- PowerScore Staff
- Posts: 8950
- Joined: Feb 02, 2011
- Mon Jun 06, 2016 10:57 am
#26185
Setup and Rule Diagram Explanation
This is a Linear/Grouping Combination game.
The game scenario asks us to determine the annual bonuses for seven employees. Each employee receives a bonus in the amount of $1k, $3k, or $5k, and each belongs to one of two departments—Finance and Graphics:
Since the bonus amounts have an inherent sense of order, it is best to use them as our base. This creates a Linear/Grouping setup, in which each of seven variables is being assigned to one of three groups. Because each employee must receive exactly one bonus, the game is Balanced. However, since the number of employees receiving each bonus amount is left unclear, the game is Defined-Moving.
Logically speaking, either variable set—the employees or the bonus amounts—can be used as the grouping base. In fact, the answers to the List question use the employees as the base. So, is this a good enough reason to revise your setup? Probably not. Since the bonuses have an inherent sense of order but the employees do not, it would be far easier to represent the implications of the rules if the order were inherent to your base, not to your variable set. Using the employees as your choice of base is not necessarily a mistake, but it is probably less efficient in the long run.
With the basic structure in place, let us now turn to the rules.
The first rule establishes that no one in the Graphics department receives a $1k bonus. This rule creates three Not Laws:
In a highly unusual gesture, the second rule introduces an entirely new conceptual element into the game: apparently, some employees are rated Highly Effective and others are not, which affects the bonuses they can (and cannot) receive. Rules like these are precisely why we urge you to read the entire rule set before diagramming your game. Otherwise, rules like these can easily catch you off-guard.
According to the second rule, any employee who is rated Highly Effective receives a higher bonus than anyone in his or her department who is not rated Highly Effective. Note that the rule does not allow us to compare the bonuses of employees from different departments: it is specifically limited to those working in the same department:
The last rule states that only L, M, and X are rated as Highly Effective. We can use the “HE” subscript to represent this information, or simply circle each HE variable, as shown below:
You should immediately tie the second and third rules together. Since only L and M are rated Highly Effective in Finance, their bonuses must be higher than those of K and P:
Clearly, then, neither L nor M can receive a $1k bonus. Likewise, neither K nor P can receive a $5k bonus. This generates four additional Not Laws:
By the same logic, since only X is rated Highly Effective in Graphics, his bonus must be higher than the bonuses received by V and Z:
Consequently, neither V nor Z can receive a $5k bonus. But, thanks to the first rule, neither of them can receive a $1k bonus either. It follows that V and Z must receive $3k bonuses, whereas X must receive a $5k bonus:
Is it worth representing the Fixed Numerical Distributions that govern the assignment of employees to bonuses? Well, the game does not explicitly mandate a minimum number of employees per bonus, and the rules are not restrictive enough to establish such a minimum for the $1k group. If something seems too laborious, it probably is: a detailed analysis of each distribution is neither required nor encouraged. A far simpler—and probably more useful—task would be to determine the minimum and the maximum number of employees who can receive each bonus:
This is a Linear/Grouping Combination game.
The game scenario asks us to determine the annual bonuses for seven employees. Each employee receives a bonus in the amount of $1k, $3k, or $5k, and each belongs to one of two departments—Finance and Graphics:
Since the bonus amounts have an inherent sense of order, it is best to use them as our base. This creates a Linear/Grouping setup, in which each of seven variables is being assigned to one of three groups. Because each employee must receive exactly one bonus, the game is Balanced. However, since the number of employees receiving each bonus amount is left unclear, the game is Defined-Moving.
Logically speaking, either variable set—the employees or the bonus amounts—can be used as the grouping base. In fact, the answers to the List question use the employees as the base. So, is this a good enough reason to revise your setup? Probably not. Since the bonuses have an inherent sense of order but the employees do not, it would be far easier to represent the implications of the rules if the order were inherent to your base, not to your variable set. Using the employees as your choice of base is not necessarily a mistake, but it is probably less efficient in the long run.
With the basic structure in place, let us now turn to the rules.
The first rule establishes that no one in the Graphics department receives a $1k bonus. This rule creates three Not Laws:
In a highly unusual gesture, the second rule introduces an entirely new conceptual element into the game: apparently, some employees are rated Highly Effective and others are not, which affects the bonuses they can (and cannot) receive. Rules like these are precisely why we urge you to read the entire rule set before diagramming your game. Otherwise, rules like these can easily catch you off-guard.
According to the second rule, any employee who is rated Highly Effective receives a higher bonus than anyone in his or her department who is not rated Highly Effective. Note that the rule does not allow us to compare the bonuses of employees from different departments: it is specifically limited to those working in the same department:
The last rule states that only L, M, and X are rated as Highly Effective. We can use the “HE” subscript to represent this information, or simply circle each HE variable, as shown below:
You should immediately tie the second and third rules together. Since only L and M are rated Highly Effective in Finance, their bonuses must be higher than those of K and P:
Clearly, then, neither L nor M can receive a $1k bonus. Likewise, neither K nor P can receive a $5k bonus. This generates four additional Not Laws:
By the same logic, since only X is rated Highly Effective in Graphics, his bonus must be higher than the bonuses received by V and Z:
Consequently, neither V nor Z can receive a $5k bonus. But, thanks to the first rule, neither of them can receive a $1k bonus either. It follows that V and Z must receive $3k bonuses, whereas X must receive a $5k bonus:
Is it worth representing the Fixed Numerical Distributions that govern the assignment of employees to bonuses? Well, the game does not explicitly mandate a minimum number of employees per bonus, and the rules are not restrictive enough to establish such a minimum for the $1k group. If something seems too laborious, it probably is: a detailed analysis of each distribution is neither required nor encouraged. A far simpler—and probably more useful—task would be to determine the minimum and the maximum number of employees who can receive each bonus:
- $1k: As discussed earlier, five of the seven employees cannot receive $1k bonuses. In fact, there is no reason why anyone would receive a $1k bonus. Thus, the range of variables in the $1k group is 0-2.
$3k: Since V and Z must receive $3k bonuses, the minimum number of variables in this group is two. What about the maximum? There are only four remaining employees, two of whom (K and P) must receive different bonuses than the other two (L and M). Clearly, then, at most two additional employees can receive $3k bonuses, bringing the maximum number of variables in this group to four.
$5k: Since X must receive a $5k bonus, the minimum number of variables in this group is one. Four of the remaining employees (K, P, V, Z) cannot receive the highest bonus, suggesting that the maximum number of variables in this group is three.
You do not have the required permissions to view the files attached to this post.
