Suppose you chair a political party committee and now confront the problem of selecting the candidates who will run in each
of three constituencies. The three candidates at your disposal have varied campaign skills - superb, average and terrible. Suppose your opposite number from the competing party confronts the same problem.
a. With no further specification of the situation, draw two alternative extensive forms that might correspond to the task of developing a strategy for allocating your three candidates across three constituencies.
b. For each of your extensive forms, will there be a solution (Nash equilibrium) in pure or missed strategies? Why?
Hello. As with the solution I have written or you last night, this one also takes into consideration a Game Theory, considering mathematical analysis and probabilities into the decision making process. Now, the problem you are being made to consider is this - two opposing parties have the same issue, 3 candidates varying from superb, average and terrible has to duke it out in the campaign trail. Who is going against whom? Not yet decided for the simple reason that the campaign committee must chose the right candidate to duke it out with another to maximize his/her winning probability. Putting mathematics side by side with decision making and socio-political considerations seems a little off in a sense that the ideal should be choosing a candidate for his/her passion and drive to lead a constituency, not by winning ability. But in politics where percentage of the party seats equate to high stakes in controlling and influencing the government, ideal is trumped by winning probability. So now, let us answer letters a & b:
a. How many times have we observed the unsuitability of certain elected officials and marvel at the fact that they got voted in? Part of the political machinery in a two-party, first-past-the-post system that is American politics includes specializations for this very problem. So they look to specialists who turn to varied real-world mathematics for the solution. There are a few suitable choices. For me however, I would look to the idea of 'rank reversals' which is an alternative-extensive form of political strategy. Essentially, what this is like is 'reverse auction' - there are a number of politicians to choose from for the party for a particular constituency and when the candidate has been decided for a particular constituency, the individual has to choose from the vying candidates as well.
How do ...
The solution provides advise in tackling the problem presented above (see long description), simulating possibilities and discussing actions and strategies that can be taken by a political party chairman in an election to ensure that he/she is fielding the most successful candidate of different personalities and skill-sets to constituencies that would most likely elect them. References are listed for expansion. A word version of the solution is attached for easy printing.