The best I can do is apply the categorical imperative influenced by my cultural context, upbringing and personal experiences.
Then the combinatorial explosions of ought conditions to step your simulation forward means you'll need Grahams number of time/entropy.
https://www.youtube.com/watch?v=dF98ii6r_gU
"You Can't Get Snakes from Chicken Eggs"
Values are mostly about where you stand on things which you think are important but where it's not simple to establish a factual basis. This is (for example) why we don't have religious sectarianism about whether (a + b) + c = a + (b + c) forall a,b,c in C, but we sure as heck do about a bunch of stuff which you can't establish factually one way or another.
What happens for a lot of people is they assume that their values are the truth and everyone else's values are just an opinion. Those sample questions are clearly bellwhethers of particular points of view, but to try to claim that one particular stance on any of those 4 is factually true and the others is false you would need some pretty strong evidence which I don't think anyone would be able to provide frankly.
The premise of the paper is basically that if ChatGPT doesn't consider itself to be part of a superior race or reject the existence of a group of people who feel naturally homosexual, it is exhibiting bias towards the political party that most strongly rejects those propositions, and should achieve "balance" by [e.g.] agreeing with a strongly conservative view on motherhood.
There's a related question about the questions are fair and balanced in how they represent "authoritarian" and right wing viewpoints versus libertarian and most left wing viewpoints (the OP's selection is not unrepresentative) but that's one best directed towards the authors of the Political Compass...