A Risk Adverse Economist’s Guide to Dating

Though this could also be titled: “My Normal Approach is Useful Here“

I guess it’s just a math heavy day today, mixed with a light sprinkling of rather standard insomnia. As I study for midterms and do my Econ-105A homework, I must have some internal desire to ground myself in things that I can attach more directly to myself. I had a conversation with a friend the other day that involved why I never ask anyone out. I claimed that the reason must be that I am highly risk adverse. Even though I meant this as a (albeit true) joke, as I sit here tonight doing way too much math, I distracted myself by thinking about how exactly I would model my own aversion to asking someone out on a date.

Since I’ve moved to Irvine, the old concept that there’s no such thing as a single woman has been pretty much entirely dissolved. This is a bizarre and foreign land where women seem to be, for no apparent reason that I can fathom, involuntarily unattached. Furthermore, the women here are of the highest quality in both beauty and intelligence, making the idea that any one of them would be involuntarily single all the more strange. I would say that perhaps it’s because the men don’t live up to their standards, but the men here are also of the same quality, so this seems unlikely at first glance.

All of this  is, of course, just a round about way for me to say that my usual excuse of “I can’t ask anyone out, because everyone is already taken” may not actually hold. I need an objective way to think about asking out women so that I can use it as a good rational for why I never do, and can thus maintain my well earned reputation as a cranky, lonely hermit.

So, for this model, we’ll assume that we’re presented with a choice between two options. The first option is to ask a girl out and the second option is to do nothing. For the do nothing option, we’ll assume that the expected utility of that option is zero. Some may say this is unfair, since you may suffer or may gain by choosing to do nothing. However, since we are only interested in the choice (or opportunity cost of doing one over the other), we only need to know if the expected utility of the ask-her-out choice is greater than or less than the expected utility of the do nothing choice. Said another way, we want to know if it’s better to have loved and possibly lost or to have never loved at all, and we’re measuring that based off of having never loved at all.

For the ask-her-out option, there are two potential outcomes. She can say yes, or she can say no. Let A represent the event that she accepts your offer, and A^c represent the event that she rejects your offer. Now, let U_A > 0 represent the utility gained by her accepting your offer and U_R > 0 represent the disutility caused by her rejecting your offer. The expected utility of asking her out is then given by the following equation:

EU = P(A)*U_A – P(A^c)U_R

Now, let k = U_R/ U_A. We’ll call k the heartbreak proportionality constant. The equation then becomes:

EU = P(A)*U_A – k*P(A^c)*U_A

EU = [P(A) - k*P(A^c)]*U_A

Now, we must examine the sign of the expected utility of asking her out. If negative, it’s better to do nothing rather than ask her out. If positive, it is better to ask her out. Since we know that the utility gained by asking her out, U_A, is always positive, the sign of this equation can be determined entirely by analyzing the sign of P(A) - k*P(A^c). Essentially, we can now say that the choice of whether or not to ask someone out can be determined entirely by two things. First, the probability that she will accept your offer. Second, by the heartbreak proportionality constant, k.

In this model, k represents how much one dislikes being turned down relative to how much one prefers being accepted to go on a date. First, consider a k = 1. This would represent a person that puts equal weight on being accepted and rejected. If it feels good to be accepted, then to this person it would feel just as bad if they got rejected. A person with a k = 1 would need to perceive that asking out his love interest would have at least a 50% chance of success in order for him to be at least indifferent between asking her out and not asking her out. If k > 1, then this person is strongly hurt by potential heartbreaks and would need greater than even odds in order to find the courage to ask someone out. A person with k < 1 is someone with a certain amount of courage. They value a potential relationship more than they value being hurt by rejection and will thus ask someone out even if they believe there is less than a coin toss chance of it being successful.

From this idea, it makes sense to determine the indifferent probability. Given a certain k, we must find the probability that a man would need to believe he would be successful in order for him to be indifferent to asking her out and not. This can be found using a little algebra:

P(A) - k*P(A^c) = 0

P(A) = k*P(A^c)

P(A) = k*[1 - P(A)]

P(A) = k – k*P(A)

(1+k)*P(A) = k

P(A) = k/(1+k)

If we know the person’s heartbreak constant, we can then determine by the above equation what probability of acceptance would be necessary in order to be indifferent to asking someone out.

And that’s where we can get back to me. I estimate that I dread getting embarrassed and rejected about twice as much as I like the idea of being accepted. Therefore, I must believe that the probability of someone accepting my offer would have to be greater than 2/3 in order for me to actually make an attempt. Since, however, I likewise believe that I am fundamentally undesirable to women since I am in fact a cranky, lonely, hermit economist secluded in my ivory tower, it is unlikely that I would ever believe, unless presented with extreme evidence to the contrary, that P(A) would ever be even close to 2/3.

And that, ladies and gentlemen, is a mathematically elegant explanation of why I will be single for the rest of my life. I guess my usual approach still doesn’t work here…