Beyond Constraint: Measuring Brokerage Opportunity and Exclusivity

Structural hole research treats brokerage as a source of advantage and has often operationalized it with Burt’s constraint index. Johnson and Sasson (this issue) argue that constraint mostly tracks inverse network size and, with valued ties, tie-strength concentration rather than brokerage. They further argue that, as a result, the field needs to reinterpret the extensive body of past structural hole research. We agree that there is a measurement problem with constraint, but see a different problem than degree. According to structural hole theory, when other actors can connect the same pairs of contacts as ego, ego becomes easier to substitute for and ego’s position weakens. Yet in ego networks with more than seven nodes, once a competing broker is present, adding further competitors actually lowers constraint, making ego appear less constrained even as the position deteriorates. We use this lens to motivate a pair-based approach to measuring structural hole position. In our approach, the quantity P counts the non-tied alter pairs ego spans. The quantity Q describes how exclusively ego spans those pairs, with extensions that also recognize longer bypasses around ego. Their product, PQ, sums exclusivity-weighted brokerage across the gaps ego spans and, unlike constraint, does not improve when non-ego ties close gaps or create new routes around ego. For strategy, the P/Q distinction separates the number of occasions on which a broker might create value from one structural basis for capturing it: the scarcity of substitutes. We also discuss an inconvenient fact, which is that different structural-hole mechanisms — information access, timing, control, synthesis, and referral — depend on different structural conditions, so even P, Q, and their product will not be appropriate in all cases.