There's a particular reasoning antipattern I'm looking for the name of (if it's been named).

It happens when you imagine what sort of evidence would support the position you want to take, and then prematurely assume from this that the evidence exists, and then use this spurious evidence to justify the original conclusion. For example:

  • I don't feel like doing laundry today. The machines are probably being used anyway. So I might as well wait until some day when they're free.
  • I don't want to to do anything to help the homeless. It's probably their own fault anyway. There's no point in rewarding such behavior.

Is this just a variety of "motivated reasoning" or "confirmation bias" or is there a more precise name for this specific variety?

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I suggest Imaginary Evidence Fallacy.

I would call it motivated scrutinity.

In policing, illegal search often finds something. A way to harass groups you don't like is to expose them to searches with less basis. Searching a lot means you find a lot of stuff, even if it is cost ineffective or you had no reason to expect to find anything. The injustice a citizen faces when under this weapon is attention when its unwarranted.

I see the core of the algortih of the bias as: Do I like A? If yes, accept with suspension of  curiousity. If no, inquire about things connected to A. This has a high chance of stopping at a desirable state without needing to fabricate a single fact.

The way to resist falling into this is that if you are doing a detailed analysis, you should be even handed to be intereested in everything relevant to that depth. Be curious about the no and the yes.

If they had bothered to find something to support their preferred conclusion, we could call it confirmation bias.

Lazy confirmation bias?

I notice that in notation form it’s just an extra ergo in the ordinary (p→q, p, ∴q) argument to yield (p→q, ∴p, ∴q). So maybe “ergotism” or “alter-ergo” for the name of the fallacy?