network can be expected to rewire in reaction to opinion volatility .
If an abstract network rewires because of opinion volatility , in what direction can we expect it to change ? In the model outlined , anti-democratic networks prove less stable in terms of opinion volatility . If those networks rewire in response to that instability , do they inevitably become more democratic ? However , democratic networks are not immune from opinion volatility , either . Where democratic networks rewire , do they tend to become less democratic ?
In the rewiring considered here , new links are created as old links are
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