Game theory and self-management

Suppose that we have a district, which includes 15 settlements, for which it is necessary to form commissions that manage the budget ...



There are 4 parties that want to include their people in these commissions.



The attractiveness of each of the settlements depends on the development of infrastructure, the number of people, remoteness from the regional center, etc.



To simplify, let us assume that the attractiveness of each of the settlements is the same for each party and is such that:



Settlement No. 1 has 10 conventional units of attractiveness;

Nos. 2, 3, 4 - $ 5 each, the rest - $ 1 each.



Let's also assume that the budget of each locality is managed by a commission consisting of 13 members: 3 of whom are in leadership positions and 10 are members with voting rights.



The Council makes decisions by a simple majority.



The value for parties of seats in the commission is also the same and is such that:

The chairman of the commission is estimated at 20 points;

Secretary - 10;

Deputy Chairman - 5;

Member - 1.



Each party has one enemy and two neutrals.

Each party submits to you a draft of the composition of the commissions.

Each party wants to see its people in the position of the chairman in all settlements, does not want to see its enemies in the leadership in general, and it can put up with the presence of "neutrals" in the positions of deputy and secretary.



What is the simplest way to form commissions so as to equally

take into account the interests of each of the parties?



ps You still have to take some of the leading positions from one party and give them to its enemies. The point is to minimize the damage to the interests of each party.