Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear Game: Balanced, Identify the Templates.

This is an Advanced Linear game with four variables sets: the three bills, R, S, and T; the three votes of Fu; the three votes of Gianola; and the three votes of Herstein. Notably, either the three bills or the three voters could be chosen as the base. Operationally they will produce no difference. We have chosen to use the three bills as the base and create stacks for Fu, Gianola, and Herstein:

pt28_j99_g4_1.png

The choice of voting for (F) or against (A) will fill each space. Applying the rules creates the following basic diagram:

pt28_j99_g4_2.png

The rules provide a considerable amount of specific information: the number of “for” and “against” votes each bill receives; the minimum “for” and “against” votes by Fu, Gianola, and Herstein; and certain votes each voter casts. From the supplied information several inferences can be made. First, since there are two votes for the Recreation bill and one vote against the Recreation bill, and it has already been established that Fu votes for the bill and Gianola votes against the bill, it can be inferred that Herstein votes for the Recreation bill:

pt28_j99_g4_3.png

Furthermore, since only two voting options exist (F or A), dual-options can be placed on the remaining open spaces:

pt28_j99_g4_4.png

Of course, further information about some of the dual-options would affect the choices in other dual-options. Regardless, examining the diagram makes it apparent that the voting possibilities are limited. Since there are only four uncertain spaces and even those have restrictions, why not try to show every possibility? Although there are several ways to identify each possibility, the first step we will take is to look at the votes for the school bill. If Gianola votes against the school bill and Herstein votes for the school bill, only one solution exists:

pt28_j99_g4_5.png

In the diagram above, Gianola must vote for the tax bill since each council member votes for at least one bill; since there must be two votes against the tax bill, it can then be inferred that Fu votes against the tax bill.

The other scenario with the school bill switches the votes of Gianola and Herstein:

pt28_j99_g4_6.png

Unfortunately, this information does not completely determine the votes of Fu and Gianola on the tax bill. One must vote for the bill and the other must vote against. Since this produces only two scenarios, show each one:

pt28_j99_g4_7.png

Thus, since all the options for the school bill have been explored, it follows that all the options for the entire voting record have been explored. These three solutions comprise the final setup to the game:

pt28_j99_g4_8.png

With all of the possibilities fully realized, the questions can be destroyed at light speed.

[tmaksimenko]

What is the best way to set up this game?

[Jon Denning]

Thanks for the question. It might help for us to know how you went about setting up so we can see how you approached it and what we can do to refine that process...can you let us know exactly what approach you took?

Thanks!

[tmaksimenko]

I set up the council members as the base for the game (F G H) and on the side I had "for" and "against" and then I placed the bills. The game worked, but it just took me a really long time, so I'm just wondering if there was a way that I could have set it up to make it easier? Should I have had the bills as the base and placed members? What should have tipped me off as to how to set up this game?

[Jon Denning]

Gotcha! I actually set this game up with the three bills as a base and the three voters to the side producing a 3 x 3 (nine space) grid, where for each voter on each bill I put either F or A (for or against). Of course, you could swap those and have the voters on the bottom and the bills creating three spaces above each voter, too. It makes no difference. What's great about this setup is that not only can a lot of the spaces be filled in definitively, but even the uncertain spaces are then just dual-options with F/A.

Further, once you've filled in all that you can know with certainty--R is F A F for H, G, F; S is A for F; T is A for H--you can see that there are only four unknown spaces, and even those have restrictions. So I took this to its logical conclusion and wrote out all of the possibilities, of which there are only three:

1. H is For S and G is Against S, with G For T and F Against T (G must have at least one For vote, and in this case it would have to be T)

2. H is Against S and G is For S, with G For T and F Against T

3. H is Against S and G is For S, with G Against T and F For T

Set up the grid the way I've described it above and consider those possibilities. With that setup this game is very, very easy and the questions are essentially already answered. Go back and take a look and let me know if that helps!

[Georgewashington]

Can't I just set this game up using not laws instead of "A" and "F" to denote for and against? RST as the base, two slots at R, one at S, one at T. Votes for the bills would go in the slots. Votes against the bills would go under RST as not laws. This worked perfectly fine for me. Why does the Bible disagree?

[Jon Denning]

Hey George,

Thanks for the question and welcome to the Forum! You can absolutely set it up the way you've described! In fact, I just went back through it with a setup like the one below (I think this is how you've done it) and it worked beautifully (pardon the slightly awkward alignment):

H
F G/H F/G
R S T
G F H

Where the letters (F, G, H) above each bill (R, S, T) represent a vote for it, and those below represent against.

This is simply an instance where there are multiple ways to represent the situation described, with none being far and away superior. I made a choice to do it the way I described above primarily because (1) that's just how it occurred to me to do it, and (2) it allowed for three easy templates. But your way works well and would allow for the same templates if you felt like showing them (although I don't think you need to). I certainly wouldn't say the Bible (or in this case, just me) disagrees; rather they're merely two alternative and entirely valid methods of attack. So nicely done!

[DlarehAtsok]

In the book, this game was treated as an Advanced Linear one with three levels of stacks. How about a three-selection grouping game, defined-fixed and underfunded? You avoid those F and A, which can be distracting, especially since one of the variables is called F?

[Adam Tyson]

It's true that there is nothing linear about this game - no before and after, no higher and lower, etc. We tend to treat a lot of games as "advanced linear" that don't have a linear element, if the classic advanced linear setup approach works best (multiple stacks on a base). I don't see how you can avoid the two F's (For and Fu), and that's an unusual situation on the LSAT. You have to determine how Fu votes on each of the three bills, and the votes are either For or Against. So, whether you call it Grouping or Linear won't really matter - what matters is that you set it up in a way that allows you capture all the essential parts.

It's important to note that we at PowerScore are never saying that our way is the only way to set up a game or analyze a question or passage, although we tend to think it's the best way. What we are about is providing you with what we think are the best tools we can provide to attack the job of writing the LSAT. Once we've given you those tools, it's up to you to decide which ones to use and how to use them. If you have other tools, either from some of our excellent competitors or from your own intuition, you should of course keep those in your tool belt and use them when and how you like. The point is for you to have whatever you need to get the job done, and we are just happy to have the chance to help you along the way.

So, if you see another way to do this or any game, and it works better for you than what we have suggested, all we ask is two things: first, share your ideas with us (because we are always learning, too, and we might be able to use your ideas to help other students); and second, use that method in good health and crush the test!

Now, having said all that, would you be willing to show us how you would set this up as a Grouping game the way you've described? I'll admit to possibly being stuck in my rut - every time I try to visualize this game, I keep coming back to the same setup. Your description sounds accurate to me, but I just can't seem to translate it into a different diagram.

Thank you in advance!

[DlarehAtsok]

Sure . So, since you know how many people will vote for and against each group, you can visualize a defined-fixed grouping game, with R,S, and T being the groups, and respectively having 2-1-1 elements. We only have three variables (F,H,G), which must be used at least once (one for), but not more than twice (each has to be against some bill). Given the other rules, we do not have to worry about the latter, as G is not in R, F is not in S, and H is not in T. Recreation group is already filled with H and F, so we do not have to worry about it. S group must have either a G or a H, and T group must have either a F or a G. The only thing that we have to keep in mind is that G must be at least in one of these groups (as we need an affirmative for each variable). In the end, you will still have only three possibilities left (like in the book), but you could avoid all those F and A.