Calculate Kemeny's rule using gurobipy

kemeny.py

from gurobipy import *
import itertools

def better(vote, a, b):
    return vote.index(a) < vote.index(b)

def kemeny(profile):
    # a profile is a list of rankings, e.g. [(0,1,2),(1,2,0),(1,2,0)]
    C = profile[0]
    w = {}
    for a, b in itertools.permutations(C, 2):
        w[a,b] = 0
        for vote in profile:
            if better(vote, a, b):
                w[a,b] += 1
            else:
                w[a,b] -= 1
    m = Model()
    m.params.OutputFlag = 0
    x = {}
    for a, b in itertools.combinations(C, 2):
        x[a,b] = m.addVar(vtype=GRB.BINARY)
        x[b,a] = m.addVar(vtype=GRB.BINARY)
        m.addConstr(x[a,b] + x[b,a] == 1)
    m.addConstrs(x[a,b] + x[b,c] + x[c,a] <= 2 for a,b,c in itertools.permutations(C,3))
    m.setObjective(quicksum(x[a,b] * w[a,b] for a, b in itertools.permutations(C, 2)), GRB.MAXIMIZE)
    m.optimize()
    return tuple(sorted(C, key=lambda a : -sum(x[a,b].x for b in C if b != a)))