Explanation Power definition: The total number of one –stage and two-stage dominances that an individual can exert. The power of individual A i is the sum of the entries in the i th row of the matrix S = D + D 2 Calculation: For two vertices A and B, it is said that A has one-stage influence over B if there exists a directed path of length 1 between A and B. It is said that A has two-stage influence over B if there exists a directed path of length 2 between the vertices A and B. From the above graph, the influence of A on the other members is 8 (one-stage influence + two-stage influence) A has one-stage influence on C, F and E. So, total influence (one-stage) is 3. A has two-stage influences on C, B and E. Here path number to C is 1 ( A → F → C ), to B is 2 ( A → C → B and A → E → B ) and 2 in E ( A → F → E and A → C → E ). So total influence = 1+2+2=5 Therefore, the total influence of A over other members = 5 + 3 = 8 But this is not right to count two-stage influence as one stage. Because if we consider only the two-stage influence, is 5 and one-stage influence is 3. Both are not the same. Moreover, the two stage influence includes the one stage influence of a mediator. For example, C is the mediator of A to E. So, it is better to count one and two stage influence separately. We can use power dominance matrices method. Example: The results of a round-robin athletic contest are shown below. Team A beats teams B and D. Team B beats team C. Team C beats team A Team D beats teams C and D. By using the power definition above, we can rank the four teams in terms of their athletic dominance. One stage dominance D = ( 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 ) Matrix arithmetic can be used to find the two stage dominance matrix without additional counting. But we still need to count to form the one step dominance. D 2 = D D = ( 0 1 2 0 1 0 0 0 0 1 0 1 1 0 1 0 )

6th Edition

ISBN: 9780135902783

Author: Pirnot

Publisher: PEARSON

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Chapter 4.3, Problem 28E

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To criticize:

The approach in modeling influence, we counted two-stage influence as equal with one-stage influence.

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To criticize: The approach in modeling influence, we counted two-stage influence as equal with one-stage influence.

Solution Summary: The author explains that in modeling influence, it is better to count one and two stage influence separately.

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To criticize: The approach in modeling influence, we counted two-stage influence as equal with one-stage influence.

Chapter 4 Solutions

To criticize:

The approach in modeling influence, we counted two-stage influence as equal with one-stage influence.