Diagramming Conditional Rules

[ToadKing]

Hi,

For conditional rules, I usually diagram as follows:

SCENARIO:
A, B, C, and D are working at a store.
(1) If A works, B does not
(2) If B works, then C does not
(3) If D works, then (A) does not

MY DIAGRAM:
A: A ~B + ~D
B: B ~A + ~C
C: C ~B
D: D ~A

I like using my method most of the time. However, whenever there is a question like "what is the maximum amount of people who can work at a given time?" my diagram is a bit lackluster

Recently, I noticed that some people diagram by combining all the rules together to great two cohesive diagrams which accounts for all of the rules/contrapositives. I tried this method and it worked really well on PT58 Game 2 (Daycare), but on PT58 Game 3 (Summer Sessions) my diagram didn't work out because rule (3) wouldn't fit neatly into the existing rules. I am wondering whether there is a way to know if this latter method works before diagramming or not? Or should I just stick to my normal method? My only reason for trying method 2 is to save extra time but I am not currently having problems with finishing the section.

Thanks for the help!

[Dave Killoran]

Hi Toad,

Thanks for the message! The method you are using there is not unreasonable, but there are going to be times when it causes a lot of confusion and loses you time during the setup. Essentially, you are isolating each variable and then looking at what occurs with it. With four variables, that's not so bad, but with six or more variables it becomes both time-consuming and less and less clear.

As a counterpoint, I'd diagram your rules as follows:

• A B
  
  B C
  
  A D

This minimizes the number of representations but maximizes the info each imparts. It also eliminates redundancy, for example one diagram tells me the relationship between B and C from each side, instead of having to separate it out into two statements. Note that using the is key since it's a "super statement" that helps you avoid writing out each statement and it's contrapositive, a practice that I am often against (except when it's a very complicated statement or in a two-value system). It also still allows you to easily see that A and B are the two most powerful variables, and C and D are less so. It's the system that is the most concise yet retains all the power of writing out every variation, and is the system I've seen work the best over hundreds of games (and I say that after trialing multiple tweaks and alterations, such as the one you currently use).

Please let me know if that helps. Thanks!

[ToadKing]

Yes! Thank you for the help. I will keep trying it to make sure that I get comfortable with it!