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DominikPeters / __counterexamples_fair_division.txt
Last active May 2, 2020
Counterexamples in fair division
View __counterexamples_fair_division.txt
A collection of some counterexamples I've found for
fair allocation of indivisible goods, mostly via random sampling.
DominikPeters /
Created Apr 29, 2020
Maximize Nash welfare for allocating indivisible goods
# Indivisible private goods, maximum Nash welfare
# Using Gurobi, this implements the ILP formulation from
# Caragiannis, Ioannis, et al.
# "The unreasonable fairness of maximum Nash welfare."
# ACM Transactions on Economics and Computation (TEAC) 7.3 (2019): 1-32.
from gurobipy import *
import math
import random
DominikPeters /
Created Apr 29, 2020
Compute Cayley distance between two rankings
# for two permutations of [0,1,...,n], compute how many swaps (not necessarily adjacent)
# are needed to transform one into the other
# code uses: distance of a permutation from the identity permutation
# equals n - #cycles in the cycle notation of the permutation
def cayley_distance(x,y):
A = range(len(x))
inv_y = tuple(y.index(a) for a in A)
comp = tuple(x[inv_y[a]] for a in A)
cycles = 0
DominikPeters /
Created Apr 29, 2020
Simple implementation of the Probabilistic Serial fair division mechanism
from fractions import Fraction
def probabilistic_serial(profile):
"input is a list of preference lists"
N = range(len(profile)) # agents
O = range(len(profile[0])) # items
supply = {o : Fraction(1,1) for o in O}
allocation = {(i,o) : Fraction(0,1) for i in N for o in O}
while any(supply.values()):
# in each iteration, at least one remaining item is fully depleted
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