That's not helping me at all.
In order to help you, I have to know what you need help doing.
I know the fact value distinction.
You suggested political values (which I'm re-interpreting as either "value" or "policy preference") presuppose facts. I think our definition of "value" must diverge if that is what you think is the case, and assume you are referring to policy preferences instead.
I'm asking for specific examples so I can understand how you personally apply that.
I'm not sure what you're asking for examples of, but here are some of my values:
Honesty. Correctness. Efficiency.
Here are some of my policy preferences:
Free speech (including lies or simple wrongness). Bodily autonomy (including abortion, drug usage, and sexuality). Market autonomy (that is, what is commonly referred to as capitalism).
The underlying axiom underneath my policy preferences is autonomy and self-responsibility. My central personal value is integrity.
Here is a new paper of mine (12 pages) on suspicious agreement between belief and values. The idea is that if your empirical beliefs systematically support your values, then that is evidence that you arrived at those beliefs through a biased belief-forming process. This is especially so if those beliefs concern propositions which aren’t probabilistically correlated with each other, I argue.
I have previously written several LW posts on these kinds of arguments (here and here; see also mine and ClearerThinking’s political bias test) but here the analysis is more thorough. See also Thrasymachus' recent post on the same theme.