Preference of "cheaper and more efficient" over "more efficient and cheaper"

Would "cheaper and more efficient" be ever so slightly preferred over "more efficient and cheaper"? The same goes with "more", and any other pair/group of comparatives, of which one uses "more" or "less" while the other doesn't.

My intuition favours the former to totally eliminate any possibility or relation made between "less" or "more" and the other comparative it is not meant to describe, although I acknowledge that ambiguity is not a concern, and even in my daily life I use both naturally. How much preference do you think should be given to the former, if it should be given any at all?

In addition, what would be the appropriate term for this? My first guess was "order of comparatives", but that didn't yield any results on Google.

(Some other examples: "Slower and less alert" instead of "less alert and slower" and "Chaster/holier and less sinful" instead of "less sinful and chaster/holier") Thanks for reading this! :)

While choosing between 'cheaper and more efficient' and 'more efficient and cheaper' you are basically right to "favour the former to totally eliminate any possibility or relation made between 'less' or 'more' and the other comparative it is not meant to describe".

It is generally understood that in a sentence such as

they were more enthusiastic and helpful after they heard the details of the project

the 'more' is supposed by most readers to apply to both 'enthusiastic' and 'helpful.' If for some reason you intend 'more' to apply only to 'enthusiastic' then for perfect clarity you would have to rewrite it as

they were helpful and more enthusiastic after they heard the details of the project

But in your example, the 'more' or 'less' could not apply to words like 'cheaper' or 'slower' because they are already in the comparative form and 'more cheaper' is usually ungrammatical. (Debatable example of possible exception: "Site A quoted a high price for this product. Prices on Sites B and C are cheaper, of which the prices on Site C are more cheaper! I need to look at Site D to know which site is quoting the cheapest price." Note: As pointed out by OP in comments, "even cheaper" is the accepted usage rather than the debatable 'more cheaper.' Further, 'lowest price' may be the more typical expression but 'cheapest price' is commonly used here in Indian English.)

I cannot think of any rule, however, that insists 'cheaper' should always come before 'more efficient' -- but that's the way it is usually found written, and it does sound much better: therefore I suppose it's a matter of style!

Which led me to this very similar question and some very interesting responses that perceptively discuss both the grammar and the style of your matter:

https://www.puritanboard.com/threads/english-grammar-help-comparative-adjectives.46364/