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“a confusion about preference orderings” by nostalgebraist

22 min • 11 maj 2025

Here's a confusion I have about preference orderings in decision theory.

Caveat: the observations I make below feel weirdly trivial to me, to the point that I feel wary of making a post about them at all; the specter of readers rolling their eyes and thinking "oh he's just talking about X in a really weird way" looms large in my mind as I type. It feels like I'm probably just unaware of some standard term or concept in the literature, which would make everything "snap into place" if I knew about it. If so, let me know.

diagrams

Let's say I draw something like this:

Here, the letters represent something like "world states," and an arrow like <span>_mathrm{A} rightarrow mathrm{C}_</span> means "C is preferred to A (by the 'agent' whose preferences this graph describes)."

For now I'm being hand-wavey about exactly what's being expressed here, but [...]

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Outline:

(00:41) diagrams

(02:28) preferred vs. accessible

(06:07) two readings

(08:48) preference cycles

(15:09) so what?

The original text contained 4 footnotes which were omitted from this narration.

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First published:
May 11th, 2025

Source:
https://www.lesswrong.com/posts/bEy3DKi9C3pJ4LpDW/a-confusion-about-preference-orderings