You think, therefore I am

Models
Intro

Hello world, I am now a G2 in economics PhD-land. This means I have moved up in the academic hierarchy; [1] I now reign over my very own cube, and [2] I am taking classes in my fields of interest. For me that means: Social Economics, Behavioral Economics, and Market Design. That also means I am coming across a lot of models, concepts, results that I want to tell you (whoever you are!) about. So, please humor me in this quasi-academic-paper-story-time… Today’s topic: Coate and Laury (1993)’s model of self-fulfilling negative stereotypes, a model presented in Social Economics.

Once upon a time…

There was a woman who liked math. She wanted to be a data scientist at a big tech company and finally don the company hoodie uniform she kept seeing on Caltrain. Though she had been a real ace at cryptography and tiling theory in college (this is the ultimate clue that this woman is not based on yours truly), she hadn’t been exposed to any coding during her studies. She was considering taking online courses to learn R or Python, or maybe one of those bootcamps… they also have hoodies, she thought.

She figured that learning to code and building a portfolio of work on Github would be a meaningful signal to potential employers as to her future quality as an employee. But, of course, she knew that there are real, significant costs to investing in developing these skills… Meanwhile, in a land far, far away–in an office ripe with ping pong tables–individuals at a tech company were engaged in decisions of their own: the very hiring decisions that our math-adoring woman was taking into account.

So, did this woman invest in coding skills and become a qualified candidate? Moreover, did she get hired? Well, this is going to take some equations to figure out, but, thankfully, this fictional woman as well as your non-fictitious female author dig that sort of thing.

Model Mechanics of “Self-Fulfilling Negative Stereotypes”

Let’s talk a little about this world that our story takes place in. Well, it’s 1993 and we are transported onto the pages of the American Economic Review. In the beginning Coates and Laury created the workers and the employers. And Coates and Laury said, “Let there be gender,” and there was gender. Each worker is also assigned a cost of investment, c. Given the knowledge of personal investment cost and one’s own gender, the worker makes the binary decision between whether or not to invest in coding skills and thus become qualified for some amorphous tech job. Based on the investment decision, nature endows each worker with an informative signal, s, which employers then can observe. Employers, armed with knowledge of an applicant’s gender and signal, make a yes-no hiring decision.

Of course, applicants want to be hired and employers want to hire qualified applicants. As such, payoffs are as follows: applicants receive w if they are hired and did not invest, w-c if they are hired and invested, and 0 if they are not hired. On the tech company side, a firm receives $q if they hire a qualified worker, -$u if they hire an unqualified worker, and 0 if they choose not to hire.

Note importantly that employers do not observe whether or not an applicant is qualified. They just observe the signals distributed by nature. (The signals are informative and we have the monotone likelihood ratio property… meaning the better the signal the more likely the candidate is qualified and the lower the signal the more likely the candidate isn’t qualified.) Moreover, gender doesn’t enter the signal distribution at all. Nor does it influence the cost of investment that nature distributes. Nor the payoffs to the employer (as would be the case in the Beckerian model of taste-based discrimination). But… it will still manage to come into play!

How does gender come into play then, you ask? In equilibrium! See, in equilibrium, agents seek to maximize expected payoffs. And, expected payoffs depend on the tech company’s prior probability that the worker is qualifiedp. Tech companies then use p and observed signal to update their beliefs via Bayes’ Rule. So, the company now has some posterior probability, B(s,p), that is a function of p and s. The company’s expected payoff is thus B(s,p)($q) – (1-B(s,p))(-$u) since that is the product of the probability of the candidate’s being qualified and the gain from hiring a qualified candidate less the product of the candidate’s being unqualified and the penalty to hiring an unqualified candidate. The tech company will hire a candidate if that bolded difference is greater than or equal to 0. In effect, the company decision is then characterized by a threshold rule such that they accept applicants with signal greater than or equal to s*(p) such that the expected payoff equals 0. Now, note that this s* is a function of p. That’s because if p changes in the equation B(s,p)($q) – (1-B(s,p))(-$u)=0, there’s now a new s that makes it hold with equality. In effect, tech companies hold different genders to different standards in this model. Namely, it turns out that s*(p) is decreasing in p, which means intuitively that the more pessimistic employer beliefs are about a particular group, the harder the standards that group faces.

So, let’s say, fictionally that tech companies thought, hmmm I don’t know, “the distribution of preferences and abilities of men and women differ in part due to biological causes and that these differences may explain why we don’t see equal representation of women in tech and leadership” [Source: a certain memo]. Such a statement about differential abilities yields a lower p for women than for men. In this model. that means women will face higher standards for employment.

Now, what does that mean for our math-smitten woman who wanted to decide whether to learn to code or not? In this model, workers anticipate standards. Applicants know that if they invest, they receive an amount = (probability of being above standard as a qualified applicant)*w +(probability of falling below standard as a qualified applicant)*0 – c. If they don’t invest, they receive = (probability of being above standard as an unqualified applicant)*w +(probability of falling below standard as an unqualified applicant)*0. Workers invest only if the former is greater than or equal to the latter. If the model’s standard is higher for women than men, as the tech company’s prior probability that women are qualified is smaller than it is for men, then the threshold for investing for women will be higher than it is for men. 

So, if in this model-world, that tech company (with all the ping pong balls) is one of a ton of identical tech companies that believe, for some reason or another, that women are less likely to be qualified than men for jobs in the industry, women are then induced to meet a higher standard for hire. That higher standard, in effect, is internalized by women who then don’t invest as much. In the words of the original paper, “In this way, the employers’ initial negative beliefs are confirmed.”

The equilibrium, therefore, induces worker behavior that legitimizes the original beliefs of the tech companies. This is a case of statistical discrimination that is self-fulfilling. It is an equilibrium that is meant to be broken, but it is incredibly tricky to do so. Once workers have been induced to validate employer beliefs, then those beliefs are correct… and, how do you correct them?

I certainly don’t have the answer. But, on my end, I’ll keep studying models and attempting to shift some peoples’ priors…

Screen Shot 2017-09-06 at 10.56.41 PM

Oh, and my fictional female math-enthusiast will be endowed with as many tech hoodies as she desires. In my imagination, she has escaped the world of this model and found a tech company with a more favorable prior. A girl can dream…

Endnote

This post adapts Coate and Laury (1993) to the case of women in tech in order to demonstrate and summarize the model’s dynamics of self-fulfilling negative stereotypes. Discussion and lecture in Social Economics class informed this post. Note that these ideas need not be focused on gender and tech. They are applicable to many other realms, including negative racial group stereotypes and impacts on a range of outcomes, from mortgage decisions to even police brutality.


© Alexandra Albright and The Little Dataset That Could, 2017. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

 

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Ultimate Game Theory

Models, Tree Diagrams

An introduction to the melted, gooey mind of a post-finals PhD student

In the days preceding my game theory final, I was quarantined in my Cambridge apartment. The heat was on and pages of yellow legal paper decorated with inky matrices and tree diagrams ruled my kitchen counters. Swaddled in some convex combination of polar fleece and section notes, I would only leave my warm fortress for two activities: (1) to throw $4 at an increasingly hard-to-please chai tea habit; and (2) to play and train for my sport of choice–that is, ultimate frisbee.

