Skip to main content

Russian twitter accounts used both Pro and Anti-vaccine messaging during the 2016 election.

A new study published this month in the American Journal of Public Health has revealed that twitter accounts operated by the Russian-backed Internet Research Agency (IRA) consistently targeted users with both pro and anti-vaccine messages between 2015 and 2017. According to researchers at the Annenberg Public Policy Center and SUNY Buffalo, the intent was twofold: sow discord in the USA by amplifying inflammatory news, and create believable posting histories for the fake twitter accounts. To study the effect of these fake accounts, 2.8 million tweets by 2,689 separate accounts were analyzed using network analysis and grouped according to behavioral patterns such as language and common themes. Due to the size and density of the data in use, machine learning was utilized to identify what topics a specific tweet contained. By identifying the most common topics discussed by a particular account, it could be grouped with other accounts that employed the same strategies. Using this method, nine different thematic communities were identified:

1. Hard news
2. Anti-Trump,
3. Pro-Trump,
4. Youth talk and celebrities,
5. African Americans and Black Lives Matter
6. Mixed international topics
7. Ukraine,
8. Soft news
9. Retweets of various topics and hashtag games

These groups were organized into a network, with nodes representing twitter accounts (and size of nodes indicating account’s reach in terms of retweets) and edges representing topical similarity between accounts.

In part B of the above graph, only the red colored nodes are accounts which discussed vaccines. The Pro-trump group and the “soft news” group had the highest amount of vaccine related discourse, while Anti-trump accounts mentioned vaccines very little and Ukraine oriented accounts did not mention the subject at all. Furthermore, pro-trump accounts generally shared anti-vaccine views while other groups were neutral or pro-vaccine. Researchers believe that this strategy of duel messaging was an attempt to build credible and realistic personas for later employment. However the amplification of anti-vaccine discussion by these accounts was and is incredibly damaging to public health in America, and has likely exacerbated the coronavirus situation. Vaccine messaging was also tentatively correlated with real-world events related to vaccines, such as a vote on mandatory school vaccinations in california. The health implications of an organized effort to target specific communities with anti-vaccine messaging are striking, and may represent an entire new dimension of cyber-warfare and propaganda. Increasing polarization has already been a worrying trend throughout the United States, and public trust in a non-partisan medical establishment has been a cornerstone of public health initiatives for decades. The effects of efforts by state-backed actors like the IRA has already been considerable and in the future may become even more damaging.



Polarizing Tweets by Russian Trolls on Vaccination Targeted Groups in 2016

Pandemic Effects on Social Networks and Echo Chambers

In the era of COVID-19, our worlds have shrunk into neighborhoods, households, and computer screens. Our social connections have been influenced greatly by our lives in isolation. Before, you would interact with many acquaintances with whom you have weak ties to during your everyday routine. For example, you might interact with a classmate, coworker, or mailman in person, but now, when you must put in the effort to connect to people virtually, those relationships aren’t a priority anymore. Instead, you spend more time with people who you have strong ties to like family, parents, and close friends.

Social isolation has a huge impact on our social network and beyond. For example, while our world has shrunk, we also have the demanding obligation of voting during a time of a polarizing presidency, a pandemic, and a widespread movement protesting police violence and systemic racism. This article from the New York Times demonstrates how distancing can possibly affect voters’ choices. It states that “spouses, parents, and close friends who you have strong ties with exert the most powerful pull on voters’ behavior because your closest friends and family probably have similar politics as you, and more casual acquaintances are likelier to upend your assumptions.” Even if you do not have the same politics as your closest friends– or more likely, your family– social isolation has led people to communities and ideas that they are comfortable with. It has become easier to ignore people you disagree with without casual or facilitated in-person interactions.

Much like the political echo chambers present on social media platforms like Facebook and Twitter where users encounter people whose beliefs and opinions are similar to them, social isolation has led to real-life echo chambers. Amid loneliness, diminished trust, and the dissolution of social capital, these echo chambers reinforce strong ties and diminish weak ties. Your weak ties may not be broken entirely, but they may be less used in the network and become weaker. On the other hand, social isolation has also pushed almost all people online. The possibility of mobilizing people and building social capital virtually has increased. Perhaps now, there are also more possibilities for forming new weak ties and acquaintances through the Internet. 

This issue addresses the topic of tie strength and strong and weak ties which we discussed in week 2 of class. It discusses the pandemic’s impact on altering strong and weak ties and broader social networks by weakening weak ties, strengthening strong ties, and creating echo chambers. This topic demonstrates a real application of strong and weak ties and its extreme relevance to our lives today.

