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…

Game Theory Approach to the Pitcher’s Duel

I’ve been kind of drawn in by the NLCS this year. I’m a long time Giant’s fan and seeing them actually winning games and having a good chance at going all the way is a bit of an uplifting experience. On top of this, baseball is a highly strategic game. The choice of pitcher in one game will limit the choice of pitcher in the next game. Offensive lineups must sometimes be changed to optimize a variety of scoring strategies. My team winning, combined with a chance to think about strategic behavior, is always a good way to get me interested.

So, all this got me to start thinking about the so called pitcher’s duel. My question is: Why open a series with two ace pitchers? This is a pretty common practice that two top pitchers go head to head, but is there a reason that coaches would want to do this? Couldn’t a team put a lousy pitcher up against a great pitcher and throw the first game in order to give themselves a better shot at later games by wearing out the top pitcher early? Of course, if one team knew that the other team was going to do this, nothing would stop them from switching their pitching strategy, and on and on like that.

The choice of pitchers is a simultaneous game. For my thought process, we’ll assume that pitchers are chosen in secret by each coach. I start with a simple model. There are two teams and they will play one game against each other. Each team can either play their ace pitcher or their second-tier pitcher. If an ace plays and ace, there’s a 50% chance that either will win. If a second plays a second, the same thing will happen. If an ace plays a second, the ace will have a 75% chance of winning the game.

I could draw the payoff diagram, but I’m a bit lazy so I’ll just spoil the punchline. In this single game, both teams have a strongly dominant strategy to play their ace pitcher. The game, however, gets quickly complicated if you consider multiple plays. First off, to avoid the possibility of ties, you’d have to play three games. You’d give each team a first, second, and third ranked pitcher, and assign probabilities based on each pitcher facing each other. The complication then comes in even harder because each opening match up leads to its own sub-game for the next two games.

While working out what would happen in this three game situation would be difficult, there are a few things that can be thought about. First, the probability of winning the three game series, given that you already lost the first game, is lowered even if you do have a pitching advantage in later games. If you think about a seven game series, where ace pitchers may re-enter in later games, then a dominant strategy for all seven games might not exist.

Given that it is almost impossible then to find a dominant seven game strategy, it is probably a useful rule of thumb to simply try to win every game as if that game stands on its own. Winning game one does have a dominant strategy (choose the ace pitcher). So, it’s entirely reasonable then that we often see the opening of any given series start off with a pitcher’s duel between two ace pitchers. A pitching strategy that gives the highest probability of winning each individual game as if they are played one at a time is likely the optimal strategy for winning a series. Proving this is a bit beyond my scope of practice at the moment, but perhaps I might follow up on this idea when I have more skills and time.

In Which Kyle Listens to Bluegrass Music on a Rainy October Day

It turns out that even in the paradise that is Irvine, one can have a bad day. As I awoke with every muscle in my body aching from an evening of lion dancing, I realized that my alarm had been set for P.M. instead of A.M. and I had missed my morning lecture. When I became aware that I had both missed my first class and that my body hurt all over, I promptly fell back into a coma like sleep. When I awoke, I rushed off to my discussion, arriving what I thought was about 5-10 minutes late. It turns out, however, that my discussion starts at 1 and not at 1:30 as I somehow thought. About as soon as I sat down, to the evil eyes of most everyone in the room, class was dismissed and I suddenly remembered when my class started. I apologized to the TA, made light of my belligerent lateness with him (he is a fairly cool dude after all), and headed back home on my aching legs with what I now notice are brakes that don’t work very well when wet. (No injuries, but there will be a trip to the bike shop tomorrow.)

On top of all that, it’s been raining today. It’s hard for me to really call this “rain” though. It’s more of an occasional drizzle that comes and goes. People are actually wearing coats in this weather, and I’m thinking it would have to drop about 5-10 more degrees before that was even a consideration. The drizzle is a simple cooling wind that falls with all the ferocity of the footsteps of a kitten, and I must say I somewhat enjoy a little of this weather from time to time.

So, what is the appropriate reaction to a horrible day such as this? Well, first, I think, is a matter of perspective. I can imagine a time not so long ago that a chain of events such as this may have devastated me. Now, it has become difficult to imagine how such things can bother me for more than a few minutes. I’ve seen my fair share of real troubles and hardships in life, and a day like this would gladly have been a par day only a few years ago. So, when I thought about how trouble tries to follow me where ever I go, I decided that it was a good time to turn on some good bluegrass music to carry my troubles away. (For those of you that want to play the home game, my favorite Internet bluegrass station: The Bluegrass Mix.)

