
Divide Your Rent Fairly - wallflower
http://www.nytimes.com/interactive/2014/science/rent-division-calculator.html?_r=0
======
joshstrange
If you often split the bill on anything Rent/Utilities/Drinks/etc you should
check out Splitwise [0]. They have a Web/iOS/Android apps and it has been a
life saver. I've used it for a little over a year now and it makes all
expenses a breeze. It keeps track of who owes who what and can (when enabled)
even simplify the debts so if person A owes $10 to person B and person B owes
$10 to person C then Splitwise will report that person A owes person C $10.

Note: I have no affiliation with Splitwise, I just love the product.

[0] [https://www.splitwise.com/](https://www.splitwise.com/)

~~~
mason55
I don't think this has anything to do with the article/calculator. The OP is
about an auction process to determine who pays what, not actually exchanging
the money or tracking it.

~~~
joshstrange
It has to do with splitting the cost of shared resources, I will agree that
it's not the same as the OP but I will argue that it is in the same vein and
further more that people that are interested in how best to split rent might
also be interested in a way to facilitate the collection and tracking of said
rent.

Edit: Also see Splitwise's rent calculator:
[https://www.splitwise.com/calculators/rent](https://www.splitwise.com/calculators/rent)

~~~
pkfrank
Agreed, I think it's totally relevant and thanks for the Splitwise link.

I've been waiting for Venmo to integrate roommate-inspired features for ages.

~~~
joshstrange
Splitwise used to have a link to Venmo but I can't find it now, they do have
Paypal integration that you can use (you have to pay Paypal fees though). That
said you can of course use whatever you want to exchange money and my
roommates use Venmo and Simple Instant (and goods/services like
groceries/utilities in their name) to pay each other.

------
danso
This app did not make much sense to me because I was sitting at my computer
making choices for myself and my non-present roommate. So the related article
with useful visual explanation of Sperner's Lemma may be more useful reading
if you don't have a quorum of your roommates to work with this morning:

[http://www.nytimes.com/2014/04/29/science/to-divide-the-
rent...](http://www.nytimes.com/2014/04/29/science/to-divide-the-rent-start-
with-a-triangle.html)

~~~
Anderkent
Sperner's Lemma is cool, but since it can be gamed and your preferences will
change anyway (so the envy-freeness is only temporary) it's more of a
curiosity than a true solution.

------
bendauphinee
Myself and my g/f moved into a house with 2 friends. We figured a fair way to
divide the rent and expenses.

We measured out the sqft of the bedrooms, and used the percentages of each
room from the total bedroom sqft to split the rent and any fixed expenses like
internet and lawn care (since those costs don't change based on per person
usage). We applied the same to cleaning supplies and things like light bulbs
in common spaces.

(Chosen Bedroom SQFT / Total Bedroom SQFT = Chosen Bedroom Expense %)

For power, since that can vary month to month based on usage, we split it by
the number of people in the house.

This month, one of the friends is moving out and we're taking her room over as
an office, so the power split changes to 3 way instead of 4 way, but the other
friend won't see a change in her other expenses because her percentage of the
bedrooms floor space is still the same.

Easy on math and easy to manage.

All expenses are tracked in a Google Doc shared to all of us, and at the end
of each month I run the numbers to calculate who pays what to who to balance
it out.

~~~
21echoes
The huge problem with dividing rent this way is that it's effectively saying
that a house is only as good as its bedroom. It puts the price of the kitchen,
bathrooms, common spaces, yard, etc. at exactly $0. Meanwhile, those rooms are
what most people use most of the day!

