The Game Theory of Extra Credit

There are few phrases that college students love to hear more than "extra credit." However, one professor at the University of Maryland found a way to turn extra credit against his students by asking a very simple question at the end of one of his psychology exams:

"Here you have the opportunity to earn some extra credit on your final paper grade. Select whether you want 2 points or 6 points added onto your final paper grade. But there's a small catch: if more than 10% of the class selects 6 points, then no one gets any points. Your responses will be anonymous to the rest of the class, only I will see the responses."

We can examine the potential payoffs of the possible decisions each student faces.

While this is not a true prisoners' dilemma because each student doesn't have a dominant strategy, the chances of you being the deciding vote are very slim, and only decreases as the class size increases. Thus, in a large class, each (rational) student is most likely to choose 6 points, ultimately leading to the entire class receiving zero extra credit points.

This is very cool, but I think that a teacher could combine this tactic with another phrase that college students love to hear - "the class is curved" - in order to create a true prisoner's dilemma and ensure that, for any size class, the end result will be that no one receives extra credit. Curves mean that the absolute value of your grade means nothing, and what really matters is your grade relative your other classmates. Thus, the potential payoffs become:

Each student now has a dominant strategy to choose 6 points. If less than 10% of the class chooses 6 points, then choosing 2 points would give you at best 0 relative points (if the entire class chooses 2 points) and most likely negative relative points (if at least one other person chooses 6 points). The same thing occurs if you are the deciding vote. Therefore, each student is at least as good off by choosing 6 points as they would have been if they chose 2 points.

In the end, the professor looks benevolent because he offered extra credit to his students, and the students learn a valuable lesson about game theory. The only thing irrational about this is why more professors don't use it in their classes.

UVA Men's Club Soccer's Ride to Nationals

UVA Men’s Club Soccer is going to the National Championship for the third year in a row! The event will be held in Foley, Alabama, within the next two weeks. We’ve been able to achieve this feat without any coaches, while many other club teams do have coaching staffs, as we are a completely student run organization. In the meantime, our team is hard at work training for the big event. Recently, however, we have been running into a problem of our two new players forgetting to carry the ball bags to and from practice, leaving our seniors with the task of picking up their slack. This is a small task that every new club team member has had to do for years and their failure to do so can be explained by a Prisoner’s Dilemma.

Each new player has the same choice: they can either carry the ball bag to and from practice or they can leave, knowing that someone else will pick it up. Clearly, both players would pick the dominant strategy of not carrying the ball bag. Neither player would be worse off from not having to do their simple task, leading to the pareto inefficient equilibrium. Since we do not have a coach to ensure that they do the pareto inefficient team policy, our seniors will have to keep doing the work the new players are supposed to do, not allowing us to reach the desired pareto efficient equilibrium.

Since this is a pride issue, I don’t think a coach will ever be managing the men’s club soccer team.

Player A/ Player B	Carry the ball bag	Don’t Carry the ball bag
Carry the ball bag	(13,7)	(4,10)
Don’t Carry the ball bag	(17,3)	(6,6)

Odebrecht's rent-seeking in Ecuador

Last year Ecuador's VP was arrested for corruption...yes the VICE PRESIDENT. He was receiving bribes from the Brazilian construction company Odebrecht. This company government officials from 14 different countries to secure public construction contracts. They even have a department in charge of managing this bribes. Only in Ecuador, in the last 10 years, Odebrecht paid $33.5 million in bribes to government officials. The company made $116 million in profit, as a result of these bribes.

This company was spending money on bribes to secure public construction contracts. But, even when millions of dollars were spent, this investment did not increase the total economic profit. By being hired, Odebrecht received the profit from the project that any another firm would have received if selected. This is just a matter of transfer, of which firm is hired and receives the profit of the project. However, the fact that Odebrecht spent so much money on bribes to obtain these contracts is an example of rent-seeking. These $33.5+m are resources that were spent by Odebrech but they do not increase welfare (the value of the project or the economic profit). In fact, it can be said that it even decreased welfare, as many of these projects were not completed. Odebrecht engaged in this rent-seeking behavior (bribes) to secure their place on the market. But, this $33.5+m spent on bribes, and the loss from unfinished projects represent a DWL that resulted from Odebrecht's rent-seeking behavior. They are resources that could have been spent more effectively elsewhere. Maybe Odebrecht could have used this money to improve their construction proposal and be hired in a legal manner.

