[Avodah] Paying for a common wall

[Micha Berger]

Trying to figure out the sevara behind AhS CM 158:5 left me confused.
And since I have no chavrusah, I'm yet again trying it out on you.

Reuvein ends up with a churvah completely surrounded by Shimon's churvos.
Shimon build fences around three sides, since the 4 side is still open
to reshus harabim, Reuvein gets no utility and doesn't have to chip in.
However, when Shimon puts up the fourth wall and Re'uvein uses them in
some way (demonstrating a desire to have walls), R has to pay his share
of all four walls.

The part I don't get is the definition of "his share".

If Shimon's borders are 10x10, and Re'uvein's are 5x5, they divide by
area. Re'uvein has 1/4 of the total area (25 sq amos out of 100), so
I would have thought his fair share would be 25% of the price. But the
AhS says 1/8 -- apparently splitting by area, and then again splitting
into two shares.

That's the real problem I had.

I was also wondering why they're splitting based on utility rather
than avoided cost. IOW, why is it based on area guarded? Wouldn't
it make at least as much sense to divide the cost that Shimon saved
Reu'vein?

After all, someone who benefits your field without being asked is
paid the lesser of either the costs they invested or the value they
added to you. And the value would be the price of the fence around
R's 5x5 field.

So why is it divided by the ratio of their areas (divided by 2), rather
than by the ratio of their perimeters?

GCT!
-Micha

-- 
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