Wednesday, February 16, 2011

Survey results - Split the Rent accurate to within 10%

Fairness is a funny thing. One person's fair is another person's rip-off. So it is important for a rent-splitting calculator to jive with a broadly intuitive sense of fairness. It can't just be what I think is fair - or what any one person thinks - or it won't be useful.

In order to validate and calibrate the formula I used for the rent-share calculator on this blog, I did a rather in-depth survey on "apartment sharing fairness" with my friends. Here are the results - enjoy!

How do most people split the rent?

Mostly, my survey respondents either try and adjust prices based on niceness, or just split things evenly. A few (about 20%) do something else. Nobody tries to auction rooms, which would technically be the fairest but is in reality a huge pain and very stressful.

If you, like me, have done the adjust-based-on-niceness approach, this survey is for you!

Factors that make an apartment nice or crappy

One fair way to share an apartment is that people who get nicer rooms should have to pay a little bit more for them, and people with less nice rooms should get a discount. But what makes a room nicer? People have different preferences and priorities. Our goal was to measure what factors make a room nice enough or crappy enough to be worth changing the way rent is shared. For instance, does having a walk-in closet mean you should pay a bigger share of the rent? Does having a private bathroom? Does having no windows justify a discount? To answer this question, we asked the respondents to rate the importance of many factors in determining the way rent is shared. Here were the responses on a 1-5 scale, with 5 being "very important to the way rent is calculated" and 1 being "should not be counted in the way rent is shared."

These are straight-averages (means) for each factor. As you can see, people think factors related to privacy and personal space should be taken into account when sharing rent. I don't think this is a big surprise. The importance of secondary factors like closets and windows is pretty intuitive, and this validates their inclusion in the rent-splitting calculator. "Common area size" is the most interesting case - more on this later.

My respondents don't think distances from other parts of the apartment deserve consideration, and I agree. I must admit, I threw in questions about these factors knowing people probably wouldn't care about them. It was a methodological trick to give the respondents a sense of perspective and to make sure they wouldn't just answer "Very important" to everything. Personally, I actually strongly prefer to live close to the living room of an apartment, but some people prefer a room far away from common space noise. It's not the sort of thing that money needs to change hands over, and the survey confirms this intuition.

This list of factors was used to decide which things deserve inclusion in the rent calculator's menu of modifiers. Unimportant factors should be excluded for simplicity, so for instance, I combined all sound issues into one choice in the calculator and excluded distances and flights of stairs. Convertible wall was a controversial one, as you can see from the standard deviations of my responses (n.b., axis does not start at zero).

In case you are unfamiliar with the concept of "standard deviation," it measures of how widely the responses to a question varied. As you can see, the most controversial factors were including common space in the calculation, whether you should factor in sharing with a couple ("double occupancy" on the chart), and the importance of a convertible wall. The disagreement on convertible wall might represent a genuine difference of opinion, but I think this was just an ambiguous term. Based on comments I received, it's clear people were confused over what a convertible wall is exactly. Is it an accordion style barrier, a piece of drywall which doesn't separate things floor to ceiling, or a renovation which converted one room into two? Whichever it is, what I think matters most is whether there is "no door" or "bad sound isolation." So I decided not to include "convertible wall" in the calculator before probing it further.

What's it worth?

Another way to test for how much each factor should be worth in the sharing calculation is to ask directly how much money you would pay to get a perk or get rid of a problem. Here is some nifty data on how much money you would pay to have a perk or fix a problem:

As you can see, privacy and personal space come up tops again. An interesting case is "lots of windows," which was surprisingly different from person to person in both this question and the factor question above. The maximum price one respondent was willing to pay was $300 per month for lots of windows, and several listed numbers over $150, while some had numbers in the teens. This raises a philosophical question: If the differences in preference are so great, how can you include the factor in a calculator? Shouldn't the person who cares more about having windows just get the room, especially if people are friends?

I think this is a good question, but I also think I have a good answer. The calculator's purpose in life is to provide a neutral opinion, avoid haggling, and not hurt people's feelings. Philosophically, letting someone have a nice thing that you don't care about is OK, but what if you care a little about it? Just because you don't like windows as much doesn't mean you don't like windows at all, and it doesn't seem fair to reward people for being needy. Basing things on the average values is more justifiable: If they would have been willing to pay more, they still get a bargain and you still get a discount. This gives a deal to people who strongly prefer a certain kind of room, and the amount of extra money they pay gives something back to the others.

The only way to do this perfectly "fairly" in this sense is to create an auction, but this is pretty intense/stressful/unfriendly for all but the nerdiest of economic enthusiasts, and using the average method is a great way to keep things generally fair in light of the overall demand for perks and handicaps.

