The response to an applied electric field in the q_{T}=1/2 subphase of the MC881-MC452 binary mixture system is studied by using thick homeotropically aligned cells. In the ordinary antiferroelectric SmC_{A}^{*} and 1/2 (sub)phases, some nonplanar asymmetric distortions in the antiferroelectric unit cell structure produce induced polarization in the applied field direction, starts to unwind the helix from the beginning, and tends to align the averaged tilt plane direction parallel to the applied field. In the 1/2 subphase under consideration, however, the helix resists being deformed at the beginning and then the thresholdlike steep increase of birefringence Δn occurs in the transition from 1/2 to unwound SmC^{*} at a field of less than 0.5 V/µm; we conclude that the thermal fluctuations play an important role in promoting the director flip-flopping in a single layer under the applied field and bring about additional induced polarization, which counteracts the aforementioned ordinary induced one and prevents the helix from unwinding. This suggests that the Langevin-like director reorientation is the mechanism of the V-shaped switching which was actually observed in the thin films of Mitsui mixture [Phys. Rev. Lett. 87, 015701 (2001)0031-900710.1103/PhysRevLett.87.015701] and must have been used in prototyped thresholdless antiferroelectric liquid-crystal displays.