Since nothing is ever simple for me, the music made me start thinking a lot about the common statement “I love all kinds of music, except country.” (I also think that most people that have that sentiment don’t differentiate between country and bluegrass, though some do.) I started thinking about this statement because I probably would have shared this idea myself when I was younger. Now, my perspective has changed to where I see excluding an entire genre of music as really a missed opportunity to experience a different range of human emotion. It’s often said that mathematics is the universal language. When we sent a message out into space to broadcast our existence, we sent it in binary code with a variety of mathematical constructs included since this would be the only way to send a message that says “Hey, we’re intelligent life. And if you are too, you’ll understand this.” So, if there is a universal language in math, I believe that music is the universal emotional language of humanity.

Why neglect a giant piece of emotional context that is carried in bluegrass and country music? I think about the classical Chinese performance music with which I am now involved and am reminded that most traditional Chinese music revolves around the very intricate use of the five notes of the pentatonic scale. I get the feeling that this type of music would be less rejected by the common man today than country music or bluegrass. And yet despite being a massive gap of time, space, and culture apart, they share a similar emotional context delivered in the complex and deep way that only music can. Chinese music is very environmental, often carrying with it themes of the land. It also deals with subjects of profound loss and sorrow. Suicide is not an uncommon theme in Chinese folklore. Through its music and dance, China paints a picture of its people and its land, along with its sorrows and its triumphs.

The music of Kentucky is no different, but it paints the picture of its own land, spoken in its own musical language. Bluegrass music is highly environmental as well and often sings about simple concepts. It contains large amounts of sorrow in its storytelling devices. It’s often about blue collar or farm workers struggling to make a living, or their relationship with their land or their god. The fast paced complexity of the banjo in many ways resembles the complicated play of the guqin. Why does this music get looked down upon while salsa music is considered to be sexy, or Chinese music is said to be highly cultural? It contains a unique emotional context tied to a unique land with a unique people. Neglecting this genre of music is in a way trying to claim that a piece of the human experience should be looked away from. I often sense two primary reasons that bluegrass and country music often get looked down upon.

The first reason, I think, is a kind of subtle reverse racism. Bluegrass music and country music are seen as the music of the ignorant, working-class, Christian white man. Today, that is everything that the modern multicultural perspective is suppose to despise. Most of mainstream music comes out of California today in one way or another through the major record companies, and most Californians, though I doubt they would admit it, look down on any state they consider to be Southern. Country music is against the liberal California way of life, and should be shunned in a way usually reserved for infectious diseases. Our stereotyping selves think, “Well, if they don’t want their son to grow up to be a gay Castro hairdresser, I don’t want my son to grow up to be a Mississippi preacher man!” Often, the very people that would make the argument that rap music will not turn your child into a gangster end up shying away from country music for what essentially amounts to the same rationalization. The Chinese music mentioned above soothes the pangs of white guilt by its claim of diversity, while bluegrass music pours salt on the wound.

The second reason, and the reason that brought out my own thoughts of bluegrass music on this rainy day, has to do with the topic of sorrow in love being prevalent in bluegrass music. The other common reason to look down upon country music is that it deals too often with the topics of heartbreak and whiskey, and not always in that order. Listening to sad songs makes people sad. However, once again I think that by completely avoiding presenting ourselves with the sorrow and pain of life, that we are missing a fundamental piece of our own humanity. There’s a claim these days that all anybody needs to do in life is try to be happy. What nobody ever tells you is that true happiness is not at all an easy task. Relationships will break down; people will die; the darkness will come for us all at some points in our lives. Right now, if I took five shots of whiskey, I think I could reasonably say that, at least for the evening, I would be a happy man. However, that is not really the happiness that we are suppose to be seeking. The human experience isn’t just about being happy, it’s also about dealing with the hard facts to life. It’s about working for a greater reward. Bluegrass music conveys the emotional context of a people that had to deal with hard facts of life, and worked for the rewards that their values saw fit to seek. They often did not succeed, and often feel on hard times, but they tell the story anyway.  We may not want our hearts to break, or to become restless souls, or to have people die before their time, but the human story calls into play all these things.  Saying you don’t listen to bluegrass because its sad in many ways indicates an incompleteness to the soul, or at least denial of a piece of the soul that we must all one day face.

However, maybe that’s the reason people tend to appreciate bluegrass music more as they grow older. After having myself experienced many dark and troubled times, I embraced different musical flavors that I would have never been able to relate with as much as I do now. So, when I listen to this bluegrass on this rainy day, it does carry my troubles away with it. I can sing a tune of folk melodies that relates my sorrow to the human experience, and my day of not having the alarm clock goes off can be met with a smile and a readiness for the next task at hand.