Adam Driver: Millenial Sex Symbol

About two weeks ago, I got into a debate with a friend about Adam Driver. The question at hand: “Is Adam Driver a millennial sex symbol?” What do I mean by that? The answer depends. You could focus on the “millennial” part, and argue that Adam Driver’s status as a GQ cover model is emblematic of the absurdism of the world that millennials have grown up in. You can instead focus on the “sex symbol” part, to which the answer is rarely an enthusiastic yes. After a long and heated debate, I did what anyone would do: I designed a Qualtrics survey pitting three options against each other, randomizing them, and then asking about all three options put together.

The results? “Why? Uh, I mean I guess” wins against both other options in pairwise matchings. This answer is a Condorcet winner.

However, when all options are compared against each other, this answer finishes last (and by a lot).

Why does this happen? And what does this mean? First, this survey is structured according to the assumptions of the median voter theorem: the spectrum ranges from “No” to “Why” to “Of Course,” with “Why” in the middle. The final survey shows which options are people's’ “first” choices. Obviously, for those who prefer “Of Course,” but faced with the choice between “No” and “Why” will choose “Why.” Similarly, those who prefer “No,” but faced with the choice between “Of Course” and “Why” will also choose “Why.”

The second reason points to the structuring of the agenda. When the only options are “No” and “Of Course,” “No” is a clear (albeit slight) winner. However, when all three options are included, no is not a winner. It places second in three way voting (with “Why” playing the spoiler) and still loses head to head against “Why.”

The takeaway from this is that the Condorcet winner is not always the best choice. It seems to be the most “agreeable” choice, but if it’s included just to be a spoiler, it may detract from true majority rule decision making.

Masters of Intransitive Group Preferences: The Jedi Council

A long time ago in a galaxy far, far away Condorcet's paradox reared its ugly head. In class Sabrina got to the heart of how this happens, which is when the options to choose from or vote on are viewed with varying factors and different aspects being important to each voter. As we approach the holiday season, my heart has begun to yearn for some movie marathons on TV, none more anticipated in my mind than the Star Wars Weekend on TNT. In the 3rd best movie of the entire franchise, comment to disagree I dare you, Episode III: Revenge of the Sith, there is a fascinating Public Choice problem where an unthinkable voting result occurs granting Anakin Skywalker a seat on the Jedi Council but not the rank of master. Let's look at a model that could explain this seemingly intransitive behavior by the group of "masters".

In the table below the voting preferences are shown for the model and to simplify it is assumed there are only 3 members of the council voting with only three options and a simple majority is needed to pass the decision. Decisions are as follows: MC means Anakin gets the rank of master and a seat on the council, M means he is only granted the rank of master, and C means he is only granted a seat on the council.

In a vote between MC and M, MC will win out; between M and C, M will win out; between MC and C, paradoxically C will win. This is Condorcet's paradox, where a group with transitive preferences exhibits non-transitive group preferences under simple majority. This arises because the different voters value different things in each outcome. For example, Yoda seeks to honor the old Jedi way and have a master and seat on the council be mutually inclusive, but Mace Win-du values limiting the influence and power of "the chosen one" because he believes Anakin has been corrupted. Off screen we can only assume the agenda setting power belongs to Mace Win-du because C is the result and Anakin is famously outraged leading perhaps to the crumbling of the Galactic Senate and the republic. Maybe in Episode IX coming out Christmas 2019 we will see a Borda Count and democracy will reign supreme.

ISC and the MVT

This past week, I attended the elections for the new executive board of the Inter-sorority Council and found that the Hotelling-Downs model of voting seemed to hold even within the small-scale elections of Greek life. In these elections, all fifteen chapters had representatives present with one vote for their individual chapter, as well as the ISC executive board holding one collective vote. 

In this particular election, all 15 sororities present had different preferences and desires for the ISC President to fulfill based on their chapter experiences, but there was no clear ideological spectrum because of the lack of any real party affiliation. Being that no abstentions were allowed and preferences for the candidates were somewhat symmetrical and unimodal amongst the chapters, the obvious strategy for all candidates would be to deliver speeches and platforms that appealed to the majority of voters. Because both candidates' platforms were completely mobile due to a lack of party affiliation, Harold Hotelling's principle of minimal differentiation resulted in the two candidates' speeches and platforms being almost completely identical and open-ended, presenting very similar ideas and plans for the ISC's upcoming year. 

Downs’ "The Statics and Dynamics of Party Ideologies" describes this occurrence by revealing that in this particular two party system, the candidates had an incentive to give broad, open-ended speeches, in order to discourage rational voting amongst the chapters based on policy. This is because when voters perceived both presidential candidates as having similar platforms, they were not able to actually differentiate the policies presented, and instead had to cast their vote for a candidate based on other factors such as social connections or superficial factors. Perhaps this could be the reason that so many small-scale student government elections can be decided on some pretty biased factors.

