It turns out that if you write down on the list of requirements that you would want from a voting system in order for it to be fair, the no deterministic voting system is fair. This is known as Arrow's theorem (https://en.m.wikipedia.org/wiki/Arrow%27s_impossibility_theo...).

Interestingly Arrow's theorem doesn't apply to randomized voting systems. In particular, the system of picking a random voter to decide the election satisfies (probabilistically) every standard notion of fairness.