Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Balanced game.

The game scenario establishes that six law students are divided into three trial teams of exactly two students each, a Defined-Fixed situation. Because each student is on exactly one of the teams, this game is also Balanced, and thus as each law student is placed, he or she can be eliminated from further placement consideration.

Although the numbering of the teams does not introduce a linear element, within each team there are different tasks: preparing an opening argument and preparing a final argument. Thus, the setup must account for these differing tasks within each group. With this consideration in mind, the initial setup appears as:

PT55-Oct2008_LGE-G1_srd1.png

With the basic structure of the setup in place, we can consider each rule.

Rule #1. This rule establishes that M is always paired with either G or V, creating a vertical block:

PT55-Oct2008_LGE-G1_srd2.png

However, the rule contains no specification as to which task M performs. Thus, M could prepare either the opening argument or the final argument. This could be represented either by drawing a second block that is flipped, or by using the circle notation indicating a rotating block:

PT55-Oct2008_LGE-G1_srd3.png

Operationally, because M must always be paired with G or V, M cannot be assigned to a team with any other law student. And, because one of G or V must always be teamed with M, G and V cannot be assigned to a team together.

PT55-Oct2008_LGE-G1_srd4.png

Rule #2. This rule specifies that L must prepare an opening argument and thus cannot prepare a final argument. The best representation for this rule is an L Side Not Law on the final argument row:

PT55-Oct2008_LGE-G1_srd5.png

Rule #3. This rule indicates that G or R, but not both, prepare a final argument. Because at least one must prepare a final argument but both cannot, the other must prepare an opening argument. Thus, one of G and R is always preparing a final argument, and the other prepares an opening argument. This is a difficult rule to show, but one method is to use side arrows to show the variables that are in play in each row:

PT55-Oct2008_LGE-G1_srd6.png

This representation reveals that the opening argument row is two-thirds full because L must prepare an opening argument, and the remainder of R and G must also prepare an opening argument. Thus, we can infer that if another law student prepares an opening argument, all remaining unassigned law students would have to then prepare a final argument.

This rule also links to the first rule through G, but there is no immediate inference that can be drawn from pairing the two rules.

Final Setup Thoughts: because S does not appear in any of the rules, S is a random. This leads to a final setup of:

PT55-Oct2008_LGE-G1_srd7.png

To explore a different vein of thinking about the setup, a review of the rules reveals that the team numbers do not play a role in any of the rules, and they also do not play a role in any of the questions (except question #1, which is a basic List question where team numbers could change with no effect). Thus, the team numbers do not have a linear function in this game, and the three groups could easily be nameless. As such, one approach to creating a final setup is to disregard the numbering of the teams and simply treat the teams as equal groups. This approach allows us to then place L into one of the groups as preparing the opening statement, and the R/G dual option into another group as the opening statement. The remainder of the R/G dual option cannot be placed as a final argument as it cannot be determined which law student G or R would be paired with. These decisions allow us to reach an alternate final diagram for the game:

PT55-Oct2008_LGE-G1_srd8.png

Note that in using this diagram you must understand that L does not have to be on team 1 (and thus answer choice (D) cannot be eliminated in question #1). Rather, L is simply occupying a space on one of the three teams, and since the numbers have no operational value, we have arbitrarily assigned L to team 1. If this concept confuses you, either eliminate the team numbers or instead use the prior final diagram.

[Patrick.a.anderson]

What is the most efficient approach for this game? Do you recommend creating templates? Or, making a general diagram and diving into the questions. It took me much more time than I anticipated. If possible, can you explain your diagram/inferences made?

[Jon Denning]

Hey Patrick - thanks for the question. I didn't use a template here, as I didn't find it necessary. To me this is just a Balanced Grouping game where you must create three teams with a spot for opening and closing on each, and then assign the six people into those six spaces based on the rules: M must be with G or V, L prepares an opening arg, and either G or R will prepare a final arg with the other preparing opening. So I had my six-spot setup with O and F indicating the bottom and top row, respectively, a block for M and G/V, and then beside O I put "L, R/G" (since L and R/G must fill 2 of the 3 Opening spots), and beside F I put "G/R" (since G/R will fill 1 of the 3 Final spots). Note that the team number (1, 2, or 3) is completely arbitrary, as this is just grouping and there's no "order" or linearity. For instance, putting L on the first, second, or third team is irrelevant, so long as L gives an Opening argument and is paired with someone appropriately.

I think a lot of people at this point get stuck looking for further inferences and, as I imagine you did, end up taking far too long before moving to the questions. And I can see why. The scenario I described above isn't terribly "complete' in terms of what you've been able to place definitively, but unfortunately this game, like many games, just doesn't allow for a lot of certainty in your setup. So once you've established your setup and feel that you're beginning to hunt for inferences fruitlessly, trust the truth you've been able to represent up to that point and move confidently to the questions. If there's an important inference you've missed chances are very good one of the questions will reveal it to you and you can update your initial setup accordingly while also collecting points for getting that question correct.

Hope that helps!

Jon

[SGD2021]

Hello,

Why is it that in this game we can treat the Team numbers (team 1, 2, and 3) as arbitrary? How would we know in any other future grouping game when one of the types of groups (I am assuming there are two types of groups in this game: (1) Team 1, 2, or 3 and (2) O or F) can be treated as arbitrary?

Do we care more about the O and F groups since the rules are mainly about them?

Also, would a setup like this also work for this game: (with O and F) under the slots in each row
Team 1: ___ ___
Team 2: ___ ___
Team 3: ___ ___
O F

[Robert Carroll]

SGD2021,

The team numbers are arbitrary because neither the scenario nor the rules says anything specific about one of the teams. Each team is 2 students. Each team has an opening and a final argument. The rules say nothing about any team number. So any assignment of students to teams that works would work regardless of which numbered team each student was on. Thus, the teams are interchangeable. You'll see this in any similar situation where the groups have no distinguishing features.

I wouldn't call "O" and "F" groups, but since the team numbers, as noted above, have nothing specific about them, whereas the F and O slots in each group do have rules and inferences, you'll be doing more work with the F and O rows than with the groups themselves, at least globally.

Your setup is perfectly fine. It's entirely arbitrary which dimension is used for the groups and which for the F and O element.

Robert Carroll

[SGD2021]

Thank you very much! Also, why can we not read this line: "each student prepares exactly one of either the opening or the final arg. for his team" as meaning that it's possible for there to be two opening's in a single team? Is it simply bc of common sense that we assume each team must have only one opening and one closing?

[Adam Tyson]

That, and also the way the scenario describes the situation:

Each student prepares exactly one of either the opening argument or the final argument for his or her team.

"The" opening or "the" final argument - that means that there is one of each. It might be different if the scenario had said each students prepares "an" opening or "a" final argument, because that would not necessarily indicate that an opening must be presented. So it's more than common sense; it's built into the rules of the English language here!