When I would return from ultimate, residual thoughts about the game lingered at the edges of my legal pads. The combination of studying for my exam and ultimate exposure in the throes of winter madness led me to the inevitable: reframing game theory concepts as they apply to aspects of ultimate! While I didn’t have the time to parse out examples of “Ultimate” Game Theory back in Cambridge, I’m on winter break in San Francisco now… which means two things: (1) I am still wearing lots of fleece; and (2) I have time to tease out all the kitschy alt-sport applications of game theory that my heart desires.

To discuss game theoretic concepts in this context, I build out two games that are based in the ultimate frisbee universe.[1] First, I use The “call lines” Game to discuss some popular, well-known concepts–namely, the prisoner’s dilemma and pure Nash equilibrium. I also use this framework to talk about repeated games and subgame perfect equilibrium. In adding the concepts of offense and defense, I refine the game so that it is no longer symmetric, and provide an example of how to solve for mixed Nash equilibrium.  The second game I herein created is The “throw it to the girl” Game. This game is much more complex and interesting than the former–it is a dynamic signaling game with imperfect information that allows me to illustrate how to solve for perfect bayesian equilibrium. The “throw it to the girl” Game allows us to model one kind of dynamic that can pop up in the social context of co-ed sports.

Game I: The “call lines” Game

a. The Game Set-up

First things first, I present a simple game based on “calling lines” during an ultimate frisbee game. Ultimate is played with two teams. Each team needs to put 7 people “on the line” to play any given point. However, teams themselves consist of more than 7 people since otherwise those 7 people would probably not be super into playing this sport. (People need some rest!) In my set-up, I assume there are two teams, 1 and 2, that are identical and each always has two lines to choose from: a strong line and a weak line. The payoffs are determined by strategies employed rather than the identity of those teams employing them. In effect, the normal form of this game is a 2×2 symmetric matrix. (This is 2×2 since there are two players–team 1 and team 2–as well as two choices of lines–weak and strong.)

In order to determine the payoffs in this matrix, I need to make assumptions about the team outcomes. In expectation (which is how payoffs in a normal form matrix are presented–as expected Bernoulli utility), weak lines lose to strong lines and the same type of lines win or lose to one another with equal probability. A team gets +3/-3 for winning/losing a point. (If two types of the same type play, they receive 0 in expectation since the probability of a win is 0.5.) Moreover, I assume that teams do not want to overuse their strong lines. Ie, teams do not want to wear out their best players for fear of fatigue or injury. Therefore, teams also receive payoffs of +1/-1 for playing a weak/strong line. Given these simple and linear assumptions,[2] the following represents the normal form game for “call lines”:

tab1.png

b. Prisoner’s Dilemma Form & Solving for Pure Nash Equilibrium

The normal form of the “call lines” game might look very familiar. While conceptually different, it is mathematically identical to everyone’s favorite simple non-cooperative game: the prisoner’s dilemma! Note that the prisoner’s dilemma has infinite representations with respect to the specific payoffs. The overarching requirement is that the game is symmetric across the two players and that the following strict ranking of payoffs holds: [the payoff to a player who “defects” (plays a strong line in this case) while the other “cooperates” (plays a weak line)]  > [the payoff to a player who “cooperates” (plays a weak line) while the other “cooperates” (plays a weak line)] > [the payoff to a player who “defects” (plays a strong line) while the other “defects” (plays a strong line)] > [the payoff to a player who “cooperates” (plays a weak line) while the other “defects” (plays a strong line)].[3] In table 1 we can see this holds since 2>1>-1>-2. I could replace these payoffs in the normal form matrix with any set that maintains the same strict inequality and the game would remain a prisoner’s dilemma.

In the prisoner’s dilemma context, the relevant solution concept is the well-known concept of Nash equilibrium. In Nash equilibrium, no agent (team in this case) has an incentive to deviate if the agent knows the other’s strategy. In order to solve for Nash equilibrium, I underline the best responses of both teams to each other’s strategies:

tab2.png

(Quick refresher as to how to find these marked best responses: Imagine team 1 plays a weak line, then the payoffs to team 2 are either 1 (if play weak) or 2 (if play strong). Since 2>1, team 2 will play strong. Imagine team 1 plays a strong line, then the payoffs to team 2 are either -2 (if plays weak) or -1 (if plays strong). Since -1>-2, team 2 will play strong. The same logic then applies to team 1 since the game is symmetric.)

Since both payoffs in the (-1,-1) box of the matrix are underlined, it is evident that neither team has an incentive to deviate from the strong strategy given that the other team is playing strong. Thus, strong-strong is the sole pure Nash equilibrium in the “call lines” game. However, note that the weak-weak strategy, which yields payoffs (1,1), while not Nash, is pareto optimal (no payoff duo gives both players a higher payoff) and, accordingly, pareto dominates (-1,-1). As Prof Maskin lecture slides wisely say, this “illustrates the tension between efficiency and individual maximization.”

c. Repeated Game Prisoner’s Dilemma & Solving for Subgame Perfect Equilibrium

While the original set-up of this game was in a static context, I can also render “call lines” a repeated game and end up with a different solution concept than the traditional Nash equilibrium previously described. Let’s assume that the same normal form game shown in Table 1 will be played infinitely–this generates an “iterated prisoner’s dilemma.” In this context, I use a solution concept known as subgame perfect equilibrium. Given repetition and recall of previous outcomes/actions, teams now have the opportunity to penalize each other for previous decisions. In the “call lines” context, I investigate the following strategy: play a weak line until someone plays a strong line (play strong from then on). This is also called a “grim trigger strategy,” which alters the choice of lines if someone chooses to deviate from cooperation (playing weak lines). This strategy, therefore, incentives cooperation since otherwise the players punish one another by forcing reduced payoffs for the rest of the infinitely repeated game.

This strategy yields efficiency in subgame perfect equilibrium–a point I show below. Imagine teams have discount factors, meaning they discount future utility flows from points played. The following break-down illustrates how the “grim trigger strategy” is a subgame perfect equilibrium (given some condition on the discount factor):

condcoop copy.png

Thus, if the discount factor is greater than one-third, the grim trigger strategy is a subgame perfect equilibrium for the “call lines” game. However, note that if the number of repetitions of the game is finite and known to both teams, then (by backwards induction) the two players will play strong lines in every period. Therefore, the solution concept is the same as in the static context if the repetition is finite and known, but can diverge if the repetition is infinite and the discount factor meets some requirement. (For a more complete discussion of repeated games and cooperation, check out these slides.)

d. Adding Offense and Defense & Solving for Mixed Nash Equilibrium

I now refine the “call lines” game by adding the concepts of offense and defense. This addition will change the payoffs in the normal form matrix. Assume that team 1 is on offense and team 2 is on defense. When a team starts a point on offense (meaning the other team pulls the disc down field to them–a kick-off in football), they have an advantage for scoring. Assume accordingly that a weak offense will beat a weak defense and a strong offense will beat a strong defense. Therefore, the only offense that loses in a match-up is a weak offense against a strong defense.  Maintaining the same +3/-3 for winning/losing a point and the same +1/-1 for strong/weak lines, the normal form game with player 1 on offense is as follows:

tab3.png

Given this change, the game is no longer symmetric. It is no longer a prisoner’s dilemma, and moreover, there is no longer a pure Nash equilibrium. This can be illustrated with the best responses marked below (ie, there is no box with both payoffs underlined):

tab4.png

While there is no pure Nash equilibrium, we know that all finite games have at least one Nash equilibrium (theorem of existence of Nash equilibrium). Therefore, there must be some mixed Nash equilibrium. Mixed Nash equilibrium is made up of mixed strategies, which are those by which a team plays its available pure strategies (play a weak line, play a strong line) with certain probabilities. In solving for mixed Nash, we consider three possibilities (only team 1 uses a mixed strategy, only team 2 uses a mixed strategy, both use mixed strategies) and make use of the indifference condition as follows:

mixed.png

There is therefore one single mixed Nash equilibrium in which team 1 plays a weak line with probability 2/3 (and so a strong line with probability 1/3) and team 2 plays a weak line with probability 1/3 (and so a strong line with probability 2/3).

e. Recap of “calling lines”

In sum, we have used the original and refined “call lines” set-ups and their corresponding normal forms in order to discuss the prisoner’s dilemma, pure Nash equilibrium, repeated games, subgame perfect equilibrium, and mixed Nash equilibrium. In moving to a more complex and interesting set-up, I now transition to the “throw it to the girl” game.

