9 Ways to Increase Your Happiness

Humans can be surprisingly bad at findings ways to be happy. We have certain cognitive biases that lead us to systematically mispredict what will bring us happiness and we often fail to take into account how hedonic adaptation and framing effects will impact how much enjoyment we get from things.

Luckily, research in positive psychology has found many changes people can make that will increase their happiness. But before sharing some of those, I should start off by pointing out something else that has been discovered by happiness research which is that…  just telling people about behaviors that increase happiness doesn’t improve their well-being! If you want to benefit from learning about this research, you’re going to have to put in the effort to deliberately change your behaviors and form new habits. Perhaps in the future I’ll do a post on some research on habit formation but for now a few general tips are:

  • set goals and make them as specific as possible
  • incorporate the behavior into your existing schedule and tie it to existing habits
  • record your progress and keep track of steaks of good behavior
  • give yourself notifications and reminders
  • think about how your environment nudges you towards or away from the behavior
  • consider finding ways to pre-commit to the behavior
  • find a support network or try taking on the behavior with other people
  • think carefully about other behaviors you tend to get sucked into and what makes them so addictive to see if you can replicate the effect

Keeping this in mind, let’s get on with the list.

1. Experiences Over Possessions

Believe or not, having fun experiences can actually make people happier.

But seriously, people can be quite bad at spending money on themselves to become happier and a specific mistake that they often make is spending too much money buying possessions relative to how much they spend to have experiences. While people tend to forecast that their money will be more well spent on material purchases, several weeks afterwards they tend to feel it was more well spent on experiential purchases. Additionally, people tend to report that the experiential purchase contributed more to their happiness, and this effect exists across income levels.

One potential explanation for this misprediction is that people’s enjoyment of durable goods that they buy for themselves (e.g. shoes, cars, home appliances, jewelry) tend to be especially susceptible to hedonic adaptation and people fail to take this into consideration when making their purchases. On the other hand, experiences like going hiking, out to see a show, or on a short vacation benefit from their brevity in that they do not fail prey to hedonic adaptation to the same extent (although adding variety and spacing events out can help even more).  These kinds of experiences tend to benefit from being easier to share with others and less subject to social comparison as well, meaning they also act less like positional goods.

2. Savoring

Savoring an experience is when you step outside of it to review it and appreciate it. It can be surprising how much more pleasure you can get out of an experience you were already having when your mind becomes fully focused on it and you remember to appreciate it. Some of the best ways to savor experiences are to share them with others or to talk about them with others afterwards. It can also help to think about how lucky you are to have the experience (while still believing that you are worthy of having it), be in a setting where you feel comfortable physically experiencing pleasure such as by laughing, and limit your attention to the experience and those you’re with.

Savoring can also be done through remembering. People were asked to replay happy memories in their minds for eight minutes every day for three days and to think about the events “as though you were rewinding a videotape and playing it back.” As you would imagine, this was a positive experience at the time but this led to surprisingly sustained effect with increased levels of positive emotions being observed four weeks later.

3. Gratitude

Closely related to savoring is gratitude. Being more grateful for what we have can significantly increase people’s happiness as well as have a host of other benefits.

In one experiment, subjects were asked to list five things that they were grateful for once a week for several weeks. By the end of the experiment the subjects not only reported thinking that their life as a whole was going better but they also predicted that their upcoming week would go better, reported increased relief from negative physical symptoms, and were even exercising more (about an hour extra a week). One of the ways for gratitude to have the strongest impact though is by expressing it directly to another person. Another study had people conduct “gratitude visits” where they would write a letter thanking someone who had been especially kind to them but they had never properly thanked and then they would deliver it in person. This one event led to increases in average happiness levels that were noticeable weeks later.

One tip from Spencer Greenberg for incorporating gratitude into your daily life is to finding a behavior that you already do multiple times a day and try to always think of one thing that you’re grateful for before engaging in it. The example he gave that I personally tried was trying to think of one thing you’re grateful for whenever you feel the urge to check social media. I don’t know of any studies that have been done on this specific method but anecdotally I can say that I am surprised by how effective it seems so far.

Being the receiver of gratefulness can also have very positive emotional effects and receiving gratitude can lead people to be more generous in the future. Unfortunately, not only do people underestimate how much happiness they’ll get from expressing gratitude but they also tend to underestimate how much happiness it will bring to those who receive it and they often overestimate how awkward expressing it will be. And speaking of tending overestimate awkwardness…

4. Social Connection

I probably don’t have to convince you that having regular interactions with the people you’re closest to such as family members, romantic partners, and close friends is good for you. But what you might find more surprising is that the number of interactions someone has with people they have weak ties with throughout the day is just as correlated with happiness as the number of interactions with strong ties.

