It could be argued that certain types of people are more likely to exist and thus more are matched.
EG:
The very first question about what you do at a party.
The "sit on the couch and observe" type of person is probably one of the more rare options than the "center of attention" or "dancing with people" or whatever other options there were (I forget the options I didn't pick myself)
I'm not a party goer and there wasn't an option to not attend the party. So I'd be on the couch watching other people. Not particularly a popular thing to do at parties.
Even then, it’s all the more important to find the questions with the highest entropy, given that you know someone’s already in a popular group. It’s all about evenly dividing the population based on important factors. Evenly dividing people is easy enough, and finding important factors is easy enough, but doing them both at the same time can be very tricky.
Even distribution is not the goal. Finding like-minded matches is the goal.
From a purely statistical standpoint - their claim is false about the roughly 1 in 16,777,216 chance. But the goal is to find like-minded people.
Let's create a 1 question True/False test. Let's assign the probability of answering True on the question is 70% and answering False is 30%.
You give the test to 100 people. You now have 35 pairings for "True" and 15 pairings for "False". Would it make sense to pair the "True" people with the "False" people to approach an "even distribution"? Only if your goal was to match people with "1 out of every 2 people" from a purely statistical standpoint of weighing 2 options.
The importance in this case is not distribution - but rather if these 8 questions determine who is "similar" in thinking to another person. If you asked someone their favorite color and their favorite pet - you might get a lot of matches. But many of those matches might be terrible with the people having little in common beyond that.
In the FAQ they take a step back and don't really guarantee good matching, even in the event of a match. However matches should be statistically rare (even if biased towards a specific 8 answers on the questions) and might still produce "good results". This makes it an interesting case study and one that can be tweaked and redone if we ever discover a way of asking only a few questions (I'd say no more than 10?) and accurately defining someones personality.
That's the way I see it at least. More of a case study than a statistical claim, even if they're trying to spin the statistics to spur people to take the 8 question quiz. Who knows, it may end up with a lot of good matches based on just-vague-enough questions and the likilihood of similar answers (even if, in some scenarios, fewer than the projected 16~ million and in other scenarios even more)
Even distribution is just important for doing it in as few questions as possible. If you want to do it in 8, and cover 16M distinct personalities, you're gonna need them to be very evenly distributed.
Information gain is maximized when the distribution is even.
Imagine a very extreme biased form of this where everyone answers the same way to a question, and that question is repeated 8 times with different wordings. You will only get 1 distinct personality type.
For a real-world example, take the myers briggs (MBTI) personality test. It only does 16 distinct personality types and takes about 50q to get right. Only way 8^8 beats that, without any data to predict the distributions and correlations out of the gate, or completely revolutionarily novel psychological theory, is with precogs.
There have been 0 matches with over 12,000 tests. Assuming their claim of 1/1,000~ is anywhere near remotely true - then you may have increased your chances of finding a 'good match' tenfold already with the assumption that matches will be good (there is of course the chance they won't be)
The Myers-Briggs places weight on questions to give one of the 16 personality types made of 8 traits. For example, one answer might give you 80% of INTJ and 20% INTP and by factoring the weights across all the questions will tell you if you were weighted more or less towards INTJ or INTP, even if you were more INTJ for that singular question.
In 8x8 the questions are not weighted in that way, which is an important difference. While there are 16 distinct personality traits in MBTI, there are only 8 traits. Questions can weigh towards those 8 traits in various ways. From my experience MBTI tests range from the 5 "strongly, disagree, neutral, agree, strongly" answer types and the questions are targeted to 2 (sometimes 4, but typically 2) traits.
Meaning if neutral is 50% : 50% (Not leaning towards introvert or extrovert) your answer to the question is effectively meaningless. However if you "agree" it might be 75% : 25% and if you "strongly agree" it could be 100% : 0%. You take the aggravated ratings of all the "I or E" type questions and determine if the user is introverted or extroverted based on which holds more weight across 50 questions.
