Think of a number between 1 and 10 (inclusive, so you can pick 1 or 10 as well as the numbers in between). Note down the number somewhere before you continue reading the rest of this post.
Jal and I like to discuss human behaviour, and the latest discussion was around which number is most picked when you ask someone to choose a number between 1 and 10. If all things were equal, you would expect an even distribution between the numbers, with all of them picked approximately 10% of the time. Limiting the numbers to 1 and 10 also reduces the chances that someone will pick a number based on their date of birth, because you're eliminating over two-thirds of the possible numbers.
I don't think the numbers would be evenly distributed. Mostly because a lot of people tend to favour seven or eight as "lucky numbers". Jal also said he didn't think one or ten would be very popular, because people think they're "too obvious". He hypothesised that higher numbers would be favourable over lower numbers, and figured with all those things, seven would be the most popular, followed by eight.
We discussed how we'd go about testing this, and came up with a roundabout way. The experiment doesn't quite test the question mentioned above, but I'll explain below.
I put a plate of cookies along with a sign.
The text, in case you can't see the image:
Guess my number (1-10)* and win a cookie!
Write your guess on a post-it note (with your name on the back), and place it in the cardboard box.
The number will be revealed at 12pm. If you guessed correctly, you can have a cookie. :)
*My number is between 1-10, inclusive.
I put them on two floors, along with an envelope sticky-taped to the box, with a decoy note inside it saying, "No cheating!" Jal said that by putting an envelope, people would feel that I had already picked a number, and I wouldn't try to cheat by looking at the answers and choosing the number that had the fewest responses.
As a side experiment, because why only do one experiment when you can do two, I wanted to see how many cookies would be taken before 12pm. I left 45 cookies on floor 1, and 51 cookies on floor 2 (it's different because I didn't count how many cookies I had after I paid the MrFodder tax (he always gets to sample my creations)).
Floor 1 (before)
51 cookies.
Floor 2 (before)
45 cookies.
At around 9:30am, Jal suggested I write "Guess me" on the envelopes, because at the moment, they're just background noise. As I went to add it, I bumped into people in the kitchen who asked if I was the cookie baker. They said that they were trying to work out whether they were supposed to put a number between one and ten, or if they were supposed to try and guess how many cookies were on the plate. I don't understand which part of my instructions was unclear, but I added a post-it note to both plates saying that they needed to guess a number between one and ten, not the number of cookies on the plate.
MrFodder said that the most likely explanation for people guessing the number of cookies is that they didn't read the instructions and just saw a plate of cookies and a guessing game. Since the usual task when you see something like this is guessing the number of jelly beans in a jar or something like that, that was the general assumption for what the task was.
As I was adding a note to the plate on floor 2, someone verbally told me how they worked out how many cookies were on the plate, and then they took one. In what world does that make sense? If the task is to guess how many cookies are on the plate, and then you take one after guessing, the next person is going to have a different plate to your plate! How am I supposed to work out what order the guesses were in, and how many cookies were there at the time?
I went on with my day, until 12:01pm, when Dwight came over to remind me that it was past 12pm and I hadn't revealed the number. I posted my number (6), and said that everyone could have a cookie for participating.
Floor 1 (after)
29 cookies remaining (16 cookies taken, loss of 35.6%)
Vote distribution:
14 votes:
#3 - 2 votes
#5 - 1 vote
#7 - 7 votes
#8 - 3 votes
#10 - 1 vote
Floor 2 (after)
49 cookies remaining (2 cookies taken, 3.9% loss)
Vote distribution:
27 votes
#1 - 3 votes
#2 - 1 vote
#3 - 3 votes
#4 - 2 votes
#5 - 3 votes
#6 - 3 votes
#7 - 4 votes
#8 - 3 votes
#9 - 2 votes
#10 - 2 votes
#48 - 1 vote
Then I looked at some of the names on the votes, and realised Dwight voted for every number. I laughed when I saw that he labelled one of the votes, "Future Dwight". He later told me that the "Future Dwight" vote was his real vote. So removing all the duplicate votes, and the 48, which was obviously the person guessing the number of cookies on the plate:
18votes
#1 - 2 votes
#3 - 2 votes
#4 - 1 vote
#5 - 2 votes
#6 - 2 votes
#7 - 3 votes
#8 - 3 votes
#9 - 1 vote
#10 - 1 vote
Overall:
Here is the distribution represented in chart form:
As Jal predicted, 7 was the most popular number by far, receiving 10 out of 31 votes (32.2%). If I could remember how to do significance tests from stats, I'd be able to tell you how significant that is, but I don't right now. Sadly, 2 wasn't picked at all (except as one of Dwight's duplicate votes). The numbers were a lot more distributed on floor 2 than on floor 1.
I also found it interesting that one floor (floor 1) was far more trustworthy when it came to not taking cookies than the other floor (floor 2). Though floor 1 had the election manipulator. I also thought it was interesting that even though I only had 14 votes from floor 1, 16 cookies were missing, which means that 2 people saw the cookies and didn't read the sign at all, or couldn't be bothered voting.
I bumped into someone from floor 1, as I went to check whether there were any cookies left at the end of the day, and he said that he voted, and waited for the answer to be posted, but he took a cookie as soon as he could, because he knew that there were more people on the floor than cookies on the plate, so he wanted to get in quickly before they were all gone. That might be why people were taking cookies before the result was announced.
I asked Dwight why he voted for every number, and he said that he just really wanted a cookie.
Obviously, there are some design flaws with this experiment. Firstly, it's not really a testing people choosing a number - Jal called it adversarial number choosing. So unlike the situation where you ask someone to choose a number, I was asking someone to try and guess my number. So they're not trying to choose whichever number they like, they're trying to guess which number I am most likely to pick. We figured that since most people lack any knowledge of which numbers I tend to favour, and some people didn't even know it was me doing the experiment, people would fall back to choosing a number they would like, so it almost simulates asking someone to choose a number. This is probably mistake #1.
The second mistake was the unclear instructions / set-up. As MrFodder pointed out, the general consensus when food is left out in the kitchen is that the food is up for grabs. People aren't likely to read signs, because they'll just assume the sign says, "Please take one" or something like that. D came up to me and said that when he saw the plate of cookies from far away, he assumed that I was just giving them away (as I have in the past). It wasn't until he got closer that he stopped to read the note.
MrFodder said that when it comes to user interface design, if you're doing something that isn't the norm, people will get confused. When they get confused, they will default back to behaving how they normally behave. For instance, if you go to building and you see what looks like a door, you will try to open it and walk through. If the door doesn't open (because it's a window painted to look like a door), you'll probably keep trying various handles, or look for a button / motion sensor, because that's what your past experience has taught you about doors. After failing for a while, you may finally notice a sign on the wall saying, "This is a window. The door is around the corner." Who is to blame: the person who failed to read the sign, or the idiot who painted a window to look like a door?
The third mistake was not listening to Mulder.
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