Law School Discussion

Grouping Game Conditional Reasoning Question

Grouping Game Conditional Reasoning Question
« on: January 11, 2008, 01:15:41 PM »
Hi,

I seem to have some trouble with grouping games that have a lot of conditional reasoning (e.g. the birds in the forest game of Dec 2000). I think the main issues are that I have a hard time making the correct linkages between rules and inferences and then drawing inferences from those linkages. I've looked through the PS Bible dozens of times (including the explanation for the bird game), but every time I encounter these types of games, I still run out of time and get a good amount of questions wrong.

Does anyone have any good strategies for these games? 

Also, I guess for conditional reasoning, I'd just like to know that for a scenario like:

There are 3 groups -- 1, 2, and 3.
Rule 1: If A is in group 1, then B is in group 2.
Rule 2: If C is in Group 3, then neither A nor B is in Group 1.

So the contrapositive for Rule 1 would be: If B is not in group 2, then A is not in group 1. So, does that mean that if B is in group 3, then A could be in group 2 or 3 (unless there's a rule stating that A and B can never be together)?

And the contrapositive for Rule 2 would be: If either A or B is in group 1, then C is not in group 3. But what about if A and B are both in group 1? Is C still not in group 3?

And for a scenario with:

2 groups -- 1 and 2:
Rule: If C is not in group 2, then D is in group 1.

For this rule, could I diagram that with a double-not arrow? (e.g. C<---|--->D) Can I infer from this rule that they can never be in the same group together?

Does the "not" appearing in the sufficient or necessary condition of the conditional rule matter in diagramming?

Thanks, everyone!!

Re: Grouping Game Conditional Reasoning Question
« Reply #1 on: January 11, 2008, 05:03:00 PM »
thanks again, jeffort! that chaining device is really helpful. i've found a couple of other games where that really helps!

Re: Grouping Game Conditional Reasoning Question
« Reply #2 on: January 11, 2008, 08:26:57 PM »
Yes, the games that I found included the doctors at the two clinics (June 2001, LG#3) as well as the more recent LG from June 2006 for courses in a summer program.

Re: Grouping Game Conditional Reasoning Question
« Reply #3 on: January 12, 2008, 05:44:20 AM »
Quote
Do you find this technique to be usable in most grouping games?  Pure grouping games are usually the hardest for me, but I have never used chains like this. 

I am at a total loss about why you have trouble connecting multiple conditionals that have common conditions.

I don't mean this phrase towards you, but it is relevant.  "keep it simple stupid"

I do not have a problem doing it, I just never thought of doing these questions like this.  I just ran through the rules each time something changed, but this is obviously a better strategy. 

My main question was if this technique is usable in most grouping games.  The June 1996 has two grouping games that threw me for a loop and while I don't see the possibility of making chains as described in the thread you posted, graphing the possibility for each of the two constrained sets in the last game, FG and KM, instead of listing the rules separately will make things progress more quickly.

Re: Grouping Game Conditional Reasoning Question
« Reply #4 on: January 12, 2008, 06:31:40 AM »
Quote
Do you find this technique to be usable in most grouping games?  Pure grouping games are usually the hardest for me, but I have never used chains like this. 

I am at a total loss about why you have trouble connecting multiple conditionals that have common conditions.

I don't mean this phrase towards you, but it is relevant.  "keep it simple stupid"

I do not have a problem doing it, I just never thought of doing these questions like this.  I just ran through the rules each time something changed, but this is obviously a better strategy. 

My main question was if this technique is usable in most grouping games.  The June 1996 has two grouping games that threw me for a loop and while I don't see the possibility of making chains as described in the thread you posted, graphing the possibility for each of the two constrained sets in the last game, FG and KM, instead of listing the rules separately will make things progress more quickly.

Ok,

The last game of June '96 has a lot of linking going on., the third game on that test does not.

Last game:

P <--/--> F G <--/--> H

J <--/--> K M

Note that F&G will never be with K&M since it is 3 per group.


Of course, the rules can be written out differently:

[FG] ---> P & H

[KM] ---> J


Ok, that's pretty much how I went about solving that problem the second time through.  The only difference is that I diagrammed FG -> KMPH and KM -> FGJ and then listed the possibilities for each FG|JLN KM|FHLNP X|HJLNP  With 9 variables, well 7, I lose track of who is missing and listing the possible groups seems to help.