The mathematicians of this world are not so often associated with Cupid as they are with computers. However, as the geeks are gradually inheriting the earth, they are also conquering the realm of love. Every year internet dating is more widely accepted and practiced and as it grows, so too do the volume of data and the number of analysts, working to find us our next match. This being the month of love, today we discuss the topic of online dating and finish by having a bit of fun.
Online dating – background and discussion
What can be considered online dating these days covers a number of channels - not only the traditional online dating site onto which you would register and become a member, but also social networking sites such as Facebook that you use to expand your network - by tapping into those of friends’ or colleagues’ (and therefore increasing the potential of snapping up ‘the one’) . Chatrooms/ blogs specific to your interest area would also count towards online dating if one chat leads to another romantic one.
In this post we refer to online dating as activity via a traditional online dating site - of which there aretwo main types available to the online dater:
- The first is one that you join (for free or pay a subscription) a directory of single people/ online datees, and this directory or database is maintained by the dating website. You would typically upload some personal information and as a member, have the freedom to browse and access information on potential datees.
- The second, and perhaps more interesting from an OR point of view, is the sort which would typically require you to complete a lengthy questionnaire. After some ‘processing time’, the site would recommend compatible individuals based on some matching criteria and function.
Perhaps online daters get excited by being able to ‘see’ the range of people on the directory and choose or eliminate potentials on the basis of this – deep inside we might like to think we recognise the appearance of someone we would be compatible with romantically (physical attraction aside of course!). Letting a computer do this for you will probably mean taking this step out of the decision making process. Whereas there is almost certainly technology out there to code physical appearance (e.g. symmetry of facial features), I would find it surprising if regular dating sites include the ‘similar symmetry score’ variable! Physical attraction and romantic compatibility are of course two very different kettles of fish.....
So, if we’re sold on the idea that a computer (i.e. some mathematical algorithm) may well do the ‘matching’ job more efficiently and effectively, how much confidence can we place in the recommended matches bringing the prospect of love?
The types of ‘computer matching’ methods employed would be interesting, and we can only speculate what these are. Not surprisingly, the websites we looked at did not share how they do member matching. It is reassuring to know, however, that EHarmony use a ‘scientific approach to matching highly compatible singles’, using something like 250 variables, gathered from the initial questionnaire. We also found out that eHarmony do employ operational researchers! On the flip side, others (type 1 as discussed above) were proud that their site is ‘run by humans, not a computer’ and therefore do not operate ‘any 'computer matching' or claim to know what type of person you should date’.
So a dating site which uses rigorous scientific method(s) of matching may work generically to this model:
- Register your details/ fill in a questionnaire collecting data for today’s match or research into future matches as algorithms are improved. You will be asked to apply any filters to narrow down the data. You may even be asked to rank your matching criteria – i.e. to influence the weighting.
- After a ‘processing time’, the computer produces a list of potential matchees. To continue with the scientific theme, you may be provided with a % compatibility with these matchees based on the information provided. Wehey - you are matched!
- Potential methods may include finding, statistical nearness/distance or clustering, Multi Criteria Decision Type methods or even data mining on ‘successful’ partnerships.
Whatever the method, we thought we would have a go ourselves at matchmaking International OR bloggers. Over the past few months INFORMS (the US society for Operational Research) has been running a blogging challenge. The’ve designated a topic and let the international OR Community do their best. December was ‘OR and Holidays’; January was ‘OR and Politics’ and February is ‘OR and Love’. Of the bloggers who wrote articles for the December and January INFORMS Blog Challenges, who is most compatible? How could we have ensured that nobody was alone for Valentine’s day?
At this point we would like to apologise if we have offended any of our bloggers by including them in our matchmaking exercise – we hope people understand that this is only an exercise, though who couldn’t use a new friend?
We took the 19 participants, and built our dataset: Blog platform, twitter presence, occupation, blog challenge topics and participation, location, blog popularity, etc. Note that gender is NOT a parameter as we are being Platonic Cupid here, seeking to ensure that our bloggers are not alone on Valentine’s Day. After consulting our people at our own Relationship Science Research Centre of Excellence, we established a weighted algorithm for measuring compatibility. We were now prepared to start delivering recommendations:
- Laura McLay and Anna Nagurney make the best match.
- Tallys Yunes and Laura McLay make the next best match.
But wait, we’ve got trouble. Laura is already taken. If we’re going to create harmony in the OR blogging community, we’re going to have to find each person a friend. The problem gets deeper. Not only now do we need an excellent methodology for determining compatibility, we must find the best matching for our entire population, maximizing public welfare.
We are presented with a classic optimisation problem, a maximum weight matching, the same type that the Capgemini OR team solve for their clients, delivering real business value. We must select the nine best couples (decision variables), such that the total compatibility across all couples is maximal (the objective function). Each person may only be in a single couple (constraints). We use our compatibility algorithm to produce our rewards matrix, and go about seeking our optimal matching.
Compatibility Matrix (anonymised). As this is about compatibility, read as a heat-map not a stoplight. Red is good in this instance:
Using our favourite package, we seek to find the nine best couples in order to maximise total public compatibility. They are:
- Anna Nagurney and Laura McLay
- Ian Frommer and Paul Rubin
- Michael Trick and Tallys Yunes
- Larry D’Agostino and Robert Randall
- David Smith and Thiago Serra
- Francisco Marco-Serrano and Niclola Petty
- John Angelis and Michale Watson
- John Poppelaars and Patricia Randall
- Hakan Kjellerstrand and Phillip Mah
And I’m sorry Shiva Subramanian, but there are an odd number of bloggers in our group so you’ll just have to... be paired up with the Capgemini OR Blog Team, who we largely excluded as they are not a person. If it’s any consolation, you weren’t our least compatible person, you just weren’t in our optimal solution.
Perhaps China may wish to employ this sort of Operational Research technique. As a centrally planned society with as many as 40 million men who will never find a wife, maximising social happiness is a laudable goal.
Note: A special apology goes out to Robert and Patricia Randall. We may need to train our compatibility algorithm on some real data.