Logic Games: United Grouping Theory Flashcards
Undefined
The number of variables to be selected in an Undefined game is not fixed and is only limited by the total number of variables (lack of definition)
Defined
The exact number of variables to select is fixed in the scenario or rules
Partially-Defined
Minimum and/or maximum number of variables to be selected, but the exact number of variables selected can’t be determined
Moving
You will have a defined number of slots, but the spread of the slots can vary from situation to situation
Fixed
These are straightforward and they tell you the number of slots and how many slots per group
Uniform Variables
If the variables in the selection pool all have the same basic characteristics
You can move the variables where ever you want (of course adhering to rules) but there aren’t restrictions
Subdivided Variables
The selection pool is divided into specific sub-groups and each sub-group has a unique characteristic
Balanced
The number of variables selected is equal to the number of spaces available
Unbalanced
Number of variables to be selected IS NOT equal to the overall number (can be overloaded or underfunded)
Overloaded
There are extra candidates for the available spaces
Underfunded
There are not enough candidates for the available spaces (so most of the time, they say that multiple variables can be reused)
If X is selected, then Y is not selected
X <–I–> Y
Situations the Double-Not Arrow Covers
1) R is selected, H is not selected
2) H is selected, R is not selected
3) Neither R nor H are selected
X will be selected if and only if Y is selected
X <—-> Y
Situations the Double Arrow Covers
1) A and B both selected
2) Neither A nor B are selected
X will be selected if but only if Y is selected
X <—-> Y
X will be selected if yet only if Y is selected
X <—-> Y
Situations to use Blocks in Grouping Games
1) When working with diagrams that have vertical components
2) When diagramming rules that contain 3 or more variables in a positive or negative grouping relationship
3) Represent groups that must occupy a specified number of spaces
X and Y cannot be selected for the same team
X <–I–> Y
Restriction: Limited variable placement options
When a variable can only be placed into a limited number of places (split option for ex) the situation is inherently restricted and inferences result
Restriction: Restrictions on a space or spaces
When a single space or set of spaces has limited number of variables available for placement
Structural Limitations: Small Group Size
When one of the groups is relatively small, and sometimes this can be affected by rules
Two-Value Systems
Occurs in Defined, Balanced games where two groups have everyone assigned to them
If one variable isn’t in one group, it must be in the other, and you can make powerful inferences from those
Hurdle the Uncertainty
Certain spaces may be restricted for specific variables, but even though you diagram positive and negative relationships, you can still determine one space with one variable because of inferences