E.g., if one bedroom is a tiny 70 sqft and the other a whopping 210 sqft, your
algorithm would have the smaller pay only 25% of the rent! Is their home life
really 66% worse/cheaper just because their bedroom is small? They have equal
access to the TV, couch, oven, fridge, laundry, etc. etc. etc.

~~~
dkokelley
The way we did it was to evenly split the common spaces among the renters,
while accounting for room size.

individual_rent = total_rent * (room_size + common_share)/house_size)

Utilities are split evenly among roommates.

It works, although I probably would have prefered to use something like the
system here were I to do it over. Things like "has a master bathroom so you
don't have to share with everyone else" tend to be worth more per square foot
than regular bedroom space.

------
rbcgerard
Found this fairly annoying - only because I went through this exercise
recently, and now all the research i did has been made redundant.

I bought this book to help me out:

[http://www.amazon.com/Fair-Division-Cake-Cutting-Dispute-
Res...](http://www.amazon.com/Fair-Division-Cake-Cutting-Dispute-
Resolution/dp/0521556449/ref=sr_1_1?ie=UTF8&qid=1398781523&sr=8-1&keywords=fair+division)

It's a great book, though it didn't include exactly what i was looking for
regarding this subject. I emailed one of the authors and he kindly pointed me
in the direction of Sperner's Lemma:

[http://www.inet.tu-
berlin.de/fileadmin/fg234_tdc1-s11/FDS_SS...](http://www.inet.tu-
berlin.de/fileadmin/fg234_tdc1-s11/FDS_SS_2012/Script/Sperner-rental.pdf)

and I was able to find:

[http://www.math.hmc.edu/~su/fairdivision/calc/](http://www.math.hmc.edu/~su/fairdivision/calc/)

Which is the same sort of calculator...

Anyway same end result...though i highly recommend the book above if anyone is
interested in the subject.

~~~
Steuard
In particular, the NYT's new calculator is a reimplementation of the
calculator you found by Francis Su and his student(s) (which it cites).

------
npongratz
My favorite introduction to the subject of fair division was Ian Stewart's
"Your Half's Bigger Than My Half!", _Scientific American_ , December 1998:

[http://www.whydomath.org/Reading_Room_Material/ian_stewart/y...](http://www.whydomath.org/Reading_Room_Material/ian_stewart/yourhalf.html)

It's an interesting, accessible, practical application of mathematics and
logic. Fun for the whole family!

------
alex-g
Sperner's Lemma is probably my favorite mathematical result. It is easy to
explain, and pretty easy to prove, but it has a higher than average number of
"aha" moments along the way. The mathematics is not too intimidating -
probably the scariest thing is the generalization to n dimensions, which
requires induction. It is also fun to explain the connections to Nash's
theorem and so on, as invoked in this article.

------
oleganza
Reminds me of an old puzzle: how to split bread in two parts so no one is
upset? Alice splits, Bob chooses the one he wants. If both prefer at least
half, Alice will try hard to split as close to 50/50 as possible and, most
importantly, no one will feel bad because everyone had his say.

~~~
watwut
I want to be the one who chooses. It is humanly impossible to split the bread
to two exact parts. Choosing which part is bigger is easy in most cases.

~~~
mturmon
Toss a fair coin to see who cuts and who chooses.

------
tammer
Interesting that almost all the comments thus far are regarding the actual
content of the article and intention of the page rather than the relative
novelty page itself. I think that alone is evidence that the Times has hit its
stride as a 21st century news outlet.

------
viggity
There is a register wall. if you search google for "divide your rent fairly",
and click on it from the search results, it'll let you in.

[https://www.google.com/search?q=divide+your+rent+fairly&oq=d...](https://www.google.com/search?q=divide+your+rent+fairly&oq=divide+your+rent+fairly)

~~~
Wilduck
Alternatively, visit the linked article directly in an incognito window.

------
ihaveqvestion
Can someone explain why the outcomes differ when the roommates are in a
different order? Imagine an apartment with one nice room and one terrible
room, total rent $1000, and two roommates, one rich, one poor. The poor
roommate will always chose the less expensive room, the rich roommate will
always chose the nice room unless the price difference is greater than $500.

If the rich roommate is Roommate A, then it converges to a 50/50 split, each
paying $500. If the rich roommate is Roommate B, it converges to a 75/25
split, with the rich roommate paying $750. What's going on there?

[EDIT: Also, I've just discovered with three roommates that the results may be
displayed without the first roommate ever choosing at all. ???]

~~~
yuliyp
It doesn't guarantee a perfect allocation, but one that is compatible with
everyone's preferences. A is willing to pay up to $750 for the nice room and
up to $250 for the bad room. B is willing to pay up to $500 for either room.
Any solution where A takes the expensive room for $500-$750 and B takes the
cheap room for $250-$500 will leave both content with their choice. B could do
better by being strategic and switching his preference to only taking the
cheap room for no more than $300, however.

~~~
ihaveqvestion
Thanks, I think that's what I was misunderstanding.

------
coob
Does this still work if one person has an upper limit on how much they can
spend that is less than an equal split?

