Gero Schwenk and Torsten Reimer (2008)
Simple Heuristics in Complex Networks: Models of Social Influence
Journal of Artificial Societies and Social Simulation
vol. 11, no. 3 4
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Received: 14-Sep-2007 Accepted: 22-Mar-2008 Published: 30-Jun-2008
We call this rule the " Contact All " or ALL rule. According to the second rule, agents contact only those neighbors who have at least the same (or a higher) status value wjas the agents themselves.
We call this rule the " Higher Equal " or HE rule. Its inclusion is based on observations in research on collective choice, which indicate that group members who have high levels of expertise or status are, at times, more influential in the group decision process than members who have low levels (e.g., Bonner, Baumann, Lehn, Pierce, & Wheeler 2006). Both rules include the searching agent himself/herself as an information source.
IAi designates the inference of agent A made on a specific alternative i. This inference IAi is computed in two steps. Firstly, the available opinion oji of neighbor j on alternative i is weighted with the latter neighbor's status wj. Secondly, all k neighbors' weighted opinions wjoji are summed up. Agent A chooses the inference IAi with maximal value as her preference OA.
As can be seen in Table 1, we have considered all possible combinations of contact and decision rules. The FTL -rule is listed only once, because it makes no difference whether the leader (by definition, the member with the highest status) is selected from amongst all neighbors or only from amongst the subset of higher status neighbors.
|Table 1: Contact and Decision Rules Considered|
|Contact Rule||Decision Rule|
|HE (Higher Equal)||UWM (Unit Weight Model)|
|HE (Higher Equal)||WADD (Weighted Additive Model)|
|HE (Higher Equal)||MIN (Minimalist)|
|HE (Higher Equal)||FTL (Follow the Leader)|
|ALL (All Neighbors)||UWM (Unit Weight Model)|
|ALL (All Neighbors)||WADD (Weighted Additive Model)|
|ALL (All Neighbors)||MIN (Minimalist)|
|Figure 1. Small world network ( n =21, k =2, pr =0.1). The network has been created by introducing shortcut ties to a regular ring network, where every node is connected to two neighbors on each side|
|Table 2: Employed Variations of the Small-World Model ( n =21, k =2).|
|Rewiring Probability||Network Characteristic|
|pr=0||Cyclic Regular, high clustering|
|pr=1||Random regular, no clustering|
|Figure 2. Mean faction sizes over networks with decreasing clustering. Results were sorted according to the size of the faction in an individual simulation run, regardless of the actual choice-alternative favored. A majority is reached at eleven.|
Different patterns of faction sizes were observed for strategies containing an HE- or ALL contact rule. As expected, the decrease of network clustering generally led to smaller sizes of minority factions.
|Figure 3. Group level outcomes over networks with decreasing clustering.|
|Figure 4. Probability of decision change of high status members over networks with decreasing clustering (cyclic regular, small world, random regular).|
|Figure 5. Probability of decision change in high status members in a small world network over status distributions of increasing steepness.|
|Figure 6. Status distribution of partners in an empirical network. Partners are numbered according to seniority.|
|Figure 7. Empirical influence network. Highly connected partners are located in the center of the network. Dark and wide arrows represent high status relations. Green nodes represent an "as - is" and red nodes a "less flexible" policy opinion. Partners are numbered according to their seniority.|
|Figure 8. HE - relevant subnet of the empirical influence network: highly connected partners are located in the center of the network. Dark and wide arrows represent high status relations. Green nodes represent an "as - is" and red nodes a "less flexible" policy opinion. Partners are numbered according to their seniority.|
|Table 3: Preference distributions for the considered strategies in the network. The two possible preferences were "keep case assignment as it is" and "organize case assignment less flexible via a central authority." As can bee seen, the final distributions of opinions depart considerably from the initial distributions.|
|Strategy||n(as-is)||n(less flexible)||Equilibrium cycle|
|HE - UWM||34||2||7|
|HE - WADD||34||2||5|
|HE - MIN||Majority||Minority||Fluctuating|
|HE - FTL||26||10||3|
|ALL - UWM||36||0||4|
|ALL - WADD||36||0||4|
|ALL - MIN||36 (p=0.77)||36 (p=0.23)||Mean=17.8|
2 Originally, we employed both high and low valued linear status distributions. As expected, both induced exactly the same process behavior.
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