A dictionary definition of compatibility (one a, three i's !) is 'The state of being compatible; in which two or more things are able to exist or work together in combination without problems or conflict.'
There are any number of different ways to detect a compatibility match between two people. Some are based on tests and personality analysis. Some are based on random elements or just luck. Some of these are worth having a look at.
One of the more common methods to compare compatibility is to look at the zodiac or star signs of each of the people. Essentially, the logic is that people with different star signs tend to have slightly different personalities.
For example, people born under the Zodiac sign of Taurus are known to be practical, reliable people. They might be good with money and so on. People born under the sign of Capricorn are considered to be ambitious, driven and determined, but also practical and helpful. It's therefore assumed that these two personality types would fit well together.
For people that believe in horoscopes, these traits are important and can become a part of their ability to form a relationship.
This is a classic internet compatibility option. There's a lot of simple websites where you can enter either just your first name or your full name and get a compatibility match with someone else. Clearly, this kind of match is almost completely random. There is some basis that people from certain social classes might be given certain names or types of names. Therefore, someone with a posh name might be attracted to someone with a similarly posh name.
In reality, this is highly unlikely to be the case and it's much more likely to produce random results which have little basis in truth.
Another typical method for checking compatibility is looking at location and dates of birth. While this is likely to get a reasonable match in terms of finding a partner, it's not likely to get anywhere close to finding a match in terms of personality. A combination of this along with names is typical in simple internet type of matching but it's more or less completely random and not likely to produce any meaningful result.
These types of matching are based in a general way on personality types. The logic is that someone who is interested in something, let's say for example football, is likely to follow a football team or football show on Twitter. In doing so, that match gives an idea of what that person's personality type or certainly interests are. It's also true of course that looking at someone's Twitter Followers is also likely to give an idea as their personality.
This idea is hardly new and is of course the basis for most behavioural advertising techniques, particularly on social networks.
It's therefore likely to quite an easy and effective way to understand someone's personality and match this against someone else's personality. It does though require both people to be active users on a single social network and therefore provides some limitation to working effectively. If one or both users is not active then it's more likely that they ended up following a fairly random selection of people or media personalities or companies. In which case, the results are likely to reflect that random nature rather than any deep rooted personality traits.
The basic logic behind question based matching is to ask a series of questions that will provide some insight into their personality. For example, you might ask what the person prefers to do in the evening such as 'going to the cinema' or 'staying in with Netflix'. In doing so, you build up a picture of the person as a 'going out' or 'staying in' kind of person. The logic continues from this that a person who likes going out is likely to be a good match with another person that likes going out.
It's a reliable method and can produce some good results. It has three flaws though. The first is that it doesn't always follow that two people that are exactly matched will get on with each other. In other words, just because their interests are aligned, it doesn't mean that they are 'compatible'.
The second problem is that the questions are typically leading and need careful cross referencing to produce an accurate picture of the person. People tend to understand the question quite quickly and tend to lean towards answers that reflect what they think will be a more attractive trait. For example, people tend to lean towards 'going out' rather than staying in because being sociable and outgoing is often seen as a more 'attractive' personality trait. So given a slight leaning towards 'staying in' as a personality, someone might actually go for 'going out' because they feel that's what would be more attractive. In doing so, they change the results and end up actually with a match that's not correct.Finally, the answers tend to be very polarised. Most people don't like going out or staying in all the time. The answer is more likely to be 'it depends' than anything else. However, giving an answer of 'it depends' doesn't create much of a profile so the end result tends to be very fuzzy.
There are two main types of compatibility testing on the internet. The first is one sided where you might answer a series of questions about you and a series of questions about the other person. In reality, this doesn't mean very much because there's tendency to answer on behalf of someone else through your own eyes. You are more likely to polarise the results than provide a true picture of the other person. In which case the results of one sided testing are, at best, not very good.
Taking the test from both sides where each side isn't watching can provide the most accurate method of running a compatibility test.