New Math Reveals the Cheapest Way to Make Everyone Agree
Want everyone to adopt your idea? New math shows the cheapest way to tip a network.
A new paper studies an optimal intervention problem for linear threshold models: networks where each agent adopts action 1 if and only if the fraction of its neighbors doing so is at least a prescribed threshold. Assuming a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, the paper asks for the minimum intervention cost needed to ensure global convergence to the all-1 configuration. The main contribution is a new graph-theoretic quantity called the oriented path number — the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost coincides with the oriented path number; in the general case, it is the main ingredient of a bound on the optimal intervention cost.
- People copy their neighbors: most of us adopt a new habit only once enough friends already have.
- Researchers found the cheapest way to flip an entire network ties to the 'oriented path number' — the fewest one-way routes that cover everyone.
- The practical payoff: health campaigns, marketers and policymakers could aim at the handful of people who tip everyone else, instead of spreading effort everywhere.
Why It Matters
Could help health campaigns, marketers and officials change behavior with less money and fewer wasted ads.