It think it’s… sort of the reverse? Flipping a coin results in Brownian motion, which is an example of a “martingale”, a function whose expected future value is equal to its current value; and the evolution of a share price being a martingale (at least under a modified probability measure) is exactly the condition for the market to not have arbitrage:

https://en.m.wikipedia.org/wiki/Risk-neutral_measure

I’m not sure exactly how the arbitrage works, though.

But the argument in the paper seems to be not that there’s noise but that there’s too much of it. In fact, it assumes that the expected vote share over time is subject to Brownian motion with specific parameters (which is a rather flawed assumption), but then concludes that 538’s probability distribution is more swingy what he’d calculate from those parameters.