Social Networks and Their Effect on Mental Health

“Teen Social Networks Linked to Adult Depression”, posted on Medical Xpress by Karessa Weir of Michigan State University, looks at how teens’ social networks influence their depressive symptoms in adolescence and then again in adulthood. In the study referenced done at Michigan State University, teens were asked to name up to five male friends and five female friends, and their depression was then tracked. An interesting initial conclusion derived by this study was that sociability had little effect on adulthood male depression, but had a sizeable impact on the long term emotional health of women. The study identified naming few friends in adolescence for both genders led to poor emotional health in adulthood. However, it is theorized that women face far more societal pressure when it comes to how others perceive their social status, therefore young women feel far more pressure to be popular and have more friends. 

The article then went on to state that women who had large social networks as adolescents in fact had poorer mental health in adolescence than their peers with few friends, but went on to be more emotionally satisfied. This is attributed to the fact that the social pressures and psychological burdens demanded of popularity in adolescence prepare women emotionally and socially for dealing with academia and the workforce. It is interesting to think how early social networks are so influential to future emotional and professional success. Those with few friends in youth went on to be more depressed in the future, as they were less societally prepared for adulthood. The ebb and flow of depressive symptoms is described as resembling a U-shape, in which depressive symptoms peak in adolescence and early 30s, while subsiding in early adulthood. Again, the severity these peaks is drastically more severe in women than in men due to societal expectations for women to be sociable.

This has a clear correlation to what we have studied in class in terms of social networks, where being a more connected node has influences on your emotional state. Societal expectations placed on women to conform to popularity ideals make it such that there is far more pressure for women to become a powerful node with many connections, which in the moment leads to emotional and psychological strain, but prepares these women for being a powerful and highly connected node in the future and for making future strong connections. We also see the real life impacts of being a node with few connections, being increased depression regardless of gender. It is then interesting to extrapolate what it means to be a local bridge or a highly connected node beyond the social structure itself to the influence of this on the life trajectory of the individual node, thus translating the power structures we see to their real life impacts.

COVID-19: Another Large Example of the Prisoner’s Dilemma and the Significance of Networks

This article, written by a columnist for the Stanford Daily, examines the vitality of cooperation and compromise in relation to the current pandemic by analyzing the implications of social distancing from a game-theory perspective, namely the Prisoner’s Dilemma. 


Cooperation Among State Governments: 


As state-mandated lockdowns have been the most common and organized preventative measures that local governments have taken, analyzing its potency has been an effective way to highlight the importance of communication and mutual cooperation between bordering states and their simultaneous lockdowns. In the article, the author uses California and Arizona as two states whose governments can obtain the maximum social benefit when cooperating with each other, from both an economic and public health stand point. Hypothetically, if both Arizona and California were to keep their restaurants open and not comply with the federal-government’s recommended lockdown, the outcome would be one that may boost each states’s businesses in the short term but cause a massive escalation in Covid cases, which can even hurt businesses in the long-term, as it would cut off a large portion of many restaurants and recreational services’ clients.

If Arizona were to comply with lockdowns but California were to remain active, then California may benefit in the sense that not a lot of people from Arizona would be traveling to California and spreading the virus there; California would primarily only face domestic spreading of the virus. However, because California would not comply, Arizona would face an influx of cases from California, which undermines their efforts of having a lockdown and lowering the spread within the state. However, if both states complied, businesses may face short-term losses, but the overall spread of the virus would be lower in both states, and, assuming that human lives are valued more than short-term business losses, both states would be better off by complying with lock-down policies. 


Compliance from Citizens: 


Similarly to governments, individuals must also comply with one another in order to ensure that the spread of the virus is as minimal as possible, thus obtaining the maximum social benefit. The following image depicts a scenario with two agents who have the option of wearing a mask and not wearing a mask. I assigned values of 0 and 1, respectively, to the hypothetical payoffs of individuals wearing a mask and not wearing a mask; 1 indicates that individuals are less likely to transmit the disease and receive it themselves: 

As illustrated from the matrix above, a pure-strategy Nash-Equilibrium is met only when both individuals cooperate and wear masks. Interestingly, this option not only maximizes society’s overall benefit, but it represents both players’ best responses, which both happen to be their dominant strategies. As studies have shown that wearing a mask helps other people from getting infected more than it helps the individual wearing a mask from getting infected, the matrix above indicates that it is not only imperative for individuals to wear masks for their own sake but for others’ as well. 


