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Sometimes an entity's (be it a person, company, or a government) predictions/choices/decisions seem to be completely arbitrary (based on no evidence or observation).
A very colorful example of this is South Park's Margaritaville episode. When learning that a bank is going bankrupt, a board of judges or whatever decapitate a chicken, and throws its beheaded body into a pit divided into different areas with actions written on them, such as "Bail out", "Do nothing", "Pay $10000", "Sue", etc. The headless chicken runs around for a while until it finally drops motionless on one of the areas in the pit. The judges' verdict is based on where the dead chicken lands.
In Armenian we have an idiom "մատից հոտ քաշել", which literally means "to smell one's finger". Smelling one's finger, of course, does not give one any useful informations, so basing one's forecasts/choices on the "results" of smelling one's finger is completely random and arbitrary. For example, in Armenian one could say:
You can't trust the weather forecast. I think they simply smell their finger and come up with a prediction.
How does he know all this?
He doesn't, he just smelled his finger. (i.e. his claims are based on nothing)
or (in a maths class)
Teacher: Can a rational number raised to the power of an irrational number be a rational number?
Teacher: See, you have to prove it, you don't get to just smell your finger and answer yes or no.
Hopefully the South Park example and the մատից հոտ քաշել examples fully convey what situations I am talking about. So what idioms are there in English that can describe the arbitrary decision-making/choices?