8x8 does not weight the questions to determine personality traits. The questions must match exactly to determine a match. In comparison, Myers-Briggs can have two people be INTJ who answered questions very differently but their aggregated weights of each question added up to them both being an INTJ.
Again: this should be treated as a case study. Since questions aren't weighted, this is different than most personality tests. This isn't a personality test - but finding someone who thinks exactly as you do in regards to these 8 questions.
The largest flaw is if these are the wrong 8 questions to ask and if matches lean towards "good" or not. Which can be determined after enough matches. Making this a neat case study. :)
E:
TL;DR If 12,000 people took a MBTI I guarantee there would be many matches already. This isn't a personality test - this is a line of thinking test. Whether the questions will result in good matches or not will be left to when there are any matches to begin with.
the MBTI example and use of weighting only makes it more clear that this "case study" is dead from the start, because it shows it takes many questions just to ascertain someone's position on each eigenvector. For example, the most important explanatory personality trait is masculinity vs femininity. How do you ascertain that with one question and 8 answers? For example a question asking if you are male or female only tells you so much and not the whole story. none of the real underlying important explanatory variables can be directly measured with a question, or 8 questions.
And I highly doubt they have no matches in 10k samples, especially given the homogeneity of their audience. And if so then they are just measuring traits of personality that, while diversified, nobody cares about. Check out the birthday paradox. Even if there are 16M possibilities, the chance that two random people in 10,000 matched is much higher than you think.
If it were trying to match people based on their personalities and not their direct line of thinking - you would be correct.
Until the results speak for themselves (ie. accuracy of matches) you have no way of knowing if this is a complete failure or successful venture. Although you are free to speculate that it will be meaningless due to the methodology, you have no evidence to back that up yet.
Many dating sites work on a similar principle, although they all use weighted questions. Weighted questions for personality increase possible matches by narrowing down the preciseness necessary. The goal here is to decrease possible matches by requiring exact matches.
Dating sites want to match you with someone quickly who is "close enough" to be compatible based on a personality test and their user data of what answers pair well with other peoples' answers.
8x8 doesn't care how long it takes to find a match, they want an "exact match" to be compatible based on how you answer arbitrary questions.
8 questions was chosen because to have answers be "100% exact" are already rare. If they chose 50 questions - the chances of an exact match become increasingly rare as to possibly never exist in a persons' life time.
E:
The birthday paradox is 1/365, and I'm well aware of the statistics of someone out of a group of 20 random people sharing a birthday with another person of that same group.
They intend to look for matches offline with a few days delay. The count of people who have taken it looks like it is updated live.
It is quite possible that they have not tried to do the match online. Given their demonstrated competence, I wouldn't be surprise if it comes as a shock to them that they can simply put results in a flat file, sort, and then scan them for matches very quickly...
According to the Reddit page the number of tests and matches found is accurate.
There were 11,300~ tests when the page last loaded for me. They are caching the results of the tests and refreshing non-live time in an attempt to put less stress on the server.
There were 0 matches at that time. While I'm wary of site-counters - I'll give them the benefit of the doubt.
At 15,000~ there should be a match. So while pretty high at 12,000~ it's still in the realm of possibility that there is not a match, just very unlikely.
There's also the chance they haven't had the ability to check for matches because their servers been down so often so they haven't been calculating for them. So there is a chance that there is a match in the data but it hasn't been calculated and so wasn't showing when I checked at 11,300~
and it only gets worse as possibilities become less evenly distributed! we are approaching 100% probability this is all bullshit and won't work at all.
That was an interesting read - though I skipped after the "game is over part". I'll have to go back and read the rest later for "what he should have done."
As an aside, I'm now worried about serial killers trained in using information theory to prevent themselves from being caught. Although not having a supernatural Death Note makes that a lot more difficult.
EG: The very first question about what you do at a party.
The "sit on the couch and observe" type of person is probably one of the more rare options than the "center of attention" or "dancing with people" or whatever other options there were (I forget the options I didn't pick myself)
I'm not a party goer and there wasn't an option to not attend the party. So I'd be on the couch watching other people. Not particularly a popular thing to do at parties.