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The LB Bible recommends that you diagram the game as follows:

H __ __ __

G __ __ __

F __ __ __
R S T

Does this not seem a bit complicated?
What indication will tell me to graph it like this?

I naturally diagrammed the game like this:

__ __ __ __ __ __
f a f a f a
F G H

*the "f" and "a" stand for for/against.

What did everybody else do and why?

It appears the graphs aren't showing up as I thought, but you see what I mean.

I did it the way the logic game bible diagrams. You need to do it this way because certain bills have rules with them. Like in Rule 2 you have two people for a bill, with the diagram you have it would be very hard to see what bills are what.

You need to diagram in a grid like this when you have two sets, one of which must act on another.

John Cloe Bill will each go to the store and they will either buy a hotdog, chips, or drink.
Exactly two people will buy hot dogs
Each person will buy at least one item, but no one will buy all three
ect ect

H
C
D
J C B

When you have a grid you can quickly see which people buy hot dogs and know only two can have Y in the hot dog row, and you'll know that no one can have three Y in a column.