def gen_output(u1, u2):
    """
    Inputs:
    u1 : first column
    u2 : second column
    Outputs:
    y : binary variable (1 or 0) ; 1 if x2 is preferred ; 0 if x1 is preferred
    p: actual preference probability
    """
    # utility function value generation
    diff = u2 - u1
    y = 1*(diff > 0.)
    #p = probit_link_func(3*diff)
    #y = bernoulli.rvs(p)
    return y