~~~
ronaldx
The algorithm is likely to ask anyone to choose a favoured room from an equal
split, so in theory the algorithm won't work if someone has a smaller-than-
equality budget.

The algorithm depends on everyone having a personal way of splitting the cost
of the house so that they would be equally happy with any room. If you are
only willing to spend less-than-equality on a particular room, you should be
prepared to spend more-than-equality on another room to compensate.

Someone without that possibility might get a result incompatible with their
needs or might be taken advantage of by a knowledgeable enemy player, I would
think.

So in theory, no, this method won't work perfectly. But in practice, yes, you
might still get a decent result.

This algorithm is good for cake-cutting, since everyone likes to receive cake,
but less good for rent-splitting, since not everyone likes to pay rent.

------
TTPrograms
People value different rooms differently. Auctions are usually good solutions
to this. Idea:

1) Each roommate secretly prices how much they would pay for each room. 2) The
highest payment proposed is allocated the selected room. The payments are gone
down in decreasing value until everyone is assigned a room. 3) Rent is divided
among the renters in amount proportional to the bids accepted.

------
MCarusi
This is probably going to be helpful for people who can't afford to pay 1-2
months of rent due to not having a job, so they can calculate what they'll owe
down the road.

I've seen situations where one person is "temporarily" handling the lion's
share of the rent, and as that temporary situation becomes indefinite,
resentment starts boiling.

------
thom
Sperner's lemma feels very much like eBay's proxy bidding - you put the
maximum you're willing to pay in, and eBay will bid up to that value and not
over.

And then with ten minutes left, you go back to the auction and start
desperately typing in higher and higher numbers because you have to have teh
shiny, rationality be damned.

------
HUSSTECH
Of all the things to appear on HN! In a kind of joke response to a recent
house search with a couple of friends, I made a site that splits the rent
based on room size. Rough round the edges, but feel free to try it out.
[http://whogetsthesmallroom.com/](http://whogetsthesmallroom.com/)

------
balls187
Fair is an interesting concept.

How do you set the rent?

If it's an apartment, it's the fixed cost set by the landlord, but what if you
are the landlord?

Do you set the rent to be based on the mortgage, or based on rents for similar
properties?

With that same logic, if you had a place that was below market, could you set
rent to market and charge that?

------
baking
This seems buggy to me, but I'm not familiar with the algorithm. In my test
case, neither roommate agreed to pay more than $562.50 for room 1, but the
result was that roommate A had to pay $578.13 so it seems kind of arbitrary.

Edit: Never mind, I didn't notice that it allowed me to continue.

~~~
YokoZar
Also note that it provides error bars around the result -- in your case 578.13
minus those error bars was probably less than 562.50.

------
ttty
Quite fair: [http://www.nytimes.com/interactive/2014/science/rent-
divisio...](http://www.nytimes.com/interactive/2014/science/rent-division-
calculator.html?_r=1#2|100|A|Roommate%20A|B|Roommate%20B|1|Room%201|2|Room%202|1221111221212)

$98.44 and $1.56

xD

~~~
TheCoelacanth
Your example would indicate that both roommates had a strong preference for
room A over room B, so in that sense it is fair for the person getting room A
to pay more.

------
likeclockwork
Why not just divide the total rent by the total square footage to get a rate
for the space and then have each person pay for their private space plus a
their share of the common space?

------
esquivalience
This is quite a claim. I find the difficulty with "fair" is that it means
different things to different people.

------
JosephBrown
Now can we figure out a way to split expenses like cable (some may not want
it), lawn services (how frequent), etc?

------
SyncTheory13
I've lived with tons of roommates the last 5 years and do not see the utility
in this... There are jut too many factors to take into consideration. We are
currently in a 4-bedroom house with other amenities. Two of the bedrooms are
very small, and two are large. First, each room starts at a base amount to
take into consideration the shared spaces... Which is $50 for us. So...
$700/mo. total - $200/mo. for all 4 rooms = $500/mo. leftover. Then we split
the rooms into amounts that we agreed seem fair based on the sizes. As a
median, $500/4 = $125. The large rooms are $165, small rooms are $85. Add in
the $50 from before and we have:

Large Room: $215 Large Room: $215 Small Room: $135 Small Room: $135

Basically, you're paying a base price for the shared space, then an additional
price for the approximate square footage of your room. We avoid going into
exact measurements to keep it simple.

