How Can I Find True Love Using Game Theory?

Based on the top search results, you could:

Learn from religious advice (love is what God says it is)

Find your true love’s zodiac sign through a five question quiz (I will love a Taurus)

Consider phone counseling (only to realize you are the real problem)

Man, what a rip-off. How did these answers come up as the most relevant results? They give basically no practical advice.

For all you romantics, there is real hope

It comes from a problem in statistics.

For the sake of this discussion, I define true love as the best person who is willing to date you. Even if that’s not exactly true, I’m wiling to live with that definition. Because if you think your true love is someone that won’t date you, well, I’m not sure any advice can help you.

So for all you reasonable romantics, I offer this hope: if you follow this advice, you’ll maximize your chance of finding true love. The advice will give most people about a 37 percent chance of finding true love.

Yes, it’s not perfect—but I’d say that’s pretty good for a really difficult problem.

Modeling the True Love Game

Dating and relationships are complicated social interactions so they need to be simplified before coming up with any meaningful analysis.

In this statistics game, you search for your true love by dating and having relationships with various people. Your only goal is to find the best person willing to date you—any thing less is a failure.

Here are some ground rules (basically the same rules as on MTV’s show Next):

You only date one person at a time.
A relationship either ends with you “rejecting” or “selecting” the other person.
If you “reject” someone, the person is gone forever. Sorry, old flames cannot be rekindled.
You plan on dating some fixed number of people (N) during your lifetime.
As you date people, you can only tell relative rank and not true rank. This means you can tell the second person was better than the first person, but you cannot judge whether the second person is your true love. After all, there are people you have not dated yet.

Now, I know some of these rules are not realistic, but I think the game captures many of the dynamics of the dating world. So let’s take this as a starting point.

How does the game play out?

You can start thinking about the solution by wondering what your strategies are. Ultimately, you have to weigh two opposing factors.

–If you pick someone too early, you are making a decision without checking out your options. Sure, you might get lucky, but it’s a big risk.

–If you wait too long, you leave yourself with only a few candidates to pick from. Again, this is a risky strategy.

The game boils down to selecting an optimal stopping time between playing the field and holding out too long. What does the math say?

The basic advice: Reject a certain number of people, no matter how good they are, and then pick the next person better than all the previous ones.

The idea is to lock yourself in to search and then grab a good catch when it comes along. The natural question is how many people should you reject? It turns out to be proportional to how many people you want to date, so let’s investigate this issue.

To make this concrete, let’s look at an example for someone that wants to date three people.

Example with Three Potential Relationships

A naïve approach is to select the first relationship. What are the odds the first person is the best?

It is equally likely for the first person to be the best, the second best, or the worst. This means by pure luck you have a 1/3 chance of finding true love if you always pick the first person. You also have a 1/3 chance if you always pick the last person, or always pick the second.

Can you do better than pure luck?

Yes, you can.

Consider the following strategy: get to know–but always reject–the first person. Then, select the next person judged to be better than the first person.

How often does this strategy find the best overall person? It turns out it wins 50 percent of the time!

For the specifics, there are 6 possible dating orders, and the strategy wins in three cases.

(The notation 3 1 2 means you dated the worst person first, then the best, and then the second best. I marked the person that the strategy would pick in bold and indicated a win if the strategy picked the best candidate overall.)

1 2 3 Lose

1 3 2 Lose

2 1 3 Win

2 3 1 Win

3 1 2 Win

3 2 1 Lose

You increase your odds by learning information from the first person. Notice that in two of the cases that you win you do not actually date all three people.

As you can see, it is important to date people to learn information, but you do not want to get stuck with fewer options.

So do your odds increase if you date more people? Like 5, or 10, or 100? Does the strategy change?

The answer is both interesting and surprising.

The Best Strategy for the General Case

From the example, you can infer the best strategy is to reject some number of people (k) and then select the next person judged better than the first k people.

When you go through the math, the odds do not change as you date more people. Although you might think meeting more people helps you, there is also a lot of noise since it is actually harder to determine which one is the best overall. So here is the conclusion:

The advice: Reject the first 37 percent of the people you want to date and then pick the next person better anyone before. Surprisingly, you’ll end up with your true love 37 percent of the time.

The advice is unchanged whether you plan to date 5, 10, 50, 100, or even 1,000 people. Here is a table displaying specific numbers:

Number of people you want to date (N)	Number of people you should reject (k)
4	1
5	2
10	3
25	9
50	18
100	37

Now I was simplifying matters just a bit because “rejecting 37 percent” is an approximation. There is some math that goes into the exact answer.

To be precise, the exact answer is to find first value of k such that

The full proof is fascinating, though somewhat technical. I encourage my avid math readers to check it out:

How to Find a Spouse A Problem in Discrete Mathematics With an Assist From Calculus

A Lesson Learned?