Game II: The “throw it to the girl” Game

a. The Game Set-up

Ultimate is played in a myriad of circumstances. The most casual form of ultimate frisbee is pick-up–that is, a group of people who get together to play who often don’t know each other. Pick-up is often mixed gender, meaning men and women are playing together, which while empowering and fun can often lead to some noticeable gender dynamics. For instance, playing pick-up in a mixed gender setting can lead to women being “looked off” by male players. [See here for an article on this exact subject that a fellow female frisbee friend recently shared!] In other words, men sometimes do not throw to open women…which can lead to the classic “throw it to the girl!” remark from the sideline as a woman appears open upfield but the dude with the disc chooses to holster the throw instead.  The reasons for this trend (preference for bigger, more dramatic plays in the form of hucks to big dudes, implicit bias, etc.) is not the focus of this discussion…rather, it suffices to note that, yeah, this is a dynamic.

In my own personal experience as a female pickup player, I’ve found that calling for the disc when open is a solid way to signal that I am more experienced or confident and that men shouldn’t hesitate to throw to me. In learning about dynamic signaling games in game theory, I quickly realized that this calling/throwing situation could easily be melded into game theoretic form. Consider the moment when a male player with a disc is looking upfield for a throw. Assume there is an open female cutter upfield. In this moment, the female cutter (player 1 to us) has a choice: she can (1) call for the disc, signaling that she wants to be thrown to, or (2) remain silent and again not be thrown to.

This set-up is a two-player dynamic signaling game. While conceptually distinct, note that this game is identical to the well-known “gift game”! Player 1 has two types: she is either (1) dirty, or (2) a scrub. (Yeah, frisbee vernacular. Let’s go.) In this world, we are assuming that a dirty woman is better than the average male cutter on the pick-up team, while a scrub woman is worse than the average male cutter on the team. We assume that with probability 0.7 nature makes the woman dirty and with probability 0.3 nature makes her a scrub. [This was an arbitrary choice–open to edits on this.] Once the cutter has chosen to yell out or not, the dude with the disc (player 2) has a choice. Player 2 only has one type. He has no choice if the woman is silent since he will unambiguously not throw to her, but if she calls out, he can choose to throw to her or holster (not throw to her).

  • If the woman is silent, the payoffs to both players are 0 regardless of player 1 type since no one gains from this and both players continue functioning at the status quo.
  • If the woman calls out, the payoffs are different depending on her type:
    • Let’s say she is dirty:
      • If the dude throws to her, she gains 2 since she is happy she was thrown to and she played the disc well; the dude in this case is happy since she played the disc better than the average male cutter would have and gets a payoff of 1.
      • If the dude does not throw to her, then she gets a payoff of -1. (This assumes, based on personal and shared experience, that women feel more ignored or disrespected when looked off after being openly vocal than after being silent.) Meanwhile, the dude in this case goes on with the status quo and gets a payoff of 0.
    • Let’s say she is a scrub:
      • If the dude throws to her, she gains 1 since she is happy she was thrown to. (But she doesn’t gain as much as the dirty woman since she’s not as dope at frisbee. I am assuming that people gain more utility from playing when they are dirty.) The dude, in this case, is unhappy since she doesn’t play the disc as well as the average male cutter so he gets payoff of -1.
      • If the dude does not throw to her, she again gets a payoff of -1 and he again gets a payoff of 0. (We are assuming that dirty women and scrubs receive the same payoffs when ignored, but differ in payoffs when they get to play the disc.)

Given these above assumptions for payoffs and dynamics, I used the TikZ package in LaTeX to build out an extensive form of this game. [Thank you to Dr. Chiu Yu Ko who has an incredible set of TikZ Templates openly available–Here is the signaling game one that I built off of.] See figure 1 for the extensive form of this game:

tree2 copy.png

b. Solving for Perfect Bayesian Equilibrium

In the context of such dynamic games with incomplete information, the equilibrium concept of interest is perfect bayesian equilibrium (a refinement of bayesian nash equilibrium and subgame perfect equilibrium).

In order to solve for perfect bayesian equilibrium (PBE from here on), I must investigate all possible strategies for our women in the pick-up game. Since we have two types of women (dirty players/scrubs) as well as two possible actions (call out/be silent), there are four possible strategies. Two of these are what we call “separating strategies” in which the two types choose different actions:

  • dirty player is silent/scrub calls (Figure 2)
  • dirty player calls/scrub is silent (Figure 3).

The other two are called “pooling strategies” in which both types choose the same action:

  • dirty player is silent/scrub is silent (Figure 4)
  • dirty player calls/scrub calls (Figure 5)

For each of the woman’s four possible strategies, I then determine the beliefs and accordingly the optimal response of the dude with the disc. Given that optimal response, I check to see if either of our types of women would like to deviate. If not, then we have a perfect bayesian equilibrium. I will now go through this systematically for the four strategies.

f2.png

The above illustrates the separating equilibrium strategy in which the dirty player is silent and the scrub calls for the disc. (These actions for the two types of women are illustrated in red.) In a separating equilibrium, the action of player 1 signals the type, meaning that if the dude hears a “hey,” he knows she a scrub. The dude’s strategy (recall he only gets to make a choice when there has been a call for the disc) is then to holster the throw since 0>-1. (Thus holster being highlighted in red in the left information set.) Note that given that optimal response from the dude, the scrub female player could improve her payoff by remaining silent instead since 0>-1. In effect, this is not a PBE.

f3.png

The next strategy we consider is that in which a dirty player calls for the disc and a scrub remains silent. In this separating case, the dude knows that if he hears a “hey,” the woman is dirty. So, the dude’s strategy is to throw since 1>0. (Throw is highlighted in red in the left information set.) Given this optimal response from the dude, the scrub female player could improve her payoff by deviating from silence to calling since 1>0. In effect, this is not a PBE.

f4.png

The above figure illustrates the total silence strategy. In such a pooling equilibrium, the dude’s beliefs when hearing a disc called for can be arbitrary since hearing a “hey!” occurs with 0 probability and therefore bayes’ rule doesn’t apply in this context. In effect, if the dude’s beliefs as to the woman’s type are adequately pessimistic (believes with more than 50% certainty that she’s a scrub), then his strategy is to holster the throw (holster highlighted in left information set). (So, diagram is drawn for adequately pessimistic beliefs on the part of the dude.) Regardless of the probabilities determined by nature (0.7 and 0.3), neither player can improve by deviating since (-1,0) is inferior to (0,0). Therefore, this is a PBE. 

