It is hard (or impossible) to directly obtain the analytical expression for the stationary distribution of the poll-delay voter model. But we can look at various possible approximations, with the Beta distribution being the prime suspect. To fit the Beta distribution (or any other two-parameter distribution), we need to know two stationary moments of the model. Deriving the stationary mean is a trivial problem, while deriving the stationary variance is more involved.

In this post, let us use the Yule-Walker equations to obtain the expression for stationary variance of AR(2) process.

Important thing to notice about the poll-delayed voter model is that it is a second order auto-regressive process. In [1] we have used this observation to derive an analytical expression for the stationary variance for the model. To understand how this result came to be, the following video by ritvikmath might prove useful.

References

• A. Kononovicius, R. Astrauskas, M. Radavičius, F. Ivanauskas. Delayed interactions in the noisy voter model through the periodic polling mechanism. Physica A 652: 130062 (2024). doi: 10.1016/j.physa.2024.130062. arXiv:2403.10277 [physics.soc-ph].

In the last few posts, I have introduced you to two variations of the voter model enhanced with polling mechanism [1]. These two variations differed in whether the announcement of poll outcome is delayed or not. This time, we will explore the distributions obtained from these models.

Last Sunday in Lithuania, a protest took place against the proposed changes to property tax laws. The protest itself reminded me of a video I watched some time ago. The video was about Georgism - an idea that most taxes could be abolished (or significantly reduced) if we instead taxed land more heavily.

While I think Georgist land value taxation is a not perfect solution, it is an interesting alternative worth our consideration. Especially, as a replacement for the typical taxation of labor. I invite you to watch an introductory video by BritMonkey.

We have already seen the basic workings of the poll-delayed voter model introduced in [1]. Previously, we have assumed that polling information is being revealed with delay and that the delay coincides with the polling period. However, quite often, processing polling information does not take a lot of time, so the information becomes available almost immediately. So, what changes when we remove this delay?