In the first part, the two respective properties of the two definitions of chaaness you mentioned apply after rescaling and shifting of utility functions is done, right? I.e., the properties actually say "after rescaling and shifting the points, if you move the Pareto-frontier points for a player up, they should get more utility" and "untaken options are irrelevant if you don't change the scale after removing them". Now, I don't see why these properties are interesting and what they correspond to in real life. In contrast, if they applied before rescaling and shifting, then they would be quite interesting. So, can you please elaborate why they are interesting as they are and what they actually mean as they are?
In the first part, the two respective properties of the two definitions of chaaness you mentioned apply after rescaling and shifting of utility functions is done, right? I.e., the properties actually say "after rescaling and shifting the points, if you move the Pareto-frontier points for a player up, they should get more utility" and "untaken options are irrelevant if you don't change the scale after removing them". Now, I don't see why these properties are interesting and what they correspond to in real life. In contrast, if they applied before rescaling and shifting, then they would be quite interesting. So, can you please elaborate why they are interesting as they are and what they actually mean as they are?