Motivated by the observed cosmic matter distribution, we present the following conjecture: due to the formation of voids and opaque structures, the average matter density on the path of the light from the well-observed objects changes from Ω M ≃ 1 in the homogeneous early universe to Ω M ≃ 0 in the clumpy late universe, so that the average expansion rate increases along our line of sight from EdS expansion Ht ≃ 2/3 at high redshifts to free expansion Ht ≃ 1 at low redshifts. To calculate the modified observable distance-redshift relations, we introduce a generalized Dyer-Roeder method that allows for two crucial physical properties of the universe: inhomogeneities in the expansion rate and the growth of the nonlinear structures. By treating the transition redshift to the void-dominated era as a free parameter, we find a phenomenological fit to the observations from the CMB anisotropy, the position of the baryon oscillation peak, the magnitude-redshift relations of type Ia supernovae, the local Hubble flow and the nucleosynthesis, resulting in a concordant model of the universe with 90% dark matter, 10% baryons, no dark energy, 15 Gyr as the age of the universe and a natural value for the transition redshift z 0 = 0.35. Unlike a large local void, the model respects the cosmological principle, further offering an explanation for the late onset of the perceived acceleration as a consequence of the forming nonlinear structures. Additional tests, such as quantitative predictions for angular deviations due to an anisotropic void distribution and a theoretical derivation of the model, can vindicate or falsify the interpretation that light propagation in voids is responsible for the perceived acceleration.