  We have studied long range orders of electric quadrupole moments described by
an effective pseudospin-$\frac{1}{2}$ Hamiltonian representing pyrochlore
magnets with non-Kramers ions under [111] magnetic field, in relevance to
Tb$_{2}$Ti$_{2}$O$_{7}$. Order parameters and phase transitions of this
frustrated system are investigated using classical Monte-Carlo simulations. In
zero field, the model undergoes a first-order phase transition from a
paramagnetic state to an ordered state with an antiparallel arrangement of
pseudospins. This pseudospin order is characterized by the wavevector
$\boldsymbol{k}=0$ and is selected by an energetic or an order-by-disorder
mechanism from degenerate $\boldsymbol{k}=(h,h,h)$ mean-field orders. Under
[111] magnetic field this three-dimensional quadrupole order is transformed to
a quasi two-dimensional quadrupole order on each kagom\'{e} lattice separated
by field-induced ferromagnetic triangular lattices. We discuss implication of
the simulation results with respect to experimental data of
Tb$_{2}$Ti$_{2}$O$_{7}$.
