  We investigate the effects of delayed interactions on the stationary
distribution of the noisy voter model. We assume that the delayed interactions
occur through the periodic polling mechanism and replace the original
instantaneous two-agent interactions. In our analysis, we require that the
polling period aligns with the delay in announcing poll outcomes. As expected,
when the polling period is relatively short, the model with delayed
interactions is almost equivalent to the original model. As the polling period
increases, oscillatory behavior emerges, but the model with delayed
interactions still converges to stationary distribution. The stationary
distribution resembles a Beta-binomial distribution, with its shape parameters
scaling with the polling period. The observed scaling behavior is
non-monotonic. Namely, the shape parameters peak at some intermediate polling
period.
