From the Wikipedia fined-tuned universe page
Mathematician Michael Ikeda and astronomer William H. Jefferys have argued that [, upon pre-supposing MWI,] the anthropic principle resolves the entire issue of fine-tuning, as does philosopher of science Elliott Sober. Philosopher and theologian Richard Swinburne reaches the opposite conclusion using Bayesian probability.
(Ikeda & Jeffrey are linked at note 21.)
In a nutshell, MWI provides a mechanism whereby a spectrum of universes are produced, some life-friendly and some life-unfriendly. Consistent with the weak anthropic principle, life can only exist in the life-friendly (hence fine-tuned) universes. So, MWI provides an explanation of observed fine-tuning, whereas the standard QM interpretation does not.
I glanced at Ikeda & Jefferys, and they seem to explicitly not presuppose MWI:
our argument is not dependent on the notion that there are many other universes.
At first glance, they seem to render the fine-tuning phenomenon unsurprising using only an anthropic argument, without appealing to multiverses or a simulator. I am satisfied that someone has written this down.
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