Live from New York...

Comedy. You either love it or hate it, but it’s a phenomenon nonetheless, capturing Youtube feeds, small talk, and Saturday nights. For over 40 years, Saturday Night Live has been a centerpiece of American culture, reaching audiences far and wide regardless of socioeconomic class, age, gender, or (to an extent) political beliefs. Over the course of it’s exciting history, SNL has changed the game, providing an alternate route for millions of voters to obtain crucial information or impressions about candidates, whether they watch the show for this purpose or simply saw a five minute sketch by chance. In reference to the 2016 presidential election, Dean Obeidallah of SNL reflected, “eighty million people watched the debate, 130 million people will vote, 50 million others are still looking for places to get their news, and comedy can fill that gap."

In class we talked about the cost of knowledge and the fact that there is an ideal balance between knowledge and ignorance, based on the costs of obtaining said knowledge, which may not be the same for each person. In many cases, the cost of building in time to learn about the candidates (information that would be useful in voting) prevents voters from doing so, especially given the comparatively high cost of voting as compared to marginal benefit. Spending a few minutes watching SNL or something similar provides a quicker alternative to reading the Wall Street Journal or watching CNN, and it captures a sector of comedy-inclined voters who wouldn't necessarily be engaging in these additional activities anyway. 

It should be noted, however, that obtaining information about the candidates from an artistic standpoint rather than a supposedly completely factual one could have further implications. As is noted in the NBC News article, voters were potentially influenced by Ferrell's positive rendition of George W. Bush on SNL before the 2000 election. Backlash against SNL for being "too liberal" could also influence potential voters, and over-the-top renditions of candidates on the show could even lead to higher levels of expressive voting, depending on the views of the viewer. However, one thing is for sure--SNL has changed the game in terms of how we learn about our current events and how we decide which way to vote. 

Choosing the American Idol Condorcet Winner

On Friday, I was just having one of those days where I was in my ‘feels’, so I turned to Spotify to find a song that matched the mood. Quickly, I turned to my ‘feels’ playlist, and clicked shuffle hoping to find the perfect song. I lucked out, and on came one of the most fitting songs, Daniel Powter’s “Bad Day”. Next thing I knew, I was singing along and really vibing. After the song was over, it really got me reminiscing of the good old days when I used to watch American Idol with my family. This song in particular took me back to season 5 of American idol. This American idol season was a very important to me for a couple of reasons. For one, Elliot Yamin was one of the contestants, and he was a Richmond native. Naturally, I was his biggest fan, and I tried my hands at trying to slip in a few votes for him. The second reason, which is the one that pertains to this class, is the elimination of Chris Daughtry. The elimination was shocking because he had delivered an unbelievable performance, but he was found in the bottom two with himself and Katharine McPhee. When asked who should leave, Simon Cowell said that McPhee was going to be the one to receive the boot, but in the end, he was shocked to figure out that he was wrong. America had spoken, and they said Daughtry deserved the boot.

The decision discussed above was an important decision because the shocking early exit for Daughtry and the handful of others that followed after inspired the save feature. In American idol, we see the Hare style of voting at play. Each vote that is tallied is considered a first-place vote, and at the end of the night, whoever as the least amount of first place votes is the one that is going to be eliminated. That was the case for Chris Daughtry, but the judges thought otherwise. They thought that he was the best candidate out of the bunch, but he found himself in a similar situation as Romer during the 1991 Louisiana election. The judges had a gauge for what the audience wanted, but how did the Condorcet winner not end up winning? We had a paradox upon our hands. Chris Daughtry could’ve beaten any other contestant in a pair election, but he couldn’t win the American vote with all candidates squaring off with each other. In order to prevent this from happening in the future, the people another and the contestant another chance to pick the next (Condorcet) American Idol winner.

PhRMA: The Most Notorious Rent-Seeker

Our talk in class of rent-seeking brought reminded me of what some consider the most flagrant manifestation of rent-seeking, activities of the pharmaceutical lobby. The pharmaceutical lobby, formally known as the Pharmaceutical Researchers and Manufacturers of America(PhRMA), spent $25.4 million on lobbying activities in 2017, which is a 30% jump from their expenditures in 2016. PhRMA drastically increased their lobbying expenditures in response to President Trump’s hardline stance on drug pricing. They claim to need to price drugs as highly as they do in order to cover the costs of innovation and accurately reflect the value of the drug. The administration, along with most Americans, finds these claims outrageous and drug prices unnecessarily high.

