Proponents of the theistic fine tuning argument and opponents of the multiverse hypothesis argue that, while the multiverse might explain why some universe is fine tuned, it doesn't explain why this particular universe is fine tuned. The argument goes thus: under naturalism, the probability of (any) universe having constants with the life permitting values is vanishingly small. A life permitting universe is more likely under a theistic hypothesis than under a naturalistic one. Therefore, it is more likely that the theistic hypothesis is true, than it is a naturalistic one. This judgement of epistemic improbability is arrived at by considering the range of possible values (we believe) the constants could have taken*, and considering how many of those would be in the life permitting range. It turns out, only a tiny fraction would permit life (as far as we know).
The Multiverse Objection
Proponents of the multiverse hypothesis argue that, in a suitably vast multiverse, comprising universes which realise the entire possible range of values, the probability of a life permitting universe is essentially 1 - it is guaranteed. To which opponents of the multiverse hypothesis object that, while the multiverse explains how some universe would be fine tuned, it doesn't explain why this universe has the life permitting values.
The theistic objection fails, however, for a very simple reason.
If we consider the large sample space of possible universes - it is this large sample space which underwrites the theistic claim that a life permitting universe is improbable, in the first place - we can see that this universe forms part of that sample space. If it didn’t, then it simply couldn't have existed.
A suitably vast multiverse actualises all universes in the sample space, including this universe. Hence, it adequately explains why this universe is fined tuned.
The Cosmic Lottery
To illustrate this, we can imagine a cosmic lottery in which the sample space (of possible universes) is represented by a drum containing all possible universes, each with a different set of values for the constants - one of which being this universe and it's associated values. In this cosmic lottery, the universe which corresponds to this one, is one among a huge number. Hence, in a lottery where only one ball or universe is chosen (from the sample space), the odds of this universe being chosen and actualised, is "vanishingly small". However, in a lottery where every universe from the sample space of possible universes is selected and actualised, it is inevitable that this universe i.e. the universe corresponding to the set of values we observe in this universe, is selected and actualised.
*The ex nihilo nihil fit principle entails that, under a naturalistic single universe hypothesis, either no other set of values could have been taken or the values are variable. If the values are variable, then life permitting values are not improbable.
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The only problem with all this is:
There is not a single empirical indication that we live in a multiverse.
We have empirical evidence for exactly one singleverse.
What remains, then, is to compare the different hypotheses and examine which one is the most plausible.