Re: Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Moving, Balanced, Numerical Distribution game.

One popular approach to this game is to use the seven judges as the base. While this approach can work, separating the judges into the For and Against groups is more effective, in part because it turns the game into a two-value system, which has a dramatic effect on the contrapositive of several rules, and in part because it better captures the fact that there are at least two judges in each group. Remember, always look to first establish the composition of the groups in any game. In this case, because each group has at least two votes, there are two unfixed numerical distributions in operation: 5-2 and 4-3.

The only way to track the variables in the rules is to use subscripts indicating which way each judge voted.

The key inference to this game is that at least one L must vote for Datalog because all three cannot vote against Datalog. If all three L’s attempted to vote against Datalog, then both C’s would have to vote for Datalog, which is impossible according to the given rules.

Once it has been established that at least one L must vote for Datalog, this information can be applied to the other rules and it can be inferred that when the CCL block occurs it must occur on the Against side, and also that when the LLL block occurs it must occur on the For side. This understanding helps eliminate some of the uncertainty that initially appears to be present in this difficult game.

The LLL rule yields an interesting inference via the contrapositive, that if one C votes for Datalog, then at least one L votes against Datalog. This inference is largely useless in the game.

F93_Game_#3_setup_diagram 1.png

[rameday]

So i had a massive problem setting up this game. I did C,M,L as my base which I see from the back of the book that you aren't supposed to do. I also have no idea how this game works.

What do you do if faced with a game like this, when even after going through the answer sheet you are still incredibly lost.

A

[KelseyWoods]

Hi A!

I'm a little confused....where did you get C,M,L as your base? Are you talking about the October 2003 game with the finance committee and the incentives committee on page 5-110? Or do you mean the game from February 1993 on page 5-108 with the judges who are conservative, moderate or liberal?

Please advise and I'll be happy to help you out!

Best,
Kelsey

[rameday]

Ooops typo. Yes I mean't the latter. The game with the judges.

[KelseyWoods]

Hi A,

Okay! When you choose your base for a Grouping game, you should choose what you have the most information about based on your scenario and rules. In this case, you really had two options. You could use the seven judges (CCMMLLL) as your base, or you could use the For and Against votes. Neither way is wrong, per se. It's just easier to make some inferences and to represent the 3rd rule if you use the two group approach.

To help you see this, try to do the game again, this time using the For and Against votes as your base and see how the setup goes and how the questions go.

When you don't fully understand the explanation of a game in the back, try the game again, incorporating some of the setup suggestions and see what else you can figure out on your own. It's often much easier to fully understand a game if you try to work through it and figure out how to get to some of the inferences and/or answers on your own rather than just reading the explanation.

So give it a try now that you know F & A make a great base and let us know how it goes the second time through!

Hope this helps!

Best,
Kelsey

[nicolle828]

I'm a bit concerned because when I did my initial diagram, I missed the inference that three Liberals could not vote against due to the rule that if three Liberals voted the same way then no Conservative could vote that way and there was already a Conservative in the against column. Is there a hint to avoid a mistake like that?

[Dave Killoran]

Hi Nicolle,

One thing I always do it match rules with each other based on a common variable. That's a type of linkage, of course, but it makes sure you that your chances of missing an inference like this are as low as possible.

The other thing that happens is that—like a lot of inferences—once you get into making your first hypothetical, you will see the inference pretty quickly thereafter. It's one of the reasons that missing inferences is often not fatal in a game (although it does cost lost time which is a problem; better to see it beforehand, obviously).

Please let me know if that helps. Thanks!

[oktos92]

Hello,

Thank you for the previous explanations on this question. It really helped so far in better understanding the best approach to solve this game set. However, I will like to clarify the confusion I experienced while approaching this question the first time: When I first saw this question, I decided to make C, M, L the base and drew two bars above C, two bars above M and three bars above L. I was trying to follow the principle that I should choose as my base what I have the most information about based on the scenario and rules. Why does it seem as if this principle is not directly working here or am I the one making a mistake?

Aanu

[BethRibet]

Hi Aanu,

Thanks for writing. With grouping games, it's not a given that you'll always have a base, as you would with a linear game.

For this game, your "groups" are basically: For Datalog, and Against Datalog. And what you know is that each group has a minimum of two votes, and at least one conservative voted against Datalog. The other two rules are conditional, so I would basically put in a little time to diagram out the possibilities with rule 1 and rule 2.

For instance, Rule 1 is totally determined. If you've got both conservatives and one liberal voted the same way, we know they voted against, because there are only two conservatives, and one must vote against. The rule tells us the moderates must vote with them, which accounts for five votes. Since each group must have at least two votes, we know the remaining two liberals voted for. Like this:

Against For
CCLMM LL

You can map out rule 2 similarly, and if you want to be exhaustive, you can also map out possibilities if the conditions are not met for either Rule 1 or Rule 2.

Hope this helps!
Beth

[Mike13]

Hi,

I am currently working my way through the on demand course and haven't gotten to the lesson on numerical distribution yet, so hopefully I will get better after that. But, I was working on this problem in the homework for section 5 of the course and and just completely confused.

I don't understand how one would get to the "key inference" that is below. I think I have re-read this problem 20 times and can't understand how you figure out that one L must vote for Datalog and 2 against it. Why couldn't you have all three liberals vote for the proposal and the 2 conservatives against it? Wouldn't that still comply with the rules?

Thanks for the help!

- Mike