  The discrepancy between the amplitudes of matter fluctuations inferred from
Sunyaev-Zel'dovich (SZ) cluster number counts, the primary temperature, and the
polarization anisotropies of the cosmic microwave background (CMB) measured by
the Planck satellite can be reconciled if the local universe is embedded in an
under-dense region as shown by Lee, 2014. Here using a simple void model
assuming the open Friedmann-Robertson-Walker geometry and a Markov Chain Monte
Carlo technique, we investigate how deep the local under-dense region needs to
be to resolve this discrepancy. Such local void, if exists, predicts the local
Hubble parameter value that is different from the global Hubble constant. We
derive the posterior distribution of the local Hubble parameter from a joint
fitting of the Planck CMB data and SZ cluster number counts assuming the simple
void model. We show that the predicted local Hubble parameter value of $H_{\rm
loc}=70.1\pm0.34~{\rm km\,s^{-1}Mpc^{-1}}$ is in better agreement with direct
local Hubble parameter measurements, indicating that the local void model may
provide a consistent solution to the cluster number counts and Hubble parameter
discrepancies.