In this example, the rent that pharmaceutical companies are seeking is extremely valuable. It not only includes the economic profit from higher drug prices, but also any additional economic profit gained when healthcare regulation and trade policy favor their industry. Given that pharmaceutical companies earn billions of dollars from blockbuster drugs under current regulatory conditions, the rent (economic profit) they stand to gain is much greater than the amount they expend on rent seeking activities. While $25.4 million is clearly a lot of money, it is relatively small compared to the rent in question. Therefore, I would predict that the percentage rent dissipation, total investment in rent seeking activityrent, would be quite low. In relation to other industries PhRMA is redirecting a lot of resources toward rent seeking activity. However, when taken in the context of the pharmaceutical industry, the resources they are redirecting towards rent seeking are not unreasonable given how valuable the rent they stand to gain is. While PhRMA has too much money and control in politics, their headline-grabbing rent-seeking expenditures are not as wasteful as we all assume.

To Vote or Not To Vote

As everyone knows, last Tuesday was election day! I sent in my Texas absentee ballot early but happened to be in Dallas on Tuesday. I got a call around 3 pm that there was something wrong with my ballot and that the only way I could vote in the election was to go vote in person. Upset, I called my mother who suggested I hop on a flight to Houston and go vote before 7pm (She was being facetious, but humor me please). I rolled my eyes at her whilst doing a quick marginal benefit – marginal cost analysis in my head. 

The cost, both in lost time and money, of taking a detour to Houston made me ponder the importance of marginal cost in my decision to vote. In class, Professor Coppock mentioned two examples to illustrate the impact of MC. On one hand, when Switzerland (?) made the cost of voting zero by allowing people to vote from home, voter turnout actually went down because of the loss of expressive utility. On the other hand, voters in rural New Zealand are less likely to vote because the cost of getting to the polls is so high. These two examples show that while a low MC does not make an impact on people’s decision to vote, a high MC does and cannot be overlooked.

My decision to vote absentee, which had a very low MC, and my decision not to fly to Houston, which had a very high MC, illustrate the same point. I did not care about my vote's probability of having an impact – I was voting to have a Democrat (and my favorite teacher’s sister-in-law) as my representative for the first time in 50 years, and that was enough for me. I also did not really care about letting people know that I had voted. What I did care about was the loss of time (I probably wouldn’t have gotten back to Cville until at least noon the next day) and the serious cost. Given the same decision – to vote or not to vote – I made two different choices. I both voted and did not vote, and neither choice influenced the outcome of the election, although it might have impacted the future.

Tullock and Textbooks

I'm sure we have all been annoyed by the ridiculous amounts of money we have to pay for textbooks at the beginning of each semester. While reading about the college textbook industry, I realized that it presented a situation very similar to the monopoly seeking behavior discussed by Tullock in the paper we read for last week's class. Although there are multiple publishers who compete with each other in the large textbook industry, courses that require a textbook usually do not allow students to buy just any textbook on the subject. Rather, they require every student in the class to purchase a specific book. In this way, Professors are able to award their chosen textbook publisher the right to a monopoly over the books for each class they teach.

As a result, textbook publishers spend resources to receive that right from professors just as Tullock predicted they would. In the textbook industry this is done through the employment of textbook representatives. These representatives attempt to get professors to choose their books by forming relationships with them, sending them information regarding the products they offer, and sometimes buying them food. The companies are paying their representatives in order to have the best chance at being awarded this monopolistic opportunity. These representatives are very reminiscent of lobbyists in Washington and are a good example of the monopoly seeking behavior Tullock discussed in his paper.

Am I an irrational voter?

I woke up on Tuesday morning having already decided that I would be abstaining from voting in the 2018 midterm elections. An hour or so later I found myself in my car driving back to Northern Virginia to cast my vote. It ended up being about a 5 hour round trip. Since I was previously planning to abstain, I had not requested an absentee ballot, registered to vote in-person absentee, or registered locally in Charlottesville. I'm somebody who thinks that they have very strong political opinions. That being said, the Senate race in Virginia was seemingly very one sided, and I strongly disliked both the D and R candidates in that race. My congressional district has been a very unchanging blue seat for years. There was little to no hope that my vote would impact either of these elections in my favor. What was it that changed my mind? What flipped the switch of apathy to the civic engagement setting?

