Grouping Symbolizations

[Lina]

On page 190 of the LGB, the explanation to #5 states that the double not arrow is being used since there is no vertical element in the setup. Thanks for making the distinction above, to show the differnece between the linear game diagram block indicating adjacency and the grouping game diagram for association. I was a bit confused for the diagram to #2, because I diagrammed it using the double not arrow, with W on one end and XY on the other. I realize now that it would not necessarily be true. So is it when there are 3 or more variables that have a restriction, we use the linear game block diagram?

Thanks for your help!

[David Boyle]

On page 190 of the LGB, the explanation to #5 states that the double not arrow is being used since there is no vertical element in the setup. Thanks for making the distinction above, to show the differnece between the linear game diagram block indicating adjacency and the grouping game diagram for association. I was a bit confused for the diagram to #2, because I diagrammed it using the double not arrow, with W on one end and XY on the other. I realize now that it would not necessarily be true. So is it when there are 3 or more variables that have a restriction, we use the linear game block diagram?

Thanks for your help!

Hello Lina,

It does seem a little confusing maybe. --As for your last sentence: the book notes on p. 188, I think, under observation #2, that a block with three or more variables can (or should) be diagrammed in a block. There is a good common-sense reason for this, i.e., if you use arrows, how would you diagram three variables or more at a time? With just two elements, there's the double not-arrow, which clearly and obviously shows that two variables don't like each other. But with three elements, how would you use arrows to signify that A could go with B, B with C, and A with C, but not all three at the same time? It could be visually confusing and difficult. So a block is a better symbol to use for three variables or more.
Hope that helps,

David

[Lina]

Thanks David. In reviewing your response and the section on Diagramming the Groups- it is much clearer. I was confused by the difference of how diagrams are set up for one group (9 candidates for a 5 person group) versus 2 or more groups, where the symbols change for this vertical setup. For the horizontal groups, I didnt know why blocks used to symbolize adjacency in linear games would not work, and why the double not arrow is not used in vertical set ups. I will do some practice problems and test my understanding. If you have any clearer ways of making these set ups distinctive for me, that would be helpful.

[Jason Schultz]

Hi Lina.

I was confused by the difference of how diagrams are set up for one group (9 candidates for a 5 person group) versus 2 or more groups, where the symbols change for this vertical setup.

The symbols do not change when you go from a vertical to a horizontal setup, but the orientation of them should change. Otherwise, you run the risk of conveying the wrong information. For example, imagine you have a game where 9 people are being assigned to apartments in a 5 floor building. Now take your post:

For the horizontal groups, I didnt know why blocks used to symbolize adjacency in linear games would not work,

Since you have a vertical setup, if a rule came along that said "A cannot live immediately above B", then a horizontal block [A/B] would show the wrong rule: that A could not live on the same floor as B. To properly convey what the rule is saying, you would need to orient the block vertically.

and why the double not arrow is not used in vertical set ups

It also can be, but again should be oriented along the same axis as your diagram.