It seems very normal to expect that the rule will be more restrictive or arithmetic in nature. But if I am supposed to be sure of the rule, then I need to test more than just a few possibilities. Priors are definitely involved here.
Part of the problem is that we are trained like Monkeys to make decisions on underspecified problems of this form all the time. I’ve hardly ever seen a “guess the next [number|letter|item] in the sequence problem that didn’t have multiple answers. But most of them have at least one answer that feels “right” in the sense of being simplest, most elegant or most obvious or within typical bounds given basic assumptions about problems of that type.
I’m the sort of accuracy-minded prick who would keep testing until he was very close to certain what the rule was, and would probably take forever.
An interesting version of this phenomenon is the game: “Bang! Who’s dead”. one person starts the game, says “Bang!”, and some number of people are metaphorically dead, based on a rule that the other participants are supposed to figure out (which is, AFAIK, the same every time, but I’m not saying it here). The only information that the starter will give is who is dead each time.
Took me forever to solve this, because I tend to have a much weaker version of the bias you consider here. But realistically, most of my mates solved this game much faster than I did. I suspect that this “jump to conclusions” bias is useful in many situations.
It seems very normal to expect that the rule will be more restrictive or arithmetic in nature. But if I am supposed to be sure of the rule, then I need to test more than just a few possibilities. Priors are definitely involved here.
Part of the problem is that we are trained like Monkeys to make decisions on underspecified problems of this form all the time. I’ve hardly ever seen a “guess the next [number|letter|item] in the sequence problem that didn’t have multiple answers. But most of them have at least one answer that feels “right” in the sense of being simplest, most elegant or most obvious or within typical bounds given basic assumptions about problems of that type.
I’m the sort of accuracy-minded prick who would keep testing until he was very close to certain what the rule was, and would probably take forever.
An interesting version of this phenomenon is the game: “Bang! Who’s dead”. one person starts the game, says “Bang!”, and some number of people are metaphorically dead, based on a rule that the other participants are supposed to figure out (which is, AFAIK, the same every time, but I’m not saying it here). The only information that the starter will give is who is dead each time.
Took me forever to solve this, because I tend to have a much weaker version of the bias you consider here. But realistically, most of my mates solved this game much faster than I did. I suspect that this “jump to conclusions” bias is useful in many situations.