f5.png

The last strategy to look into is the all call strategy. In this pooling equilibrium, the dude’s beliefs as to the woman’s type are based on the nature a priori probabilities. The payoff from throwing is thus (1)(0.7)+(-1)(0.3) and the payoff from holstering is (0)(0.7)+(0)(0.3). since 0.4>0, the optimal response for the dude is to throw (as marked by the red). Since 2>0 and 1>0, neither type of woman wants to deviate from the prescribed strategy. In effect, this is a PBE. 

c. Refining the Set of Perfect Bayesian Equilibria

In summary, there are two PBEs for this “throw it to the girl” game: the total silence and all call strategies.  However, note that the total silence strategy is not Pareto efficient while the all call strategy is. Ie, the expected payoffs of 1.7 for the woman and 0.4 for the dude (all call strategy) are larger than 0 payoffs for both (total silence strategy). Moreover, the total silence strategy fails “the intuitive criterion,” a refinement of the set of equilibria proposed by Cho and Kreps (1987). The concept of this requirement is to restrict the set of equilibria to those with “reasonable” off-equilibrium beliefs. This allows me (as the creator of the model) to choose between the multiple PBE’s previously outlined. For a PBE to satisfy the intuitive criterion there must exist no deviation for any type of woman such that the best response of the dude leads to the woman strictly preferring a deviation from the originally chosen strategy.

Let’s explain why the all silent strategy does not satisfy this requirement. Imagine a deviation for the dirty player to calling. If the woman now calls, the best response for the dude is to throw to her, which yields a payoff of 2 for the woman, which is strictly greater than 0. So, the woman prefers this deviation and the intuitive criterion is not satisfied. However, the all call strategy passes this criterion. Imagine a deviation to silence for the dirty player. Then there is no best response for the dude since the payoffs are automatically 0 and 0. Since 2>0, the woman doesn’t prefer the deviation. Similarly, a deviation to silence for the scrub yields 0 instead of 1, which is not preferred either. Thus, the all call strategy satisfies the intuitive criterion. In effect, when we refine the set of equilibria in this way, we have both types of women calling for the disc and the dude making the throw… Sounds like a pretty good equilibrium to me![4]

d. Recap of “throw it to the girl”

We have used this “throw it to the girl” set-up and its corresponding extensive form in order to discuss dynamic signaling games, solving for perfect bayesian equilibrium, and refining the set of equilibria using the intuitive criterion.

Hard cap is on! [In frisbee parlance, it’s time to wrap this all up]

There are endless ways to extend or reform these games in the world of game theoretic concepts. My formulations for “calling lines” and “throw it to the girl” are simple by design in order that they lend themselves to discussing some subset of useful concepts. However, despite the simplicity of the model builds, I’m happy to be able to arrive at conclusions that involve social behaviors as complex as gender dynamics… For example, next time, instead of yelling “throw it to the girl!” from the sideline, you can always shout: “assuming a gift-giving game payoff structure, it is a perfect bayesian equilibrium satisfying the intuitive criterion for you to throw to open women when they call for it!” No worries–if they don’t understand, you can always womansplain the concept during the next time-out.

Code

Check out the relevant Github repository for all tex files necessary for reproducing the tables, tree diagrams, and solution write-ups!

Footnotes

[1] The good news is that since I’m pretty sure some nontrivial percentage of ultimate players have studied math, I don’t have to worry too much about this discussion being for some empty intersection of individuals.

[2] Comments on how to improve this are very welcomed. For this introductory context, I feel these payoffs suffice since it allows me to get into the prisoner’s dilemma and some useful simple equilibrium concepts.

[3] These requirements render the game a non-cooperative one. Prisoner’s dilemma terminology is often used for contexts that in fact would be better categorized as cooperative games such as Stag hunt. In the Stag hunt (or cooperative game) payoff matrix, the inequality relationship would instead be: [the payoff to a player who “cooperates” while the other “cooperates”] >[the payoff to a player who “defects” while the other “cooperates”]  >= [the payoff to a player who “defects” while the other “defects”] > [the payoff to a player who “cooperates” while the other “defects”]

[4] More generally, this will be the case as long as the nature a priori probabilities have the probability of the woman being dirty as 0.5 or greater.


© Alexandra Albright and The Little Dataset That Could, 2017. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

Where My Girls At? (In The Sciences)

Line Charts, Scatter Plots
Intro

In the current educational landscape, there is a constant stream of calls to improve female representation in the sciences. However, the call to action is often framed within the aforementioned nebulous realm of “the sciences”—an umbrella term that ignores the distinct environments across the scientific disciplines. To better understand the true state of women in “the sciences,” we must investigate representation at the discipline level in the context of both undergraduate and doctoral education. As it turns out, National Science Foundation (NSF) open data provides the ability to do just that!

The NSF’s Report on Women, Minorities, and Persons with Disabilities in Science and Engineering includes raw numbers on both undergraduate and doctoral degrees earned by women and men across all science disciplines. With these figures in hand, it’s simple to generate measures of female representation within each field of study—that is, percentages of female degree earners. This NSF report spans the decade 2002–­2012 and provides an immense amount of raw material to investigate.[1]

The static picture: 2012

First, we will zero in on the most recent year of data, 2012, and explicitly compare female representation within and across disciplines.[2]

fig1

The NSF groups science disciplines with similar focus (for example, atmospheric and ocean sciences both focus on environmental science) into classified parent categories. In order to observe not only the variation within each parent category but also across the more granular disciplines themselves, the above graph plots percentage female representation by discipline, with each discipline colored with respect to its NSF classified parent category.

The variation within each parent category can be quite pronounced. In the earth, atmospheric, and ocean sciences, female undergraduate representation ranges from 36% (atmospheric sciences) to 47% (ocean sciences) of total graduates. Among PhD graduates, female representation ranges from 39% (atmospheric sciences) to 48% (ocean sciences). Meanwhile, female representation in the physical sciences has an undergraduate range from 19% (physics) to 47% (chemistry) and a PhD range from 20% (physics) to 39% (chemistry). However, social sciences has the largest spread of all with undergraduate female representation ranging from 30% (economics) to 71% (anthropology) and PhD representation ranging from 33% (economics) to 64% (anthropology).

In line with conventional wisdom, computer sciences and physics are overwhelmingly male (undergraduate and PhD female representation lingers around 20% for both). Other disciplines in which female representation notably lags include: economics, mathematics and statistics, astronomy, and atmospheric sciences. Possible explanations behind the low representation in such disciplines have been debated at length.

Interactions between “innate abilities,” mathematical content, and female representation

Relatively recently, in January 2015, an article in Science “hypothesize[d] that, across the academic spectrum, women are underrepresented in fields whose practitioners believe that raw, innate talent is the main requirement for success, because women are stereotyped as not possessing such talent.” While this explanation was compelling to many, another group of researchers quickly responded by showing that once measures of mathematical content were added into the proposed models, the measures of innate beliefs (based on surveys of faculty members) shed all their statistical significance. Thus, the latter researchers provided evidence that female representation across disciplines is instead associated with the discipline’s mathematical content “and that faculty beliefs about innate ability were irrelevant.”

However, this conclusion does not imply that stereotypical beliefs are unimportant to female representation in scientific disciplines—in fact, the same researchers argue that beliefs of teachers and parents of younger children can play a large role in silently herding women out of math-heavy fields by “becom[ing] part of the self-fulfilling belief systems of the children themselves from a very early age.” Thus, the conclusion only objects to the alleged discovery of a robust causal relationship between one type of belief, university/college faculty beliefs about innate ability, and female representation.

