The emission mechanism and the origin and structure of magnetic fields in
gamma-ray burst (GRB) jets are among the most important open questions
concerning the nature of the central engine of GRBs. In spite of extensive
observational efforts, these questions remain to be answered and are difficult
or even impossible to infer with the spectral and lightcurve information
currently collected. Polarization measurements will lead to unambiguous answers
to several of these questions. Recent developments in X-ray and gamma-ray
polarimetry techniques have demonstrated a significant increase in sensitivity
enabling several new mission concepts, e.g. POET (Polarimeters for Energetic
Transients), providing wide field of view and broadband polarimetry
measurements. If launched, missions of this kind would finally provide
definitive measurements of GRB polarizations. We perform Monte Carlo
simulations to derive the distribution of GRB polarizations in three emission
models; the synchrotron model with a globally ordered magnetic field (SO
model), the synchrotron model with a locally random magnetic field (SR model),
and the Compton drag model (CD model). The results show that POET, or other
polarimeters with similar capabilities, can constrain the GRB emission models
by using the statistical properties of GRB polarizations. In particular, the
ratio of the number of GRBs for which the polarization degrees can be measured
to the number of GRBs that are detected (N_m/N_d) and the distributions of the
polarization degrees (Pi) can be used as the criteria. If N_m/N_d > 30% and Pi
is clustered between 0.2 and 0.7, the SO model will be favored. If instead
N_m/N_d < 15%, then the SR or CD model will be favored. If several events with
Pi > 0.8 are observed, then the CD model will be favored.
