import math


def build_old_mild_beliefs(num_agents, low_pole, high_pole, step):
    """Builds mildly polarized belief state, in which 
    half of agents has belief decreasing from 0.25, and
    half has belief increasing from 0.75, all by the given step.
    """
    middle = math.ceil(num_agents / 2)
    return [max(low_pole - step*(middle - i - 1), 0) if i < middle else min(high_pole - step*(middle - i), 1) for i in range(num_agents)]