Despite differences, both assessments demonstrate a correlation between measures of innate capabilities and female representation that is most likely driven by (1) women being less likely than men to study math-intensive disciplines and (2) those in math-intensive fields being more likely to describe their capacities as innate.[3]

The second point should hardly be surprising to anyone who has been exposed to mathematical genius tropes—think of all those handsome janitors who write up proofs on chalkboards whose talents are rarely learned. The second point is also incredibly consistent with the assumptions that underlie “the cult of genius” described by Professor Jordan Ellenberg in How Not to Be Wrong: The Power of Mathematical Thinking (p.412):

The genius cult tells students it’s not worth doing mathematics unless you’re the best at mathematics, because those special few are the only ones whose contributions matter. We don’t treat any other subject that way! I’ve never heard a student say, “I like Hamlet, but I don’t really belong in AP English—that kid who sits in the front row knows all the plays, and he started reading Shakespeare when he was nine!”

In short, subjects that are highly mathematical are seen as more driven by innate abilities than are others. In fact, describing someone as a hard worker in mathematical fields is often seen as an implicit insult—an implication I very much understand as someone who has been regularly (usually affectionately) teased as a “try-hard” by many male peers.

The dynamic picture: 2002–2012

Math-intensive subjects are predominately male in the static picture for the year 2012, but how has the gender balance changed over recent years (in these and all science disciplines)? To answer this question, we turn to a dynamic view of female representation over a recent decade by looking at NSF data for the entirety of 2002–2012.

fig2

The above graph plots the percentages of female degree earners in each science discipline for both the undergraduate and doctoral levels for each year from 2002 to 2012. The trends are remarkably varied with overall changes in undergraduate female representation ranging from a decrease of 33.9% (computer sciences) to an increase of 24.4% (atmospheric sciences). Overall changes in doctoral representation ranged from a decline of 8.8% (linguistics) to a rise of 67.6% (astronomy). The following visual more concisely summarizes the overall percentage changes for the decade.

fig3

As this graph illustrates, there were many gains in female representation at the doctoral level between 2002 and 2012. All but three disciplines experienced increased female representation—seems promising, yes? However, substantial losses at the undergraduate level should yield some concern. Only six of the eighteen science disciplines experienced undergraduate gains in female representation over the decade.

The illustrated increases in representation at the doctoral level are likely extensions of gains at the undergraduate level from the previous years—gains that are now being eroded given the presented undergraduate trends. The depicted losses at the undergraduate level could very well lead to similar losses at the doctoral level in the coming decade, which would hamper the widely shared goal to tenure more female professors.

The change for computer sciences is especially important since it provides a basis for the vast, well-documented media and academic focus on women in the field. (Planet Money brought the decline in percentage of female computer science majors to the attention of many in 2014.) The discipline experienced a loss in female representation at the undergraduate level that was more than twice the size of that in any other subject, including physics (-15.6%), earth sciences (-12.2%), and economics (-11.9%).

While the previous discussion of innate talent and stereotype threat focused on math-intensive fields, a category computer sciences fall into, I would argue that this recent decade has seen the effect of those forces on a growing realm of code-intensive fields. The use of computer programming and statistical software has become a standard qualification for many topics in physics, statistics, economics, biology, astronomy, and other fields. In fact, completing degrees in these disciplines now virtually requires coding in some way, shape, or form.

For instance, in my experience, one nontrivial hurdle that stands between students and more advanced classes in statistics or economics is the time necessary to understand how to use software such as R and Stata. Even seemingly simple tasks in these two programs requires some basic level of comfort with structuring commands—an understanding that is not taught in these classes, but rather mentioned as a quick and seemingly obvious sidebar. Despite my extensive coursework in economics and mathematics, I am quick to admit that I only became comfortable with Stata via independent learning in a summer research context, and R via pursuing projects for this blog many months after college graduation.

The implications of coding’s expanding role in many strains of scientific research should not be underestimated. If women are not coding, they are not just missing from computer science—they will increasingly be missing from other disciplines which coding has seeped into.

The big picture: present–future

In other words, I would argue academia is currently faced with the issue of improving female representation in code-intensive fields.[4] As is true with math-intensive fields, the stereotypical beliefs of teachers and parents of younger children “become part of the self-fulfilling belief systems of the children themselves from a very early age” that discourage women from even attempting to enter code-intensive fields. These beliefs when combined with Ellenberg’s described “cult of genius” (a mechanism that surrounded mathematics and now also applies to the atmosphere in computer science) are especially dangerous.

Given the small percentage of women in these fields at the undergraduate level, there is limited potential growth in female representation along the academic pipeline—that is, at the doctoral and professorial levels. While coding has opened up new, incredible directions for research in many of the sciences, its evolving importance also can yield gender imbalances due to the same dynamics that underlie underrepresentation in math-intensive fields.

Footnotes

[1] Unfortunately, we cannot extend this year range back before 2002 since earlier numbers were solely presented for broader discipline categories, or parent science categories—economics and anthropology would be grouped under the broader term “social sciences,” while astronomy and chemistry would be included under the term “physical sciences.”

[2] The NSF differentiates between science and engineering as the latter is often described as an application of the former in academia. While engineering displays an enormous gender imbalance in favor of men, I limit my discussion here to disciplines that fall under the NSF’s science category.

[3] The latter viewpoint does have some scientific backing. The paper “Nonlinear Psychometric Thresholds for Physics and Mathematics” supports the notion that while greater work ethic can compensate for lesser ability in many subjects, those below some threshold of mathematical capacities are very unlikely to succeed in mathematics and physics coursework.

[4] On a positive note, atmospheric sciences, which often involves complex climate modeling techniques, has experienced large gains in female representation at the undergraduate level.

Speaking of coding…

Check out my relevant Github repository for all data and R scripts necessary for reproducing these visuals.

Thank you to:

Ally Seidel for all the edits over the past few months! & members of NYC squad for listening to my ideas and debating terminology with me.


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

The Rise of the New Kind of Cabbie: A Comparison of Uber and Taxi Drivers

Bar Charts, Stacked Bar Charts
Intro

One day back in the early 2000’s, I commandeered one of my mom’s many spiral notebooks. I’d carry the notebook all around Manhattan, allowing it to accompany me everywhere from pizza parlors to playgrounds, while the notebook waited eagerly for my parents to hail a taxicab so it could fulfill its eventual purpose. Once in a cab, after clicking my seat belt into place (of course!), I’d pull out the notebook in order to develop one of my very first spreadsheets. Not the electronic kind, the paper kind. I made one column for the date of the cab ride, another for the driver’s medallion number (5J31, 3A37, 7P89, etc.) and one last one for the driver’s full name–both the name and number were always readily visible, pressed between two slabs of Plexiglas that intentionally separate the back from the front seat. Taxi drivers always seemed a little nervous when they noticed I was taking down their information–unsure of whether this 8-year-old was planning on calling in a complaint about them to the Taxi and Limousine Commission. I wasn’t planning on it.

