No, you are trying to have it both ways with your counter widget. (You want to spread that cost, even though it too will be in YOUR ROOM.)
The POINT of splitting utility costs, is that the cost per tenant is [total cost of building use] / [number of tenants]
Your argument has no bearing in the calculus as a result. They dont need to know about, see, or even have an inkling of the existence of that device in your room, for it to operate in exactly the way I specified. Here, I will work out some simplified example for you.
Lets say that without the widget, all tenants each use 100$ in electricity per period.
So, without the widget, the calculus looks like this:
100$ for tenant 1
100$ for tenant 2
100$ for tenant 3
100$ for tenant 4.
------------------------------
400$ building electricity fee
/
4 tenants
-------------------------------
100$ per tenant.
Now, we increase our costs to 103$, while theirs remains the same.
103$ (US)
100$ Tenant 2
100$ Tenant 3
100$ Tenant 4
------------------------
403$ building costs
-4$ savings from efficiency of widget
-------------------------
399$ building costs
/
4 tenants
--------------------------
99.75$ per tenant.
Unless of course, you are saying this widget does not run on electricity, which by the foundation of the scenario, is fungible. That is a specific you did NOT specify. The only kind of cost you specified was electrical. Your scenario is basically asking if it is a good idea to plug in an overunity device. The answer is yes.