This pandemic also illustrates the potency of networks, as it shows how just one person with the disease can cause a cascade of infections if people and governments do not take precautionary measures. 

by Ravin Nanda – rkn36


Saving Lives with Matching Algorithms

So far in class we’ve been introduced to basic matching, where preferences over objects are not considered. Needless to say, there are many possible factors to take into consideration as we learn about larger applications of matching algorithms. But something we have been exposed to thus far is eligibility. For example, an algorithm that matches TA’s to potential office hour slots depends on the eligibility (or better yet, availability) of their schedule to permit a particular time slot. The notion of eligibility here is not complicated, since there can be only one reason for a TA to be ineligible (that they are busy), but in other contexts it can make finding a perfect match a much more nuanced process.

Imagine that instead of matching people to objects, you were matching people to other people. You would then have to make assignments based on the compatibility of two people, which makes finding the matches significantly more difficult. The matching problem discussed below is a perfect example of this complication:

For The Alliance for Paired Kidney Donation, finding a donor for a patient in need of a transplant was complicated greatly by the fact that they must have compatible blood types; a donor with blood type A is not helpful to someone with blood type B. This means that it is not enough to find a patient and a donor; they would need to find the right patient for the right donor. Alvin Roth, recipient of the Nobel Prize in Economic Sciences (2012) and the creator of a matching algorithm that did just this, used this notion of compatibility to match patients with donors in an efficient way. He assembled a set of patient-donor pairs and chained them together such that if the patient-donor pairs (x , y) and (a, b) were not eligible within those pairs, but y was compatible with a and b with x, then patient could get donor b‘s kidney, and patient could get y‘s.

This application is helpful to think about not only because it saved the lives of countless patients, but also because it expands the notion of eligibility in matching algorithms beyond the “yes or no” quality that we take into consideration for our assignments.




The effect of weak ties on mental health during the pandemic

The pandemic has drastically changed lives in many ways, one of which is the layout of social networks. Due to the need to quarantine & socially distance, the amount of casual friends/interactions has drastically decreased. While this change is necessary for public health reasons, this article from Harvard Business Review notes that severing casual interactions has a negative impact on social satisfaction; the more frequent these interactions occur, the happier people tend to be.

While our strongest relationships—like with close friends & family—are indeed supportive, casual interactions go a long way: “since we are often on our best behavior with people we don’t know well. Weak-tie relationships give us short, low-cost, informal interactions, which often provide new information and social variety. As a result, we are often pleasantly surprised by these moments.” The article notes that on a given day, people interact with roughly 11-16 weak ties. It then mentions research that shows “even a few minutes of texting is enough to improve your mood and spread joy within your social network,” while then discusses tips for increasing these interactions during a pandemic.

Using what we’ve learned about networks so far, we can think of relationships in terms of strong & weak ties: strong ties being close friends & family, and weak ties being casual friends/interactions. Note that in this network, weak ties outnumber strong ties. Even though people can still (generally) quarantine with strong ties, when more “components” are created in the network by severing weak ties, a dramatically large number of ties are cut off & the network decreases in size. Additionally, it is now much harder to create & sustain weak ties.

The article points to relevant topics from class and the current COVID era—this concept of limiting casual interactions (our weak ties) especially affects all of us students as visits to campus are limited, in-person lectures with hundreds of students & professors are essentially nonexistent, and all around, we are not surrounded by thousands of other students, faculty, & campus-goers; our daily interactions have been massively cut down.

The Supreme Court and the Prisoners’ Dilemma


During Tuesday’s interesting first presidential debate, when the question of refilling the now empty Supreme Court seat was presented, Biden maneuvered his way around the answer without a clear final response regarding what he would do if elected, while Trump loudly accused Biden of packing the court if given the opportunity. The author of “Joe Biden Should Promise to Pack the Supreme Court to Save it from Partisan Wars”, David A. Kaplan, argued that the situation we find ourselves in is a real-life version of the prisoner’s dilemma which, consequently, encourages Joe Biden to go ahead and pack the court. Therefore, I will discuss the connection between the prisoner’s dilemma and the current question of the vacant supreme court justice seat in regard to the argument Kaplan put forth.

As we have learned in class, the prisoner’s dilemma describes the choice that two prisoners are faced with: to confess or not to confess. The option with the highest payoffs (less time in prison) occurs when both prisoners decide not to confess. The option in which one player gets zero payoffs and the other gets high payoffs occurs when one chooses to confess and the other doesn’t confess. The option with the medium amount of time in prison is when both prisoners choose to confess. Rationally, both individuals deciding not to confess results in the best outcome: the least amount of time in prison. However, confessing is in fact the dominant strategy (the best response for an individual regardless of what the other does) in this scenario.