As far as utilities go, it was a nightmare to organize them every month and
collect what everybody owed, especially when people started owing over a
couple months past. Making sure to record payments, update the balances, ask
for payments, pay all the bills, and sometimes organize which bills get paid
first because we owed was a disaster.

So, for utilities, I calculated the yearly average of all of them divided by
the minimum number of roommates (4 in our case), added ~10-15% on the top, and
that was our new monthly utility bill. Everybody pays the same amount every
month. Rent is due on the 1st. Utilities are due on the 15th. I track payments
using Google Docs so they have access.

Also annoying was the process in which people bought supplies for the house
and wanting reimbursements... Sometimes people would buy the same things and
we'd have a stock of them, etc... So that extra cushion in the utilities goes
toward purchasing house supplies in bulk.

All of the money goes into a PayPal student account with a debit card.
Everybody has access to Mint.com to see transactions/balance, but only I have
access to the actual account. Anybody can use the debit card, and I get
text/email alerts for every transaction. If we end up having a large balance,
we can improve something in the shared spaces or repay debts from roommates
that had to be kicked out for owing (face it... that money is gone - Always
collect a security deposit!).

We believe this system is fair and scaleable, as it rewards people for sharing
rooms rather than making them pay more for the same space... But as the number
of people grows, the cushion in the utilities grows to a larger percentage...
Making it possible to improve our shared space living conditions as a reward
for putting up with too many roommates. For instance, supplying everything we
need for a full garden in the back yard, etc.

I apologize for this long-winded explanation, but I hope this helps somebody.
Compared to the way of normally splitting up a house, this is much simpler.
Everybody knows what they pay in rent for their room, they know how much
they'd pay if they moved their partner in, they know how much utilities are,
and everything is transparent.

The main thing I haven't figured out is chores/shared duties outside of just
cleaning up after yourself. We have a whole 100+ year-old house to
maintain/rehab, and there is a lot to do. Working on some kind of system where
people can choose from a revolving list what chores they want to do to
accumulate their points. First come, first choice. HabitRPG looks promising in
that you can get groups together and tasks go up in value the longer they
aren't done.

Also, having repercussions for late-payments/lack of chores. We're not big on
charging interest/fines to those that cannot afford it already... But will
soon be experimenting with taking away access to house amenities... For
instance, the upstairs (nicer) bathroom, the high-speed Internet, our shared
access to the local Hackerspace, etc.

~~~
nkoren
Your methodology is fair from the objective vantage point of the _rooms_ , but
not necessarily from the subjective vantage point of the _people_.

Consider the following strawman scenario: Roommate A is earning a million
dollars a year, and the other three are student artists, surviving on odd
jobs. Would it be "fair" for roommate A to to pay no more than $215 - $135 =
$80/month more than the others, when their ability to pay is so much greater?

That's obviously a contrived example, but not too different from my own
situation. I'm a consultant / business owner whose income is not extravagant,
but is reasonably above the UK mean. I have a flatmate -- who is fact a
student artist -- who contributes roughly 20% of the total costs to the
household, including utility & council taxes and whatnot. An 80/20 split may
sound terribly inequitable, but we're both paying a similar percentage of our
earnings for rent, so it's quite equitable from that perspective.

Absent this arrangement, I could still afford to live on my own, but I'd be
left with less cash at the end of the month, and my place would seem a bit
empty. My flatmate, in turn, could probably only afford to live in some tiny
squalid place far from the city centre. If we were to insist on a 50/50 split
which is "fair" from the perspective of the space & utilities (rather than
from the perspective our respective pocketbooks), then no accommodation could
be found: my flatmate could never afford to pay half the rent. But by
optimising around a _subjectively_ fair allocation of our personal resources
and preferences, I get an excellent flatmate and more spending money, and they
get a much nicer place in London than they could otherwise afford. This is a
far better outcome for both of us than we could achieve by insisting on an
"objectively fair" split.

As for your chores dilemma: just have a basic rule about not leaving one's
personal crap in the common areas. Then for the routine tasks (vacuuming,
mopping, etc.), collect an extra $5/week from everybody, and use that money to
hire a professional cleaner (or if one of the flatmates is short of cash and
particularly good at / enthusiastic about cleaning, pay them to do it).
Seriously, it's worth it. People have vastly different capabilities and
preferences when it comes to cleaning, and trying to make everybody equal in
this respect is an un-winnable game. Don't even try.

tl;dr: the less you strive for egalitarianism through uniformity, and the more
you accommodate the divergent abilities and subjective viewpoints of your
flatmates, the better you'll be able to find win/win scenarios in shared-
living situations.