Don’t settle too early.

Suppose that Americans have between five to ten relationships before marriage. This means most people are going to reject the first two or three people, regardless of the person’s quality.

Sounds odd, but it’s just too important to test the market and find that special person. Besides, this strategy improves a person’s odds from a pure random chance (10-20 percent) to almost 37 percent.

Okay great. There’s just one last thing to consider.

Doesn’t the Other Person Play the Game Too?

Game theory would be a lot easier if you could ignore how other people affect the game. So we’re not done yet.

The HUGE caveat is the other person is also trying to game you.

Imagine this: you date a few people, then finally find a great match, and then try to get more serious. Only, that’s not in the other person’s plan.

The other person happens to be less experienced than you, and you happen to be that person’s first serious relationship. As great as you might be, that person is not ready to settle.

The theory suggests you should not feel hurt if someone rejects you like this. You are likely an early victim.

To take advantage of the theory, you should consider whether the other person is ready to get serious. I guess this is why there are certain age clusters when people get married.

But there are things that counter the problem of timing. In real life, you have other strategies to increase your odds not possible in the game:

You some times can rekindle an old flame.

You cannot date simultaneously, but you can often get to know many people at the same time.

You might be able to figure out a true love without having to date many more people. It happens.

And if you are getting more serious, seek out reasonable people who only want to have one or two relationships in their lifetime. You would be in luck, because the math says you’re first in line to be their true love

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35 Responses to “How Can I Find True Love Using Game Theory?”
Hmmm…
Interesting concept, kind of amusing, but I’m not sure how well it works. I’m not sure how much love is a numbers game. If you just reject a person because they are your first serious relationship, you might lose something great.

I think your rule works if the reason you start dating someone is just for the purpose of dating someone or having a relationship. If you start the relationship because you were drawn into it, not because you wanted a relationship, but because that relationship was going to happen whether you were looking for a relationship or not, then I think chances are a lot higher than that relationship is going to work out, whether it’s your first serious one or your tenth.

I think a lot of people stay in current relationships because they’re afraid to look for something better, not because they don’t think there is anything better. I think your method works for that. If people are staying in a relationship not because they’re afraid to look for something better, but because they’re confident that they couldn’t be happier anywhere else, I think the numbers become irrelevant.

Sorry for the essay like response.

It was nice to meet you on Saturday.

By Christina on Jan 8, 2008
Interesting post, though I think there’s a few points to consider.

Lets say trying to find true love is somewhat like trying to buy a really expensive product. Clearly there are some basic needs the product must satisfy, but due to the large cost you’d not only want those basic needs met but met exceptionally well.

So then it becomes a matter of investigation. And I’d say there’s public / private information, and those can be split into objective / subjective categories.

In your example, dating is given as the only way to get information, but that’s not true.
There’s online dating sites, a person’s friends, that person’s blog, that person’s past partners, that person’s family etc.

Those public sources can help determine a lot of things about a person, and even help define your preferences without needing to date a large amount of people.

Now, the difficult part comes from the private / subjective qualities. While you can find other people’s private reactions, its unsure how they relate to your own. Think of the last time you got excited about a movie cause of the reviews but ended up hating it….its a lot like that. Those qualities are tough to determine since they’d require personal interaction to really see how much of a fit they are.

However, people can change during this process, which can invalidate a lot of the research you’re already done. That’s not generally true for a product (though new versions always keep coming out, but you can easily see how those change…) with people it can mean an appealing option is no longer great or a passed-over option now has become quite desirable.

Of course, this all assumes you understand what you base requirements are, and most people have no clue as to what *could* make them happy.

By RohoMech on Jan 9, 2008
This is a fantastic post!

Would I actually follow this method? Um, no. But I think it’s a hilariously over-logical analysis of a ritual most people would never consider examining with statistics.

By Ben on Jan 9, 2008
@Christina: I appreciate (and encourage) long responses, so thanks. Yes, I completely agree it’s dumb to reject a first relationship if you’re only doing it to follow the math. I guess the theory is off since it only cares about finding *the absolute best* person. I mean, you can’t really compare people in an absolute sense, as there are tradeoffs.

@RohoMech: Thanks for the different perspective. Yes, the assumption that you can rank people is subject, and those rankings might change too.

By Presh Talwalkar on Jan 9, 2008
@Ben, don’t you spend time evaluating other things (like what shoes to buy, which car to get etc…) why should something like a life-partner be any different?

@Presh / Christina -> Yea, in terms of finding the absolute best person, that might be overkill for people, given that the differences might be marginal but you’d need to go through a few messy breakups to get that small advantage.

Though, I found a great quote about this stuff:

Nothing defines humans better than their willingness to do irrational things in the pursuit of phenomenally unlikely payoffs. This is the principle behind lotteries, dating, and religion. – Scott Adams

By RohoMech on Jan 9, 2008
@Ben: Glad you appreciated the analysis–your comment made my day.

