The guarantees would not hold, I'm pretty sure ;) Maybe one of the authors could chip in, but my hunch is that with that you could actually introduce arbitrarily large errors. The beauty of this algorithm really is its simplicity. Of course, simple is.. not always easy. This absolute masterpiece by Knuth should demonstrate this quite well:

https://www.sciencedirect.com/science/article/pii/0022000078...

It's an absolutely trivial algorithm. Its average-case analysis is ridiculously hard. Hence why I think this whole Ordo obsessions needs to be refined -- worst case complexity has often little to do with real-world behavior.

You want every distinct item to have the same chance at the end. So when items repeat you need to reduce (not increase) the odds of keeping any given occurrence.

Let’s prove it by contradiction: Lets say you pick the larger ones and drop the smaller ones every single round, you have lost the probabilistic guarantee of 1/2^k that the authors show because the most frequent words will be the lost frequent in subsequent rounds as well. This is the intuition, the math might be more illuminating.