~~~
SyncTheory13
I'm not following... We are paying roughly market rates divided by the space
we actually use. While it could be looked at as only being fair if each pays a
percentage of their income, this (as you mentioned) reduces the benefit living
with people to get cheaper rent.

I actually do make a decent bit more than my roommates, but I choose to live
an extremely simple life for other benefits. If my rent was higher than it is
now (to match my income), living there would not be worth it and I would get
my own apartment without roommates, etc. It would also create trouble between
us as I don't always find the benefit in just having them around for how great
they are.

I can very well see how your situation works for you, but I do not agree that
my setup is at all unfair.

As far as cleaning goes, none of my roommates have the income to constantly
pay professionals... So that is why they can take a pick off the list as
opposed to being assigned tasks.

~~~
nkoren
I don't think your method is necessarily unfair. I just don't think it
necessarily _is_ fair, either. If all of your roommates have roughly equal
views on the value of money, square footage, and various intangibles (such as,
say, the quality of light in a room), then your method is probably entirely
fair -- no arguments there. If, on the other hand, they each assign very
_different_ values to space or money or those various intangibles, then it's
possible that -- despite paying similar amounts of money for similar amounts
of space -- they are actually experiencing very unequal levels of _economic
utility_ in exchange for their rent. Which would be where something like the
NYT algorithm begins to make sense, since this attempts to maximise the
utility function for all parties, regardless of how they themselves define
utility.

As for the cleaner: yours is a very common reaction that I get whenever I give
this advice to my friends. But professional cleaners are surprisingly
affordable. In multi-person households -- unless you're living close to the
poverty line -- they should be entirely affordable (much less than the
proverbial cup of coffee per day), and go SUCH a long ways towards reducing
household drama! Have you tried actually crunching the per-person numbers? You
might be surprised at the results.

------
nobotty
Boo. That registration gate can go right away.

~~~
viggity
click on the search result link, it'll kill the register wall.

[https://www.google.com/search?q=divide+your+rent+fairly&oq=d...](https://www.google.com/search?q=divide+your+rent+fairly&oq=divide+your+rent+fairly)

~~~
akilism
by far the easiest way around the nyt paywall is to just open the link in an
incognito window.

------
kennywinker
"Fair" in the good old American capitalist sense of the word. Money is
supposed to be a proxy for desire here... The one that desires the room more
gets it because they are willing to pay more for it. The reality is money
isn't an equal proxy for desire. The poorer roomate can want the big room with
every fibre of their being, but be casually outbid by a rich roommate with
money to burn.

Edit: as expected, HN swings decidedly capitalistic and my comment has been
downvoted.

~~~
CocaKoala
Money isn't being used as a proxy for desire here; it's being used as a proxy
for sacrifice. The person who is willing to sacrifice more for the room gets
it, not the person who wants it more. Fair is being used in the sense that
everybody ends up happy with the amount they sacrifice for the room that they
end up getting, because at no point are you suggesting an amount that you're
unwilling to pay.

So your comment is getting downvoted because it's wrong, not because HN is
ruthlessly capitalistic.

~~~
kennywinker
When there is an economic disparity between the two tenants, the amount of
sacrifice represented by $100 is unequal

~~~
CocaKoala
Even when there isn't economic disparity between the two tenants, the amount
of sacrifice represented by $100 may well be unequal.

Fortunately, this system involves everybody listing exactly how much they'd be
willing to pay for each room so that nobody ends up sacrificing an amount that
they're unhappy with for the room they end up living in. So even if they're
sacrificing unequal amounts, they're getting a result they're happy with.

Sounds fair to me.

~~~
kennywinker
Fair in the sense that nobody is forced to pay more than they want to / can.
Unfair in the sense that one person has more power than the other, almost
definitely because of their family history, not because of anything they have
done specifically to deserve that extra freedom and power.

My point is basically that our society allows an unjustly large economic
disparity, and to call this a "fair" method of divvying up rent ignores that
nothing involving money can be truly fair in our society.

------
dyeje
I have never heard of this system. Rent has always been (total rent / number
of roommates). This seems a bit overly complex.