@RohoMech: Funny Scott Adams said that about religion. He jokingly wrote almost the opposite side for a blog entry:

http://dilbertblog.typepad.com/the_dilbert_blog/2007/07/the-atheist-who.html

By Presh Talwalkar on Jan 10, 2008
This is a good one. There is a good book that I would recommend to all.

Why Flip a Coin?: The Art and Science of Good Decisions by C.H. Lewis. It has got a detailed analysis of the dating game but uses probability as a framework to figure out the strategy althought it has a game theory feel.
Great book and a great read.

Liked the Scott Adams quote in the followup. It reminded me of me when I was young and foolish albeit educated…

Nice.

Mahesh

By Mahesh Vallampati on Jan 10, 2008
Mahesh, I think Presh gave a similar description as what’s in the book? I say this having skimmed what shows up on Amazon.

By RohoMech on Jan 10, 2008
@Mahesh: Thanks for the book recommendation; I’ll put it on my ever expanding “to read” list.

By Presh Talwalkar on Jan 10, 2008
Very nice. I’ve long felt that more people should take care of their 37% while in high school, and select a mate while in college. You also need to put some kind of a time limit on those relationships that you know you’re going to end regardlessly.

By Mike on Jan 12, 2008
@Mike – Well, an interesting counter to your point comes from the fact that having kids later in life (for women) directly relates to living longer and the children being healthier:

http://www.kaisernetwork.org/daily_reports/rep_index.cfm?DR_ID=25649

So if you find your true love in college, you might wanna wait till later to have kids.

By RohoMech on Jan 14, 2008
This probably isn’t as inaccurate as I initially thought. Except in real life, you can go back to #1 if it turns out you were wrong. Moral of the story: shop around.

By Joon on Jan 15, 2008
@Joon: I also thought the model was very unrealistic until I started to think about it more and saw that it is usually hard to go back. Funny how that works.

By Presh Talwalkar on Jan 15, 2008
Obviously, there is the adage, “practice what you preach,” being thrown to the winds here, but I always liked Nada Surf’s proposal from their song “Popular.” Treating dating in high school like checking out a library book sounds like a great way to learn “information,” and to improve yourself as well.

By Erik on Jan 23, 2008
@Erik: It’s not always easy to follow what’s right…Wow, I totally forgot about that song, but after hearing it, it’s now stuck in my head. Blast you for mentioning it

By Presh Talwalkar on Jan 23, 2008
@All: I wonder though, is there evidence that shows acting rationally produces happier people compared to acting on emotion?

There are various social studies that tie happiness to religion / love / children / money etc, but it seems that in most cases being happy is independent of the decision process, since its a based on the interplay between expectation and how the future meets that expectation.

By RohoMech on Jan 24, 2008
@RohoMech: Excellent point. The analysis I gave only indicates *how* to find the best person. It does not say you should find the best person. Perhaps you would be equally happy with the second or third best person.

Economics often answers how you can achieve a goal. To figure out what goals are worthwhile, you better investigate psychology. Perhaps that’s why behavioral economics is such a hot topic because it addresses both topics.

By Presh Talwalkar on Jan 24, 2008
Nice one from Good Will Hunting on True Love defined from loss.

By Mahesh on Feb 5, 2008
http://www.youtube.com/watch?v=EFof9AD2YlE

By Mahesh on Feb 5, 2008
@Mahesh: Yeah, that’s a good one about experience from a good movie.

By Presh Talwalkar on Feb 6, 2008
There is a show on MTV called “NEXT” where partcipants have to choose between money and a date or get “nexted” where they get rejected or face rejection.

It would be nice to take that data from this show and see how it maps back to theory although I duoubt any of the participants would have taken a course in macro-economics or game theory.

By Mahesh on May 7, 2008
Mahesh: It would be fun to analyze that data. I actually saw one show of “Next” where the person just rejected all candidates in a matter of a few minutes. It didn’t make for good TV, so I wonder how many experiments MTV has to cut entirely.

I never can figure out why people go on shows like that. I have a feeling rational theory would not apply to them

By Presh Talwalkar on May 7, 2008
This is great. I thought about the game theoretical angle on finding the perfect partner a while back, and tried to think through a ‘Backup’ approach i.e. an agreement with a friend that in (t+x) time periods you will get together with them if you and they are both single. Typically x is when neither reasonably expect to find love, and are looking to ’settle’. But a little intuitive backwards induction shows: if you’re willing to spend the rest of your life minus x years with them, why not get together now. After all, if one of the two of you are NOT single at (t+x), the agreement falls apart and the single person of the two has a significantly lower payoff. Turns out I couldn’t build a decent payoff matrix and game theoretical approach if you expanded this to a large population, each seeking a credible, committed Backup.