Kaplan claims that the historic tendency for presidents to pack and unpack the supreme court based on party lines proves that cooperation is impossible and thus introduces the tit-for-tat strategy. To illustrate the prisoner’s dilemma in this situation, a simple payoff matrix for this situation could be set up by Player A (Democrats) and Player B (Republicans). Each player has the option to pack or not to pack the court when they are in office. If both players choose to pack the court when they have the chance, they will both have an average number of payoffs (with payoffs possibly representing later Supreme Court decisions favor them). If both players choose not to pack the court when they have the chance, they will both have the highest number of payoffs. If one player decides to pack the court while the other doesn’t, the player that decides to pack will have high payoffs while the other has zero, and vice versa. Therefore, intuitively, it would make the most sense for both players to cooperate and not pack the court, as they will share high payoffs. However, as in the prisoner’s dilemma, the dominant strategy in this matrix is to pack the court. A large part of the prisoner’s dilemma is that trust and fear play large roles; if one player does not trust the other to not pack the court, then they will also pack the court. In the current political situation, and with regard to how similar situations have been treated in the past (2016 empty seat), there is absolutely no trust and a large amount of fear at play. Therefore, packing the court is the rational response as it is “measured and proportional” (Kaplan). Once both parties consistently began to fail to cooperate and not pack the court, Kaplan states that tit-for-tat became the correct strategy in which each player mimics what the other player did before. In this case, if one party packed the court before, the other party will also pack the court when they can.

Kaplan’s article applied a strategy in game theory to a prominent topic in today’s political arena to argue that it is pointless for Democrats to continue resisting a “turn to the Dark Side” and it is time to fight “fire with fire” and publicly promise to pack the court after the election (Kaplan).

Game Theory and Preventing the Global Food Crisis Caused by Covid

Food insecurity is a crisis facing our entire world, intensified by the introduction of the coronavirus. Governments throughout the globe are fighting to keep their citizens fed and alive. To do this at maximum efficiency, international trade of agricultural products is necessary to sustain the population’s diverse nutritional needs. The coronavirus has slowed production, disrupted distribution channels, and transportation of these essential commodities. Similar to the rest of the world, the pandemic, although affecting everyone, has disproportionately hurt the poorest populations, something countries are trying to prevent in this food crisis. Keeping food prices low, for this community especially, is a top concern. The governments have had to adapt their trade strategies to provide a steady supply of food to their citizens while controlling inflation caused by the market.


Game theory can be used to analyze how the action of one player in a game can affect the payoff and action of another player and vice versa. Governments usually employ game theory when deciding how and what to export to other countries and import themselves. In normal times, each country will evaluate their food stocks and decide whether to decrease or increase its trade barriers. The dominant strategy for both parties is to lower the trade barriers and increase global food trade because they both gain the most payoff from this option. This allows the countries to maintain diverse diets as well as have food for all of their citizens. During Covid-19, these trade barriers can be more costly due to keeping all those in the food channels safe, controlling the spread of corona within the country (meaning limiting imports), and the fear of diminishing food stocks in each individual country. The country’s governments need to work to keep these barriers low. The worry is that in this game countries will change their strategy and increase their trade barriers, thinking they will be more beneficial, not cooperating in global trade. With the strategy of one country changing to increasing trade barriers, this could make other countries also change their strategy, harming the circulation of the food supply. The only way in which these countries will be able to survive with enough food for their people is through a partnership with others. This mutualistic relationship between countries with low trade barriers is essential to mitigating this crisis.

Preventing global food crisis caused by COVID-19

Determining the Dominant Strategy in Teamfight Tactics 

League of Legends is a famous 5v5 multiplayer game. In the traditional game-mode, 5 players on each team each select one champion to play, and battle it in Summoner’s Rift. In the traditional game-mode, timing and game sense are two of the most important skills. However, after nearly a decade of success with League of Legends, Riot Games decided to add a second game-mode: teamfight tactics.

Teamfight tactics is more like a card game than like a battle royale. Every player starts out with 0 coins and 0 champions. Each champion has certain traits, and when you have enough champions with the same trait on the board simultaneously, the trait is activated on the left side of your screen and you get bonus stats. As each round progresses players earn coins and can use these coins to buy champions that are randomly generated on the side screen.