There are some experiments showing good causal evidence of the benefits of interacting with strangers. People who take public transportation were asked to either have a conversation with someone sitting next to them, keep to themselves, or do whatever they would normally do. When people were asked to make predictions about each condition, they thought they would be happiest and most productive when they had to keep to themselves.  However, they actually ended up being happier when they had to talk to someone else than when they were in either of the other conditions and they reported the trip as being equally productive. This effect of underestimating how much we will enjoy interacting with strangers has been replicated in a number of settings including coffee shops, cabs, and waiting rooms. Additionally, it tends to increase the other persons happiness as well and by more than the initiator predicted. In fact, simply making eye contact and smiling at people can increase your enjoyment when you’re in a public place.

As mentioned when discussing savoring, sharing experiences can be a great way to get more enjoyment out of them. While it’s no surprise that watching a movie or comedy show can be more enjoyable with friends or a significant other, this effect is more pervasive than many people appreciate. Even just being in the presence of others can significantly affect how much happiness you get from something. For example, when eating chocolate just being in the presence of a stranger who is also having some can make people rate the experience as being more enjoyable.

5&6. Exercise and Sleep

When it comes to things that people know are good for them but still don’t do nearly enough, it’s hard to top regularly exercising and getting enough sleep. I won’t devote too many words to these two because I presume most people are already aware of the benefits and just need to find better ways of creating habits out of those beliefs.

People suffering from major depression were either prescribed an antidepressant medication (Zoloft) for 16 weeks or made to exercise three times a week for 30 minutes for 16 weeks. The two groups were then measured ten weeks after the 16-week period. While a majority of people in both groups had recovered, the recovery rate was significantly higher for those who had received the exercise treatment. Exercise also increases happiness in people more generally, and the amount of exercise needed to make an impact seems to be relatively small. Additionally, regular exercise is correlated with better academic achievement in young adults and cognitive ability in older adults.

In the case of getting a sufficient amount of sleep (7-8 hours each night), it is also correlated with a host of positive outcomes including improved immune system functioning, decreased chance of being in an accident, better learning and creativity abilities, and lower risk for many health conditions such as cancer, obesity, and stroke.  But most directly relevant, when subjects were made to sleep for a healthy amount of time (7.4 hours) they rated their mood as being significantly better and had fewer physical and emotional complaints compared to subjects who were made to sleep for around five hours a night.

7. Kindness

Not only is there are a strong correlation between being happy and having a tendency to do kind behaviors but there is also good evidence of a causal relationship where increases in the number of kind or generous behaviors someone does leads to increases in happiness. For example, having people preform random act of kindnesses increases their happiness.

While most people are aware that it can feel good to help others they tend to underestimate how much they will enjoy spending their money on others relative to spending it on themselves. People on the street were given either $5 or $20 and then they were either told they had to spend that money on themselves or on someone else. When other people were presented with this scenario, they tended to predict that they would get more happiness from spending the money on themselves than on someone else. However, when the people in the experiment were surveyed later that day the ones who were told to spend the money on someone else reported a higher increase in their level of happiness. Since this study was conducted in the U.S., one might wonder if spending money on others only had a more positive effect because the returns to someone living in a wealthy country get by spending a relatively small amount of money on themselves are insignificant. However, this effect has been replicated across a range of cultural settings and with larger amounts of money.

8. Meditation

We’ve already seen from savoring that it can be good for people to be more present and attentive to their sensory experiences rather than missing out on pleasure because of a wandering mind. People spend almost half of their time awake with their mind wandering and they tend to be less happy during this time than when they’re focused on the present moment. While being able to mentally remove ourselves from the present moment is an ability, we couldn’t and wouldn’t want to live without, it can be very nice to have the choice to not be carried off by your thoughts. This ability to recognize when we are becoming lost in our thoughts and allow them to pass in order to more fully experience the present moment can be cultivated through meditation.

People who practiced loving-kindness meditation reported increased levels of positive emotions as well as increased feelings of social closeness and implicit liking of strangers. Regular practice has also been shown to have a variety of other benefits ranging from increased gray matter to improved working memory.

