Question: I want to write the following sentence in a compact way:

"The difference between the old scheme and the new scheme lies in..."

Which one of the following is correct?

1. The difference between the old and **new scheme** lies in...
2. The difference between the old and **new schemes** lies in...
3. The difference between the old and **the new scheme** lies in...
4. The difference between the old and **the new schemes** lies in...

Option 1 sounds more natural to me but I cannot explain why. More important, English is not my mother tongue. In other words, I would like to know:

* Is it necessary to repeat the definite article for each element of the list?
* Does the common object (in this case, the scheme) become plural when it is listed multiple times with different pre-modifiers (in this case, old and new)?

Answer: 
I would say that you do not require the last two articles, as neither is the focus of identification.

What is being identified is 'the' difference :

> 
> The difference between old and new schemes lies in ...
> 
> 
> 

---

It could be argued that this is an example of the zero article, that is to say the absent article regarding 'old' and 'new'. See elsewhere on this site for 'null' and 'zero' articles and for references to Peter Masters.

For example : [Should 'one' be considered an article ?](https://english.stackexchange.com/questions/425829/should-one-be-considered-an-article)
Replacing the premodifiers with less esoteric ones (and assuming that that does not affect the analysis too greatly): 

> 
> 0' *The difference between the old model and the new model* ...
> 
> 
> 

is the undeleted (part-) sentence, obviously correct for a single new model.

...........................................................................

Deleting the head noun only, firstly with no adjustment to the singular-form 'model' (deletions usually leave the remaining sentence unaltered): 

> 
> 3' *The difference between the old and the new model* ... gives 319 000 hits in a Google search
> 
> 
> 

while 

> 
> 4' *The difference between the old and the new models* ... gives 178 000 hits.
> 
> 
> 

While there is the clear possibility that 4' refers to more than one new model (and perhaps more than one old model), and that this is thus a poorer choice when just two models are being compared, the following from a [2017 Carvoy review](https://blog.carvoy.com/28-old-vs-new-lexus-rx350/) shows that the plural-form noun *is* used in such situations:

> 
> Although the 2017 version of the RX350 carried over all the things we
>  got to know and loved about the 2015 version, the main point of
>  difference between the old and the new models is the new safety and
>  technology features integrated into the new model.
> 
> 
> 

This compares with the totally grammatical 

> 
> 4" *The difference between the two models* ...
> 
> 
> 

So in summary, both forms are used, but there is a reasonable preference for 'model' here.

...........................................................................

Going further,

> 
> 1' *The difference between the old and new model* ... gives 269 000 hits 
> 
> 
> 

while

> 
> 2' *The difference between the old and new models* ... gives 156 000 hits.
> 
> 
> 

So both further-deleted forms also seem to be accepted by many. I'm surprised by the fact that 1' seems preferred to 2', as I feel 1' sounds incongruous.