In large systems, from biology to politics, like attracts like. Individuals in social systems connect and form factions based on common interests or behaviors, such as a voting populous that divides by candidate. A biological model of malarial transmission may divide its constituents into parasites (mosquitoes) and hosts (humans), with each group playing fundamentally different roles.
Understanding groupings, or “modules,” is a key problem in network theory. Traditional clustering models assume many modules will pop up in a large population. But that approach is limited, says Laurent Hébert-Dufresne, an SFI postdoctoral fellow. Recent findings suggest that a small, finite number of tightly knit modules – those whose components play by the same rules as the system evolves – emerge in many systems, and this “hard modularity” can influence network processes.
To better explore the impact of hard modularity on networks, Hébert-Dufresne organized a five-day working group at SFI in January. His collaborators included three physicists, Antoine Allard (University of Barcelona), Jean-Gabriel Young (Université Laval in Québec), and Pierre-André Noël (UC Davis), as well as evolutionary biologist Eric Libby, an SFI Omidyar Fellow.
Modularity is typically regarded as a structural property of a network, but this group took a different approach. “We studied modularity instead as a strategy,” says Hébert-Dufresne. “Do you look for people like you, or different from you?”
Scrawling on a whiteboard and on paper, the network theorists thought through a number of simple strategy games to test the influence of hard modularity: for example, to win an election, how much effort should I spend on reinforcing the opinion of my friends versus trying to convince strangers or opponents? Should my strategy differ based on the strategies of my opponents?
Surprising observations emerged. Aggressive strategies with no chance of winning, for example, affected a game’s outcome by conferring more power to a different, otherwise unsuccessful strategy. Hébert- Dufresne compares this observation to the U.S. presidential campaign of Donald Trump, whose aggressive approach may steer the vote toward middle-ground candidates. (The meeting concluded just before the first Republican primary.)
Their approach is general enough to be relevant to a range of networks, from parasite transmission to marketing, but there remain questions Hébert-Dufresne would like to answer. “How extreme must a strategy be to completely change a game?” he asks. “Or to have no impact at all?”