In general, I used a combination of these dollar and importance numbers to calibrate how the calculator values the various perks. All of the dollar numbers were based on an $800 per month rent scenario in Boston with a specific salary of $2500 per month before taxes, so I had to extrapolate a bit. The way I extrapolated that is not that sophisticated, but it's not worth explaining here, either. So, moving on:

Share and share alike

The last type of question in the survey involved hypothetical scenarios - situations which asked you to write what you think the fair rent would be for you to pay. This was designed to get at the key issues of "sharing with couples" and "factoring in the size of the common room." From the factor question, it was clear that there was no consensus how to handle these situations among my friends. These factors had some of the highest standard deviations, and "size of the common room" was the only factor with a bimodal (two-peaked) distribution of importance; however, I do think that there is a clear way to do it, and the survey supports this concept. Split-the-rent prorates the rent by square footage, assuming common areas are shared equally among all people regardless of who sleeps where. I assumed a common space equal to the sum of the bedroom space for a normal apartment, and double or half of that for the tiny and huge cases (see "How it Works" for more description). I then compared this approach to the average response for each scenario. It worked wonderfully.

This is a clear indication that the formula is jiving with respondents' intuitions. The (C) here stands for "sharing with a couple" and you can read the full description for each scenario here if you'd like. The values above represent a less-than-10% error on each scenario, with some even less than 1%:

Why does it make sense to factor in common space? Think about it this way - if there was no common space at all, with small private kitchenettes and baths in each bedroom, it would definitely be unfair to split rent evenly - people should pay as if they had separate apartments. On the flip side, if the whole apartment were a giant commune with no private bedrooms at all, you would definitely just split it evenly (think of sleeping in a hostel or trail lodge). Let's say the "average" apartment is about half common space (including bathrooms, kitchens, coat closets, and halls) and half total bedroom space. I don't have a citation for this fact, but it's a good benchmark in any case, and anecdotally I believe it to be the "comfortable" level between smallish and generous. Since everyone in an apartment enjoys the common areas and shares them, the common space should be split evenly per person while the bedrooms should be split in proportion to their size. This means the ratio of common space to private space should set how equally the rents are shared between unequally sized rooms.

The biggest "errors" in my model happen in scenarios C and D, which are the extreme cases of small and large public living space. In Scenario C, you have a large-ish room with a small public living space, and in Scenario D you have a tiny room within a huge public living space. At first glance, this seems concerning - maybe common space has nothing to do with it and there is a fixed level of sharing that should happen. But in both cases, people thought that they should pay LESS than what I calculated, which is not consistent with that interpretation. If my formula were too "communist" (closer to paying even $), I should have underpriced Scenario D. If my formula were too capitalist (paying more for value), I should have underpriced Scenario C. Being too high on BOTH scenarios can't be attributed to an overall desire for rent to be split in a fixed way.

I think it's probably fair to conclude that this represents an "I shouldn't be the one who has to pay for this" bias. Also lending credence to this interpretation - the magnitude of the error was roughly the same in both cases. It could also be that the common space sizes I used to calculate this were not well described by the terms I used in the hypothetical scenarios. Some respondents suggested I should have reframed some of the questions with "What would have been fair for the OTHERS to pay?" instead of asking "What is fair for you to pay?" I agree this would have been interesting. It would have let me test my explanation of these results, but I wanted to to make the survey as short as reasonably possible while achieving my goals. In any case, my model gives less than 10% errors from intuitive averages even if my bias explanation is wrong, so it is definitely a good guide to the average fairness my friends would tell you for these situations.

Caveats and survey profile

This whole survey is somewhat culturally specific - I'm sure it would come out differently if I did it across different cultures and backgrounds, or possibly even other groups of friends. The sample was an unscientific sample of 42 of my gchat status checkers and facebook feed-readers. But I suspect it is broadly applicable for college educated 20-30 year old Americans, and is probably a good starting point for just about any group of people who agree that people should pay slightly more for nicer rooms.

My favorite survey comments: "Manic survey," "fun survey," "Chickens," "Too many words and numbers!", and "Goddamn it, Bittner, you're conducting this survey so you can nail us on being irrational, aren't you. Jerk."

Several people commented unprompted that who was dealing with bills and the landlord would have mattered to them, and there were few a concerns like "what am I supposed to consider about bathrooms" and "Are these all with strangers or friends" (I used strangers specifically so that people would not consider trying to be overly generous to their friends). One person was concerned over what differentials for money given in the $ section would be in reference to a baseline of $800 or a baseline over what their friends would be paying (I calibrated the survey to make these differentials to be how much you'd pay above what your friends are paying, since I believe this is what comparison people will tend to make intuitively). Several people suggested a variant of the formula I use without ever talking about it with me, which was a nice confirmation of principle.

The guy-girl breakdown was 46% male, 44% female, and 10% did not specify. The average age was 26 with a standard deviation of 7 years. The respondents had shared apartments 3.4 individual times on average with a standard deviation of 1.7 times. No one who took the survey saw my calculator first or talked with me about how I thought rooms should be shared (to my memory), and if I knew they had discussed it with me, I didn't count their response.

I hope you find it helpful! Follow me on Twitter for updates and related projects, email your thoughts to AT gmail DOT com, or check out other stuff I'm working on.

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