First, I've read that if a house is priced correctly you'll get an average of one offer every 10 showings. So far we've had 2 showings without an offer. After how many showings should we reduce the price?
This isn't enough information: you also need the number of showings necessary for a home mispriced by 5% upwards to get one offer.
Once you have that number, assign a prior. You think that the guest house is sufficient to justify the price, and have feedback from other people that it isn't. You like your opinion, but they have experience- let's put a prior of .5 that the house is correctly priced and .5 that the house is mispriced upwards. (You should pick numbers that reflect your beliefs before any showings.) Decide what threshold probability you need to lower the price of your house. (You can work this out from your time-price preference if you want to ensure consistency, but that doesn't seem very valuable. There's another way to figure this out below that's pretty cool, but is a short-term method.)
Every showing, you receive an offer or don't. If your house is mispriced, let's say the probability of an offer is 1 in 20- .05, whereas if your house is correctly priced, it's .1. The probability of not receiving an offer is thus .95 or .9. Let's call your current probability that the house is priced correctly PC, and the probability it's mispriced is 1-PC.
Each time you show without receiving an offer, PC is now (.9*PC)/(.9*PC+.95*(1-PC))=(.9*PC)/(.95-.05*PC). After two showings with that prior and those probabilities, you should believe there's a 47% chance the house is priced correctly, and a 53% chance it's mispriced. When you get an offer, PC is now (.1*PC)/(.1*PC+.05*(1-PC))=(2*PC)/(1+PC). This gives us another stopping condition we can use: "At what point will I believe it more likely the house is mispriced than correctly priced, even if I get an offer the next showing?" You can work this out (I did it in Excel, and can send you the file if you want to play around with other numbers) and figure out that after 13 showings without an offer, you'll believe PC is .33, and if the 14th showing results in an offer PC will be only .48.
(Edit: Note that this means that if your prior is only .33 that the house is correctly priced now, and you agree with the .1 vs. .05 numbers, then taking more data may not be necessary. More data will of course get you better knowledge- the stopping condition I put forward is arbitrary- but the whole decision problem of when to adjust your offer is a somewhat difficult game theoretic one.)
Thank you -- this is exactly the sort of Bayesian analysis I'm looking for.
The probability of having chosen a correct price is related, but most useful for my purposes is updating an estimate of how long it will take me to sell the house at the current listed price as information arrives in the form of showings-without-offers.
Correctly priced homes sell in 10 showings, on average. As the number of showings increase to 13, then 14 without a sale, I understand this lowers the probability that I've chosen a correct price. How should my estimate of the averag...
Like Yvain's parents, I am planning on moving house. Selling a house and buying a house involve making a lot of decisions based on limited information, which I thought would make a set of good exercises for the application of Bayesian reasoning. I need to decide what price to list my house for, determine how much time and money to put into fixing it up, choose a new home and then there's the two poker games of the final negotiations of the sale.
(I logged onto Less Wrong having just made the decision to consider posting this article, so I was kind of weirded out at first by the title of Yvain's post; but then I was relieved that the topic was somewhat different. I am used to coincidences but on the other hand they push me a little paranoid on my spectrum and I'll feel less stable for a few hours. I already know Google tracks me and who knows what algorithms could be running given a bunch of computer scientists...?)
House Story
tldr; We're listing at the appraised value +10%.
A few years ago, we purchased a beautiful house. 'We' is my husband and I and my parents. We purchased the house because it includes a guest house where my parents can retire. However, my mom continues to postpone retirement and in the meantime my husband and I decided we would a) like more light, b) like a shorter commute and c) could purchase two homes we prefer for the price of this one -- my parents would enjoy a house on the water. (Great post and spot on about the features that matter, Yvain!)
I would be happy to sell the house for +5%, covering real estate fees and new flooring we put in. However, three houses in the cul de sac have sold this year for +10% and so we listed it at that price too. Our house is bigger than theirs but not as nice (they have granite and impressive entrances and we don't). On the other hand, having the guest house makes us special.
Via agent and potential buyer feedback, we're coming to realize that we might be lucky to sell the house for +5%. At this price level, people prefer a house that is impressive and in perfect condition.
Primary Bayesian Question
My primary question is the following: how should we decide to modify our listing price as we get more information?
First, I've read that if a house is priced correctly you'll get an average of one offer every 10 showings. So far we've had 2 showings without an offer. After how many showings should we reduce the price?
Second, the other three houses sold in 6 or 7 months. After how many months should we reduce the price?
Keep in mind, we don't have to move and I estimate that I would be willing to stay in this house for about +3% per year. In other words, I would be willing to wait 2 years for a higher offer if I could sell it for +3% more by doing so.
I anticipate that after posting this I will be embarrassed that it is so pecuniary. On the other hand, this makes it concrete and the problem in general doesn't have too many emotional factors. Any money we make over the first +5% can be used as a down payment for our next house after we pay our parents back. (I did feel embarrassed, so I took out the dollar values and replaced with relative percents.)