What I meant by "diminish" is the reduction in value of something abstract.
The purpose of the principle is to set a standard of morality according to the promotion or __ of happiness among the individuals.
The blanks above should be filled with the noun of the verb "diminish".
Based on what I found on several sources on the internet, I found the noun: decrease & decline. But I cannot replace the blanks with "decrease" or "decline" because it seems to match in more concrete context such as numbers, graphs, etc. (If I don't sense it wrong).