Origin of nonlinear transport phenomena in conducting polymers has long been a topic of intense controversies. Most previous knowledge has attributed the macroscopic nonlinear I-V characteristics to individual behaviors of elementary resistors in the network. In this Letter, we show via a systematic dimensionality-dependent transport investigation, that understanding the nonlinear transport in conducting polymers must include the collective transport effect in a percolation network. The possible mediation of percolation threshold p_{c} by controlling the samples' dimensionality unveiled the collective effect in growth of percolation paths driven by electric field, enabling us to draw a smooth connection between two typically observed nonlinear phenomena, dissipative tunnelinglike and threshold-limited transport, which have been controversial for years. The possible microscopic origins of the collective transport are discussed within the Coulomb blockade theory.