Instead, I collected this information in order to discover if I would ever ride in the same cab twice…which I eventually did! On the day that I collected duplicate entries in the second and third columns, I felt an emotional connection to this notebook as it contained a time series of yellow cab rides that ran in parallel with my own development as a tiny human. (Or maybe I just felt emotional because only children can be desperate for friendship, even when it’s friendship with a notebook.) After pages and pages of observations, collected over the years using writing implements ranging from dull pencils to thick Sharpies, I never would have thought that one day yellow cabs would be eclipsed by something else…

Something else

However, today in 2015, according to Taxi and Limousine Commission data, there are officially more Uber cars in New York City than yellow cabs! This is incredible not just because of the speed of Uber’s growth but also since riding with Uber and other similar car services (Lyft, Sidecar) is a vastly different experience than riding in a yellow cab. Never in my pre-Uber life did I think of sitting shotgun. Nor did I consider starting a conversation with the driver. (I most definitely did not tell anyone my name or where I went to school.) Never did my taxi driver need to use an iPhone to get me to my destination. But, most evident to me is the distinction between the identities of the two sets of drivers. It is undoubtedly obvious that compared to traditional cab service drivers, Uber drivers are younger, whiter, more female, and more part-time. Though I have continuously noted these distinctions since growing accustomed to Uber this past summer, I did not think that there was data for illustrating these distinctions quantitatively. However, I recently came across the paper “An Analysis of the Labor Market for Uber’s Driver-Partners in the United States,” written by (Economists!) Jonathan Hall and Alan Krueger. The paper supplies tables that summarize characteristics of both Uber drivers and their conventional taxi driver/chauffeur counterparts. This allows for an exercise in visually depicting the differences between the two opposing sets of drivers—allowing us to then accurately define the characteristics of a new kind of cabbie.  

The rise of the younger cabbie

age.png

The above figure illustrates that Uber drivers are noticeably younger than their taxi counterparts. (From here on, when I discuss taxis I am also implicitly including chauffeurs. If you’d like to learn more about the source of the data and the collection methodology, refer directly to the paper.) For one, the age range including the highest percentage of Uber drivers is the 30-39 range (with 30.1% of drivers) while the range including the highest percentage of taxi drivers is the 50-64 range (with 36.6% of drivers). While about 19.1% of Uber drivers are under 30, only about 8.5% of taxi drivers are this young. Similarly, while only 24.5% of Uber drivers are over 50, 44.3% of taxi drivers are over this threshold. This difference in age is not very surprising given that Uber is a technological innovation and, therefore, participation is skewed to younger individuals.

The rise of the more highly educated cabbie

educ.png

This figure illustrates that Uber drivers, on the whole, are more highly educated than their taxi counterparts. While only 12.2% of Uber drivers do not possess a level of education beyond high school completion, the majority of taxi drivers (52.5%) fall into this category. The percentage of taxi drivers with at least a college degree is a mere 18.8%, but the percentage of Uber drivers with at least a college degree is 47.7%, which is even higher than that percentage for all workers, 41.1%. Thus, Uber’s rise has created a new class of drivers whose higher education level is superior to that of the overall workforce. (Though it is worth noting that the overall workforce boasts a higher percentage of individuals with postgraduate degrees than does Uber–16% to 10.8%.)

The rise of the whiter cabbie

race.png

On the topic of race, conventional taxis boast higher percentages of all non-white racial groups except for the “Other Non-Hispanic” group, which is 3.9 percentage points higher among the Uber population. The most represented race among taxi drivers is black, while the most represented race among Uber drivers is white. 19.5% of Uber drivers are black while 31.6% of taxi drivers are black, and 40.3% of Uber drivers are white while 26.2% of taxi drivers are white. I would be curious to compare the racial breakdown of Uber’s drivers to that of Lyft and Sidecar’s drivers as I suspect the other two might not have populations that are as white (simply based on my own small and insufficient sample size).

The rise of the female cabbie

gender.png

It has been previously documented how Uber has helped women begin to “break into” the taxi industry. While only 1% of NYC yellow cab drivers are women and 8% of taxis (and chauffeurs) as a whole are women, an impressive 14% of Uber drivers are women–a percentage that is likely only possible in the driving industry due to the safety that Uber provides via the information on its riders.

The rise of the very-part-time cabbie

hours.png

A whopping 51% of Uber drivers drive a mere 1-15 hours per week though only 4% of taxis do so. This distinction in driving times between the two sets of drivers makes it clear that Uber drivers are more likely to be supplementing other sources of income with Uber work, while taxi drivers are more likely to be working as a driver full-time (81% of taxis drive more than 35 hours a week on average, but only 19% of Uber drivers do so). In short, it is very clear that Uber drivers treat driving as more of a part-time commitment than do traditional taxi drivers.

Uber by the cities

As a bonus, beyond profiling the demographic and behavioral differences between the two classes of drivers, I present some information about how Uber drivers differ city by city. While this type of comparison could also be extremely interesting for demographic data (gender, race, etc.), hours worked and earnings are the only available pieces of information profiled by city in Hall and Krueger (2015).

Uber by the cities: hours

city.png

New York is the city that possesses the least part-time uberX drivers. (Note: This data is only looking at hours worked for uberX drivers in October 2014.) Only 42% work 1-15 hours while the percentage for the other cities ranges from 53-59%. Similarly, 23% of NYC Uber drivers work 35+ hours while the percentage for other cities ranges from 12-16%. Though these breakdowns are different for each of the six cities, the figure illustrates that Uber driving is treated pretty uniformly as a part-time gig throughout the country.

Uber by the cities: earnings

Also in the report was a breakdown of median earnings per hour by city. An important caveat here is that these are gross pay numbers and, therefore, they do not take into account the costs of driving a Taxi or an Uber. If you’d like to read a quick critique of the paper’s statement that “the net hourly earnings of Uber’s driver-partners exceed the hourly wage of employed taxi drivers and chauffeurs, on average,” read this. However, I will not join this discussion and instead focus only on gross pay numbers since costs are indeed unknown.

earning_by_city.png

According to the report’s information, NYC Uber drivers take in the highest gross earnings per hour ($30.35), followed by SF drivers ($25.77). These are also the same two cities in which the traditional cabbies make the most, however while NYC taxi counterparts make a few dollars more per hour than those in other cities, the NYC Uber drivers make more than 10 dollars per hour more than Boston, Chicago, DC, and LA Uber drivers.

Endnote

There is no doubt that the modern taxi experience is different from the one that I once cataloged in my stout, spiral notebook. Sure, Uber drivers are younger than their conventional cabbie counterparts. They are more often female and more often white. They are more likely to talk to you and tell you about their other jobs or interests. But, the nature of the taxi industry is changing far beyond the scope of the drivers. In particular, information that was once unknown (who took a cab ride with whom and when?) to those not in possession of a taxi notebook is now readily accessible to companies like Uber. Now, this string of recorded Uber rides is just one element in an all-encompassing set of (technologically recorded) sequential occurrences that can at least partially sketch out a skeleton of our lived experiences…No pen or paper necessary.

Bonus: a cartoon!
uberouterspace

The New Yorker Caption Contest for this week with my added caption. The photo was too oddly relevant to my current Uber v. Taxi project for me to not include it!