There are 5 possible ways you can change your coin balance:

Refresh: If you choose to reroll, it’s possible to see the same champions you had in a previous reroll. We’ll discuss rolling odds in a bit.

Buy XP: Your player level determines how many pieces you have on the board (if you’re level 3, you can have 3 unit pieces).

You will passively gain experience each round, but you can spend gold if you’re looking to increase your level and max number of units (up to 9 using experience).

You can see how many points to hit your next level at the bottom left of the button and you can see your current level at the bottom right of the button.

Lock: If you like the options given by a roll but don’t have enough gold to buy everything you need, consider locking your shop so you can buy when you get more gold for your next round.

Sell: You can sell your units by dragging them onto the shop or by clicking them and pressing E.


To make your team stronger, you have one of two options: Either you need to get champions that have the same traits as your existing champions so they get the buff, or you can level up to increase your team size by 1. These are two opposing strategies: One can either spend their gold refreshing their champion select in hope that a champion with a certain set of traits shows up; or say they already have the champion but not enough room on the board, they can spend their gold to buy XP. Clearly, refreshing is a much more risky strategy, but the payoffs can be great. Refreshing is dependent on luck and RNG much more than strategy, and good players will often wait till end game to spend their gold.


Although it is impossible to create a payoff matrix for such a sophisticated strategy game, it is possible to find pairs of opposing strategies. I think the most obvious pair of opposing strategies is to spend your gold early or to save it for the end game. Both strategies have their merits. Spending gold early can give you a massive advantage. Again, there is nuances on what gold can be spent on – refreshing, more characters, or XP – but all can be helpful in gaining an early advantage over remaining players. Alternatively, some players – myself included- prefer to wait until late game to invest their gold. This way, you can wait until you know which traits you are looking for to complete your team before refreshing. Additionally, saving gold grants additional bonus gold every round depending on how much you have.

Each bastion represents 10 gold, and the image above details how much bonus gold you receive each round. Including this in the game design makes economizing and playing for the late game a more appealing strategy, as you end up earning a significant number of bonus coins that can change the outcome of the game.

This, along with the ability to refresh once you already know which traits you are looking for, makes waiting until the late game to spend your gold the dominant strategy in my opinion.

Performance-Enhancing Drugs and The Prisoner’s Dilemma

Coming from a region in California where we take high school sports seriously, I definitely understood how intense the culture was as I was on the swim team and swam competitively as well. A clear memory I have from high school is when one of my friends that also swam competitively tested positive for a banned substance. With questions flooding my head at the time, I was both disappointed and taken aback that he would go to such far lengths to gain an advantage. Looking back at it now, I realize that this very scenario can be tied to game theory, which inspired me to delve into the usage of performance-enhancing drugs in sports and explore how the prisoner’s dilemma relates to this.

In terms of professional sports, the highest level of competition for an athlete, it is not surprising when scandals regarding doping occur as getting away with a winning edge can be something that is very rewarding. My article of choice connects such uses of drugs with the classic scenario of the prisoner’s dilemma. To elaborate, the prisoner’s dilemma is an example of a game in game theory that shows how cooperation and competition might clash in decision-making. It is the idea that when two individuals act out of their own self-interest, it will not produce the optimal outcome and as a result, these people find themselves in a worse situation than if they had just cooperated with each other. The article relates this concept to athletes using performance-enhancing drugs by proposing how the prisoner’s dilemma would apply in a hypothetical situation. For example, if there are two athletes (let’s call them Bob and Joe) and Bob doesn’t take the drugs, if Joe takes it, he now has an advantage. If Bob decides to take the drugs, Joe should also take the drug because then he would be on equal footing with Bob. This also works in reverse and goes to show that taking the drug is the best strategy.

As my article puts it, it would be nice to live in a world where all professional athletes refrained from using performance-enhancing drugs in sports. The issue is that when no one uses these drugs, an individual athlete may be tempted to use them in order to perform better than everyone else (which is choosing to cheat as displayed in the diagram above). This then leads everyone to also take performance-enhancing drugs, which creates this scenario where any athlete who decides not to take these drugs suffers from a competitive disadvantage. The diagram captures the very foundation of the prisoner’s dilemma in a real-world scenario because in reality, drug regulation testing exists and will punish those who are caught. Therefore, although cheating would be a best response to the other person’s choice, if both people don’t choose to cooperate with the rules and get caught, the punishment is worse than if both just followed proper etiquette. This is why in the real-world, cheating through doping is not all that common because athletes understand there is always that risk of being caught and that it may simply not be worth it.




keep looking »

Blogging Calendar

October 2020