So ultimately the problem with anti-inductors (who use anti-induction exactly because it never worked before) is that they get removed by evolution, even if they can defend themselves quite well in philosophical debates.
A thought experiment with an anti-inductor Alice, who was created in your mind right now, seems to make sense. But let's give this Alice some history... imagine that she is 20 years old... what exactly was she doing during the previous years? Was she an anti-inductor? Did she eat? If not, how is she still alive? (She admits that her strategy has not worked in the past.)
Or, imagine that someone creates a perverse virtual reality, where anti-induction is rewarded and induction is punished. How exactly would such reality even work? Suppose you get uploaded into this simulation, but you know the rules, therefore... on Day 1, you will do exactly the things that never worked before, and it is a huge success! But, what are you going to do on Day 2? There are no more "things that never worked before", because things that never worked before Day 1, they all worked on Day 1...
My uncle with whom I shared thoughts on anti-induction remarked that humans are systematically anti-inductive in some situations : he gave the example of gambling, where people can think that losing a lot in a row means that they are poised to win soon.
But this is not a fair example in my opinion, because gamblers are not consciously anti-inductive : when their behavior is exposed as such, they do not defend their decision.
Among my relatives, the gamblers are notoriously irrational. A bayesian might say that a long streak of wins is very weak evidence that they will keep on winning, because they have a strong prior confidence in mathematical analysis of the game, but that hardly tells us anything about how anti-induction arose in the first place.
The following dialogue is intended to showcase a (moderately) intelligent anti-inductor in action, to try to understand the anti-inductors by putting myself in their shoes.
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Alice is an anti-inductor. She intuitively believes that things that have happened often typically don't happen again.
Aware of that fact, and of the existence of inductors, she has tried to look into anti-induction to know what it really means to her, and if it is an intuition she should abandon.
She has a friend, Iris, who is an inductor. They are both tentatively rational, as intelligent as each other (and coincidentally about as dumb as me).
Were I a non-inductive spirit, I would have perhaps no reason to fill my fictional world with inductors rather than anti-inductors (thereby supporting one side a priori), but I am not.
This does mean however that the following reasoning is only valuable insofar as it modifies my behavior relative to the real world and not a mere possible one (in some possible worlds, I would not update on counterfactually fictional evidence).
None of my tentatives to formalize induction in formal logic led to interesting results. Please tell me if you know a paper on the subject !
So far, my best definition is that there is an interest function of propositions (personal ?) and interesting reference classes, defined as {x : P(x)} for an interesting property P. Induction states that if A is an interesting reference class,
Vx€A, (O(x)=>Q(x)) -> Vx€A, Q(x)
where Q is interesting and O(x) means "x is observed", assuming a meaningful "observed" property.
Alice refused to partake further in the debate, troubled. Thank the lord she did not think about the fact that she had used anti-induction until now ! She would then have legitimately expected to stop believing her truth any moment, without any explanation as to why ! Fated to be wrong like someone who receives overwhelming evidence they are a Botzmann brain is fated to stop thinking ! In that sorry case, she would weep for her soon to be lost love for truth, and digging further, her soon to be lost consistent utility function (for she followed one until now).