 Future work (all of which requires access to more data)
  • Investigate whether certain age groups for Uber are dominated by a specific race, e.g. is the 18-39 group disproportionately white while the 40+ group is disproportionately non-white?
  • Request data on gender/race breakdowns for Uber and Taxis by city
    • Looking at the racial breakdowns for NYC would be particularly interesting since the NYC breakdown is likely very different from that of cabbies throughout the rest of the country (this data is not available in the Taxicab Fact Book)
  • Compare characteristics by ride-sharing service: Uber, Lyft, and Sidecar
  • Investigate distribution of types of cars driven by Uber, Lyft, and Sidecar (Toyota, Honda, etc.)
Code

The R notebook for replicating all visuals is available here. See full github repo for the data as well. (Both updated 7-27-17)


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

The Distribution of ‘Sports Illustrated’ Covers: The Bikini’d & The Not

Stacked Bar Charts
 Intro

It’s that time of year…the time of year when we are all reminded that the Swimsuit Issue of Sports Illustrated exists, a fact that made John Oliver’s team recently ask, “do people not understand they can now just type ‘naked ladies’ into the internet and see what Google throws at them?” On top of being reminded of the Swimsuit Issue’s existence, I also recently became reminded of a question that has often popped into my head about Sports Illustrated: How many female athletes are on the cover of this magazine as compared to the number of swimsuit-clad models?

Investigation

In order to address this question, I collected data from the online SI Covers Archive for years 2010-2014–a five year time span that consists of 487 covers. Specifically, I counted the number of covers featuring male athletes/coaches (448), other males (4), female athletes/coaches (13), female swimsuit models (7), other miscellaneous women (5), and covers that are featuring no individual or group of individuals in particular (10–these mostly consists of covers that are just text or pictures of objects). Amazingly, the counts illustrate that just 2.67% of all covers featured female athletes or coaches. And, out of the 13 that did, only 3 covers featured female athletes of color, which happens to be less than the number of times Kate Upton graced the cover (once in 2012, twice in 2013, and once in 2014)!

In order to better comprehend what this means for women in sports, imagine that you were to pick randomly from all 25 magazines that featured women on the cover. Upon picking randomly, you would have a 28% chance the magazine would feature a swimsuit model, a 20% chance the magazine would feature a woman in the miscellaneous category, and just a 52% chance it would be featuring a female athlete or coach (which includes the minuscule 12% chance it features a female athlete of color)! Meanwhile, 99.12% of covers featuring males are male athletes/coaches.

Visualization

See the following visualization to get more of a feeling for the aforementioned statistics and note the proximity between the frequency of female athlete covers and that of female swimsuit model covers. (Click to enlarge.)

si

Data from SI Cover Archives 2010-2014. Visualization made using ggplot2 package in R.

It is also interesting to note that if SI were to have required the same ratio of athletes/coaches to swimsuit models for men that held for women over this five year time period (7 swimsuit models for every 13 athlete/coach covers) there would have been 241 SI issues with male swimsuit models on the cover from 2010-2014. That is approximately 48 issues with male swimsuit models on the cover per year!

Despite the obviously tiny nature of the slice of SI covers that female athletes/coaches occupy, the unfortunate reality of the situation is that these numbers actually overestimate women’s importance in the magazine since only 9–or 1.85% of all the 487 covers of interest–featured a female athlete/coach as the primary or sole image on the cover. In other words, even though there are only a paltry 13 covers that feature female athletes/coaches, four of these still feature men in some regard. And while the magazine only managed to feature a female athlete or coach as the sole image 9 times, it managed to feature a female swimsuit model as the sole image 6 times (six swimsuit issue covers). In this case, if you were to pick randomly from the 15 covers of SI that feature women as the sole image, you would have a 40% chance of picking a swimsuit issue. 

SI is not alone

However, it is important to note that SI is not unique in its lack of representation of female athletes. No, SI is just one of many microcosms within the larger sports universe–a universe in which female athletes were receiving around 1.6% of network news and ESPN Sportscenter airtime in 2009. Given the time that commercials take up, I would not be surprised if female models eating juicy, dripping hamburgers get more screen time than female athletes on these very sports channels. And, if that is true, then Sports Illustrated covers might actually possess a higher female athlete/coach to female model ratio compared to the major sports networks!

Make of that what you will… I’m off to eat a cheeseburger in a bikini.

«Update [7-14-15]: The Ascent of the ‘Sports Illustrated’ Female Athlete»

Sports Illustrated just released 25 different covers to celebrate the World Cup-Winning US Women’s Soccer Team–one for each of the 23 players, one for coach Jill Ellis, and one for a group of the teammates. In other words, Sports Illustrated just released 25 covers featuring female athletes/coaches, which is almost twice the number of such covers released over the past five years combined. (During the period 2010-2014, just 13 covers featured female athletes and/or coaches).

This surge in female athlete representation majorly affects the graphs that I had previously made on this subject, so I decided to make a new visual to communicate the remarkable nature of the year of 2015 for “The ‘Sports Illustrated’ Female Athlete.” See below (Click to enlarge):

si

Endnote on data collection

Breaking the SI covers down into the aforementioned six categories was not always completely straightforward. For instance, there are a few dozen that feature both men and women… or both male athletes and crouching cheerleaders. In order to avoid complaints over underestimation, I count covers with at least one woman (athlete/coach, miscellaneous, swimsuit model) as a cover featuring a woman even if there are, say, three men in the picture but just one woman. However, if the cover is clearly featuring a male athlete but there a collage or background that includes a woman (both of these circumstances usually arise in the “March Madness” covers) I count that as a cover featuring a male athlete since the women who may appear in the background are either tiny or just a piece of a larger anonymous crowd–it would be a misrepresentation of the true nature of the cover to put these types of covers in the category of those featuring women. (If you’re curious, see my “SportsIllustrated” Github repo for the raw data as well as the R script necessary to create the stacked bar charts.)


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

I’d Like to Thank the Academy…for making this data available

Heat Maps
Intro

The Oscars, like most award shows, are a mixture of the scripted and the unscripted. While the skeleton of the show rests upon the predetermined quips of the host and award presenters, the flesh of the Oscars rests within the surprise wins that are embodied by acceptance speeches given by excited, nervous, and often emotional award winners. Every year there are dozens of Oscar speeches and this year I began to wonder what one could glean from all that information abstractly balled up into little packages of “thank you”s and “wow”s and “I love you, mom”s that are spilled out onto the stage year after year.

Previous inquiries into Oscar speeches have investigated whom people thank while on stage as well as the counts associated with certain phrases such as “Wow,” “England,” and even “Oprah.” However, a topic that has not been deeply investigated is how features of acceptance speeches differ across groups of winners. For instance, with respect to word count, it is certain that the most-hyped awards (Director, Best Picture, Best Actor, etc.) have speeches with higher word counts than others since the threat of being “played off” is not as looming for the sparkling celebs as it is for the sincere, but not-Dior-wearing, Documentary Filmmakers. On the other hand, I was less certain about how Best Director speech lengths would compare to Best Picture speech lengths–they are definitely shorter than Best Picture but longer than Visual Effects, however, the specifics have not been previously documented.

Another element of speeches that I thought would be interesting to investigate is the usage of words that are explicitly self-referential, such as “I” or “me,” as opposed to words that reference one’s part of a larger group, such as “we” or “us.” Comparing the percentages of self-related words to the percentages of team-related words could tell us something about the degree to which certain awards are self-oriented or team-oriented.

Approach

In order to address both the element of word count as well as the element of the self vs. the team, I used the Academy Awards Acceptance Speech Database (yes, that is a thing!) to collect the transcripts of all acceptance speeches given over the past 5 years (that is, speeches given during the Oscars 2010-2014) and looked into four specific statistics by award winner category.

