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Let ${\mathcal G}$ be an infinite family of connected graphs and let $k$ be apositive integer. We say that $k$ is ${\it forcing}$ for ${\mathcal G}$ if forall $G \in {\mathcal G}$ but finitely many, the following holds. Any$\{-1,1\}$-weighing of the edges of $G$ for which all connected subgraphs on$k$ edges are positively weighted implies that $G$ is positively weighted.Otherwise, we say that it is ${\it weakly~forcing}$ for ${\mathcal G}$ if anysuch weighing implies that the weight of $G$ is bounded from below by aconstant. Otherwise we say that $k$ ${\it collapses}$ for ${\mathcal G}$.  We classify $k$ for some of the most prominent classes of graphs, such as allconnected graphs, all connected graphs with a given maximum degree and allconnected graphs with a given average degree.

The effect of local majority on global majority in connected graphs