However, one coincidental post I published in a previous avatar as a university economics magazine Agony Uncle was

“I’ve flitted from one unfulfilling relationship to the next. I’m unsure of what I’m looking for in a man. My mates seem to think opposites attract, but my past experience has been a real mixed bag. Does economics offer any help?”

The answer, I reckoned, lay in economies of scale in household production: http://pratiksrandomwalk.blogspot.com/2007/02/shopping-for-compatible-mate.html

By pratik on Oct 25, 2008
Pratik:
That is a great interpretation about the theory of backups, but yes, it seems like it would be hard to model.

By Presh Talwalkar on Oct 28, 2008
Arranged marriages are supposed to be at least 50% successful, so perhaps asking your parents to ask around might get some positive results.

By Francine Shapiro on Nov 14, 2008
Indeed, arranged marriages may be the case of N=1 for both parties…a case of getting “true love” if only by definition of limiting the search to one or a few people. Though I am curious on the stats of whether arranged marriages have better long term success…

By Presh Talwalkar on Nov 17, 2008
Regarding Christina’s point above: Many stay in lukewarm relationships because they are afraid that they WON’T find anyone better. It’s basically a risk/payoff type game. If they end their current relationship and don’t find anyone better, then their payoff is less (since the are now alone) than if they had stayed in that relationship. It’s similar to the stag hunt http://en.wikipedia.org/wiki/Stag_hunt People choose the safer action (staying in a lukewarm relationship) rather than the riskier action (breaking up to find someone better), even though there’s a possibility of a higher payoff IF you find someone better. If you don’t, you are at zero payoff since you are alone; so therefore, you stay in the lukewarm relationship to avoid that risk.

By FL on Dec 23, 2008
Excellent point! I actually made this same analogy a few weeks ago when discussing relationships with one of my friends…Perhaps great minds do think alike

(For more, see my article on stag-hunt)
http://mindyourdecisions.com/blog/2008/06/03/understanding-the-stag-hunt-game-how-deer-hunting-explains-why-people-are-socially-late/

By Presh Talwalkar on Dec 27, 2008
Entertaining article, though I can’t take it seriously because it is fundamentally flawed. Game theory presupposes that the people with whom you are interacting are rational. You don’t seem like a dumb guy, so I know you won’t deny that most females ARE irrational, most especially those “in love”.

Also, game theory deals with the optimization options. With that in mind, how f*cking great is a success rate of 50%? Jesus Christ, I might as well flip a godforsaken coin to determine my future spouse, as my odds of success would be identical!

By Paula on Feb 24, 2009
This is a very naive article you have written. You DON’T choose someone and reject him/her whenever you like IF you are in love with that person. When you are in love you cannot be logical about your situation. And if you have already rejected someone who you were in love with but you think the grass is greener on the other side? Then you were NEVER in love to begin with.

By saira on Apr 2, 2009
I thought it was interesting, when looking at the part of the article where you compared the results of dating exactly three people and always rejecting the first, to look at the three losing situations.

Of the three, two of them have you choosing the second best partner and only one has you choosing the worst. It seems that this strategy not only has a good chance of winning (50%) but also has better outcomes in the losing situation more often than not as well.

If I have done my maths right, I think the chance of choosing the worst possible partner is (1 / n * 2) where n is the number of potential dates. So this is 1/6 if you have three potential partners (which you have illustrated) and 1/10 if there are five potential partners. This contrasts the chance of choosing the best person which is a constant 50%, regardless of the number of potential dates.

The strategy does seem to break down if you date the best possible partner first. After this, no one will ever rank as well and you will continue dating until you run out of potential partners. Whoever is last will be chosen. I would guess that there is a threshold (probably the last 37%… for symmetry) after which you should choose the first person who ranks better than 90% (or some more mathematically chosen number) rather than 100% of your previous dates. This percentage would get lower and lower as you exhausted the pool of potential dates. Taken to the very end, when you get to the second last person, you should be able to state with some confidence whether the last person is likely to be better than this person or not and therefore whether you should date again or choose now. By adding this to the strategy you almost eliminate the possibility that you will end up with the worst possible partner. It doesn’t improve your winning percentage but it improves your losing options.

On the topic of love and this strategy’s suitability to finding it, (aimed at those complaining that this is bad advice) this is a blog on game theory, not dating advice. There is a disclaimer at the bottom of this page that says that Presh is not a financial adviser and this should be read to include that Presh is not a relationship adviser either. Finding your true love was only chosen as an example to illustrate the game. There are many aspects of human relationships that are not covered by this strategy but the strategy itself can be successfully applied to many less passionate situations such as choosing a new sofa or a house to move in to or even a new house mate to move into your house.

By David Keech on May 8, 2009