1. Mathematical Models of Leadership By Matthew Allinder

2. Progress This project has been an interesting one. How does one go about modeling leadership? Once one figures out how to construct a model of leadership, how does one know it has been done correctly?

3. Progress Continued The basic idea behind the project is to construct a signed or weighted digraph that represents the leadership being applied in real life. The type of leadership being implemented would determine the direction of the arcs, their signs (or values) and how connected the digraph was. But what do the vertices represent and how do I properly assign the arcs? Once I set up the model, what does a pulse that is introduced mean in the real world? What does the outcome of the pulse process mean?

4. The Path-Goal Theory of Leadership States that the effectiveness of a leader is based upon how he or she’s behavior motivates subordinates to accomplish goals. Leader’s behavior is determined by the difficulty/ambiguity of the task and the subordinate’s confidence in his or her own ability to perform the task. In short, the leader goes down whichever path necessary to influence the subordinates to achieve the goal.

5. 4 Main Behaviors

6. Ideas Look at social network/flow diagram and see how leadership can be added; observe how it affects the flow.

7. System Dynamics It is how one looks at complex systems’ behavior over time. Similar to the pulse process but also takes into consideration time delays. Usually involves computer modeling. Gives insight into complex systems, helps identify hidden causes.

8. What to Model? BP’s reaction to the oil spill by it’s CEO would be interesting to model. How he directs his subordinates to handle the situation, his overall style, could be assessed.

9. What about something simple? A sports team? How about a football team? The quarterback can be viewed as the leader and the other players as the subordinates. The goal of the organization is to score points. Can look into literature on hot streaks of athletes and desire for victory to determine probabilities/weights for certain arcs.

10. Football Team The pulse that is introduced is the play that is being run and the value that is produced is the likelihood that the play succeeds.

11. The End