DominikPeters

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

DominikPeters

# 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

# 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

A collection of some counterexamples I've found for
fair allocation of indivisible goods, mostly via random sampling.

DominikPeters

# Implementation of the Merge Insertion sort algorithm
# -- a sort algorithm that is efficient w.r.t. number of pairwise comparisons
# based on the description in
# https://en.wikipedia.org/w/index.php?title=Merge-insertion_sort&oldid=959884881
# This is not intended to be time- or space-efficient.
# "less" is a function such that less(x,y) is true iff x should go to the left of y
# Dominik Peters, August 2020

# imports only needed for test at the bottom
from __future__ import print_function

DominikPeters

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 = {}

DominikPeters

cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div>div>strong
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(4)
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(5)
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(6)
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(7)
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(8)
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(9)
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(10)
cmt3.research.microsoft.com##div[data-bind="foreach: questions"]>div.row:nth-of-type(15)
cmt3.research.microsoft.com##div[data-bind="foreach:reviews"] > h2

DominikPeters

# I use this together with BetterTouchTool

tell application "Google Chrome"
	set theURL to URL of active tab of first window as string
end tell
tell application "Terminal"
	do script "cd ~/Downloads && youtube-dl '" & theURL & "'"
end tell

DominikPeters

tell application "Google Chrome"
	set allWindows to get every window
	repeat with i in allWindows
		set windowProperties to properties of i
		set windowMode to mode of windowProperties
		if windowMode is "incognito" then
			close i
		end if
	end repeat
end tell

DominikPeters

Replace natbib by biblatex to get citation links

\usepackage[backend=bibtex, style=authoryear-comp, natbib=true, sortcites=false]{biblatex}
\addbibresource{main.bib}

% optional if you want (Smith 1776) instead of (Smith, 1776)
\renewcommand*{\nameyeardelim}{\addspace}

\begin{document}