Did I really want an "I voted" sticker? Did I want some sort of moral validation? Did I want to make the huge trip and skip my classes in angst just to spite Professor Coppock and the voting model he showed us? The model goes as such: E[MB] + D > MC. It's difficult to prove that my expected marginal benefit of a favorable outcome in either of those races was a high number, considering my previous commitment to abstention, and the knowledge that my vote would mean next to nothing effectively. My marginal cost in this situation was enormous. 5 hours out of the day that I could have spent studying for an exam the next day, THREE classes skipped, gas money, you name it. The cost of this voting excursion was quite large. The ONLY way that I made a rational decision is if D is larger than MC, but given how large MC was, I better have had a darn good reason for having an even highly valued D. Now I honestly don't know what pushed me to make the decision that I made-- it certainly wasn't the barrage of Facebook posts and tweets urging young people to have their voices heard. I believe it was a combination of several things: the Expressive Value of standing on my moral high ground of taking such a large burden upon myself to vote, the heightened sense of superiority to my peers in sharing the story, a bomb opportunity to write a killer blog post, fear of viewing myself as a political hypocrite, saving the babies, and possibly even seeing my dogs and having the chance to take my mother out to lunch. Am I irrational, or do I just have a wacky system of valuing my time and actions?

UVA Admissions Requirements as Rent-Seeking

Every year, thousands of students apply for a limited number of spots in the incoming first-year class at The University of Virginia. In the market for college admissions, universities are rent-seekers and prospective students pay economic rent in the form of academic qualifications.

UVA illustrates certain admissions “requirements” by publishing statistics of each class’s median SAT scores and class rank distribution. These standards merely provide a frame of reference for prospective students, since the University evaluates applications holistically. Therefore, the specific activities and qualifications for admission depend on factors beyond academia, to include: legacy status, in-state preference, extracurricular activities, quality and content of essays, and more. This ambiguity incentivizes students to strengthen their application in all areas but defines no particular course of action for admission. As a result, prospective students expend significant resources to distinguish themselves from competing applications without certainty their efforts will pay off.

UVA is an undeniably prestigious institution, aiming to fill their incoming class with the best and brightest students. By withholding precise methods for admission and opting for a holistic approach, the University essentially tells prospective students to “do as much as they can”. This behavior is rent-seeking because the University wants more applications to drive their acceptance rate down. While some other state universities guarantee admission to those graduating in the top 10% of their high school class, UVA makes no promises. These ill-defined admissions standards are a method of rent-seeking, as they increase the quality of applications across the board and improve the University’s reputation.

Prospective students pay “rent” by participating in activities they otherwise would not deem worthwhile. For example, I served as the Historian for my school’s Spanish Honor Society, not out of affection for the club but because I thought the leadership position would strengthen my application to UVA. My family even moved across state lines for in-state admission preference. If I had been rejected from UVA and instead gone to Virginia Tech, I would have deemed all the resources expended wasteful.

The Alaska Governor's Race and MVT

For those of you who missed out on the Alaska Governor’s race, let me give you a little bit of background. Alaska is a deep red state, but for the past four years it has been governed by an independent named Bill Walker. Walker decided to run for re-election this year, but was facing a stiff re-election fight from both the right and left, running against Republican Mike Dunleavy and Democrat Mark Begich. Up until mid-October, Walker and Begich had been polling similarly, in the mid to high 20s, compared with Dunleavy’s mid 40s percentages. That is, until Governor Walker dropped out of the race. As soon as Walker dropped out, he immediately endorsed Begich. What had once been a runaway win for Dunleavy became what pundits termed “volatile head-to-head matchup.”



Two-way polls conducted during the three candidate race told a different story. According to Alaska Survey Research, Dunleavy was polling 5-10 points ahead of either of his opponents in a head-to-head matchup. Thus, Dunleavy was the Condorcet winner. On election night, this was confirmed. Even with 2% of the electorate still voting for Walker, and another 2% voting for the Libertarian, Dunleavy pulled away to victory, with a commanding 52% majority.

Interestingly, Walker used the same strategy as he had used in the 2014 election. Back then, he merged his Independent campaign for governor with Democratic nominee Byron Mallett (Walker ran for Governor, with Mallett on the ticket for Lt. Gov). Together, they won a plurality of the vote over Republican incumbent Sean Parnell. Downs mentions this as a goal of political parties in The Statics and Dynamics of Party Ideologies: according to him, new political parties serve to either replace the dominant party, or be assimilated by them. While the parties were not assimilated, the based of the gubernatorial candidates were subsumed. In 2014, the supporters of the democrats were absorbed by the independent, while in 2018, the most of the supporters of the independent were absorbed by the democrat. In both cases, when one candidate dropped out, their voters were subsumed by the nearest candidate on the political spectrum, a clear demonstration of the median voter theorem.