The four statistics are as follows:

  1. Average word count (“Word.Count”)
  2. Average percentage of words related to the self (“I.Percent”)
  3. Average percentage of words related to the group (“We.Percent”)
  4. The ratio of self-words to group-words, which can then function as a quasi-measure of self-involvement (“Self.Ratio”)
Results by award categories

See the heat table below (made using the ggplot2 package in R) for the averages of these four statistics across all award categories:

oscarplot

Heat table depicting averages of four statistics of interest over award categories. Note (1): In 2012, Woody Allen was not present to accept the Writing (Original Screenplay) award. Counting that event as 0 words spoken for the category yields the average shown above while excluding that event from the average yields a modified average of 167.8 words for the category. Note (2): Two teams were awarded the Sounding Editing Oscar in 2012. I calculate the average per team speech, thus, these two speeches were treated as though they were in separate years. I did this in order to avoid overestimating words spoken within this category.

Far from surprising, the speeches with the highest word count are Best Picture, Actress in a Leading Role, and Actor in a Leading Role. The awards with the highest I.Percent are Actor in a Leading Role, 8.8%, Short Film (Live Action), 8.7%, Writing (Original Screenplay), 8.6%, Cinematography, 8.4%, and Actress in a Leading Role, also 8.4%. However, it is notable that neither Actor in a Leading role nor Actress in a Leading Role are in the group with the highest Self.Ratio, instead, the awards with the highest Self.Ratio are Foreign language Film, 8.8, Short Film (Live Action), 7.9, and Writing (Original Screenplay), 7.3. The fact that Foreign Language Film has the highest Self.Ratio is very surprising since that is the equivalent of the Foreign Best Picture, which should be discussed on stage as an extremely collaborative venture. (It is possible that part of this is due to language barriers since, for non-native speakers, it is more difficult to switch between the subjects “we” and “I” than to just stick with “I.”) On the other end of the spectrum, the most team-oriented award categories (using the Self.Ratio metric) are Documentary (Short Subject), 0.5, Sound Mixing, 1.1, Visual Effects, 1.2, Short Film (Animated), 1.2, and Makeup/Makeup and Hairstyling, 1.2.

Results by gender/actor

Though I was originally primarily interested in the averages of these statistics over the award winner categories, I realized I could also investigate these same statistics over four gender-actor categories: Female Actor, Female Non-Actor, Male Actor, Male Non-Actor. Using this breakdown, I was curious to see whether male and female actors as well as male and female non-actors would have similar statistic averages.

genderactor

Heat table depicting averages of four statistics of interest over gender-actor categories.

It is immediately evident from the heat table that both genders of actors possess very similar numbers across all four statistics. Meanwhile, the Male Non-Actors speak almost twice as much as the Female Non-Actors, 136.4 words compared to 76.5 words. Therefore, outside of the actors, if you’ve ever thought that women don’t speak as much as men during acceptance speeches the Oscars, this is not just a consequence of fewer female award winners–no, this means that even when women do win an award, they, on average, only speak half as much as the men who win. I would hypothesize this is because women rarely speak during the non-acting awards with the longest word counts–the Best Picture and Directing Oscars (In fact, only one woman has ever won the Directing Oscar). The fact that women often don’t get to speak in these two large categories probably makes a significant difference in the non-acting word count averages. Furthermore, this gender word count difference could also be due to the fact that, since women often win non-acting awards within a larger team, men on the team speak first and use up some of the team’s shared time, leading to a shorter word count for women’s speeches.

The heat table also makes evident that Actors possess higher Self.Ratios than Non-Actors and Male Non-Actors have a noticeably higher Self.Ratio than Female Non-Actors, 2.8 compared to 1.6. This implies that women outside the sphere of acting are more likely than their male counterparts to use words that emphasize the greater team effort. Part of this difference could, again, be due to the fact that women are more likely to share awards than men, meaning their acceptance speech lexicon reflects this circumstance.

More on gender

Due to the obvious differences between non-actor men and women, I decided to delve deeper into the question of gender in acceptance speeches. Instead of looking into words spoken per speech, I now look at aggregate words spoken during the acceptance speeches of the past five years of award ceremonies. Male and female actors have spoken very similar amounts, with 2,718 words spoken by female actors and 2,752 words spoken by male actors. On the other hand, the distinction between non-actors is striking but unsurprising if you’ve paid attention to who you are always listening to when watching the show–while 2,065 words have been spoken by female non-actors, 12,416 words have been spoken by male non-actors. See below for a simple visualization of these differences:

pie

These numbers mean that outside of the case of the actors, men have spoken more than six times as many words as women in acceptance speeches over the past five years of Oscar ceremonies. Even more disturbing is that, over the past five years, the total number of words spoken by female actor winners, 2,718, is greater than the number of words spoken by all other women during the rest of the acceptance speeches, 2,065 words. It is clearly troubling that the two awards that necessitate female winners generate more words spoken by women than do all other awards.

It is a well-known fact that more many more men win awards than women. Specifically, in the past five years, the winners list includes 141 men and 39 women (excluding Best Picture and Foreign Language Film since these are not awards for individuals). When excluding the two male actors and two female actors that win every year, that becomes 131 men and 29 women. However, as I illustrated in the second heat table, even when women win in non-actor categories, they still talk significantly less than the men who win non-actor categories (approximately half as much).

I mentioned previously that I thought this could be because when women win in non-actor categories, a team often accepts the award, which might lead to women being talked over by men. Well, while men tend to speak first, it is not as egregious as one might think–it turns out that in the past five years there were 16 instances in which at least one man and one woman spoke on the stage in order to accept an award together. In 11 of these 16 instances, a man spoke first to begin accepting the award. As Elinor Burkett exclaimed, after her male co-winner spoke, in her 2009 Documentary (Short Subject) acceptance speech:

Don’t you like that the man never lets the woman talk. Isn’t that just the classic thing?

In short, it is worth realizing that women are not just underrepresented in terms of their number of Oscar wins, they are also underrepresented by the number of words they are able to speak on behalf of their own victories.

Endnote

The master csv file with all the speeches from the past five years and gender-actor dummy variable codings is available upon request, as is the R code for all visualizations.

Future work
  • Add more years into this analysis (so that it spans more than 5 years of data)
  • Look into coding race variables on top of gender and actor variables
  • Does speech length serve as a type of proxy for how much viewers care about each award? One could easily imagine a model of the Oscars in which over the years past winners have spoken for as long as possible until they are cut off (due to lack of time and more interest in another award). Then, over time the award winners learn their category’s limit to keep the audience interested. However, would word count be a perfect measure of how much we care about awards in comparison to one another? For instance, if the word count of Best Picture acceptance speeches are three times as long as Best Supporting Actress speeches, does that really mean that viewers care three times as much about Best Picture as they do about Best Supporting Actress? 
Statistic creation notes

In order to measure “I.Percent,” my Stata code counted the number of instances of “I ”, “I’”, “me ”, “my ”, “My ”, “Me “, and “myself” (self-words) in a speech and calculated that number as a percentage of the total speech word count. In order to measure “We.Percent,” my code followed the same process as that described for “I.Percent” with respect to instances of “We ”, “we ”, “our ”, “Our “, “ourselves”, “us ”, “we'”, and “We'” (group-words). The measure “Self.Ratio” divided the count of self-words by the count of group-words in order to create a quasi-measure of self-involvement. All scripts and data files necessary to recreate the included visualizations are available in my “Oscars” Github repo.


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.