9. Using Your Strengths

Psychologists Martin Seligman worked with Christopher Peterson on what was essentially intended to be a positive counterpart to the DSM. Their character strengths survey (which you can take here) tests people on 24 traits that are generally thought of positively and viewed as desirable by society (which include gratitude and kindness). The survey doesn’t provide values for each of the traits but rather a ranking of them. This allows people to see which traits they excel at the most, which are referred to as their signature strengths.

To test their relevance to happiness, researchers instructed people to take the survey and then use one of their signature strengths in a “new and different way every day for one week.”  The study lasted over a six-month period and participant reports a sustained increase in happiness and fewer symptoms of depression throughout that time.

If you’re looking for a more efficient way of incorporating the use of your signature strengths into your life, then you may want to consider the frequency of their use as a factor when looking at potential jobs. It has been found that people who use their signature strengths more often at work tend to be more productive, have higher job satisfaction, report experiencing more positive emotions and engagement at work, and describe their job as a calling.

I would like to recommend the wonderful Coursera course The Science of Well-being which served as the source for most of the material in this post. Hopefully you feel like you got some useful advice for how to live a happier life, but remember, just knowing isn’t enough!








Big Changes from Little Nudges

Typically, when governments want to alter the behavior of their citizens they either try to do this using financial incentives or by making behaviors illegal, which means more extreme incentives such as even harsher financial punishments or imprisonment. Certainly, using these incentives makes sense in some cases but they always have some costs because of the harms they do to people who violate them and the economic costs of implementing them. Additionally, it is often hard to implement them in ways that will affect people asymmetrically.

There are many situations in which it would be nice push people who don’t know what they’re doing in a direction that tends to work for most people without heavily penalizing people who do know what they’re doing and would like to choose something that would work better for them than the standard option. For example, how do you make people who don’t know much about investing more likely to choose a sensible option for their retirement plan without penalizing people who do know what they’re doing from deviating from that option? There are also cases where it would be nice to push people who don’t care significantly about a decision there making towards a more pro-social choice without hurting people who have strong personal objections to making that choice. Additionally, the government or other organizations may want to help people not to engage in behaviors if they are only doing it because of time-inconsistent preferences while still allowing people to engage in it if it’s what they consistently want and would increase their long term happiness.

This idea that it sometimes good to have policies that influence people’s behaviors in asymmetric ways if known as Asymmetric Paternalism. Closely related is what is known as Libertarian Paternalism which advocates implementing policies that lead to people making better decisions without restricting their freedom in any noticeable way. These policies are commonly referred to as nudges because they are supposed to nudge people in a certain direction without forcing them to go that way.

Many of these nudges are based on taking into account cognitive biases (e.g. social proof, status quo, and framing effects) that cause people’s decisions to be noticeably influenced by factors that they consciously believe should be mostly insignificant, while others are based on taking into account the inconsistencies in people’s preferences over time. Perhaps in a future post I will give a more detailed explanation of these different psychological effects but here I want to show the results from some of these policies in order to provide an idea of what is possible. Most of the policies I am going to site were implemented by the UK government’s Behavioral Insights Team (BIT), sometimes also referred to as the Nudge Unit. One of the interesting things about the BIT, besides their effective use of psychological findings, is that they have a heavy experimental bent. It’s only because they conduct test runs for most of their policies that they implement using careful randomization that we are able to have decent estimates of the casual effects of those policies. A more detailed discussion of the work done by the BIT as well as the other nudges reference can be found in David Halpern’s wonderful book Inside the Nudge Unit.

The nudges have been broken down into four categories:

  1. Changing how easy it is to do something. Typical methods: simplifying, adding or removing roadblocks, changing defaults
  2. Changing how appealing something is. Typical methods: personalizing messages, making important points stand out, having messages be delivered by experts or at least named individuals, taking advantage of how people think about probabilities with things like lotteries, making things emotionally salient
  3. Using social proof or social commitments. Typical methods: reminding people of what most people do or what their friends and colleagues recommend would want them to do, using reciprocity and promises
  4. Optimizing the timing of decisions or interventions. Typical methods: trying it intervene before habits are formed, helping people deal time-inconsistent preferences, taking advantage of what comes before the decision with priming and anchoring

1. Easiness

Increasing University Attendance

In the UK, the number of people from groups that are under-represented at universities who attended university increased by almost 25% when they were set pre-filled financial assistance forms and had their application process streamlined. It also increased the proportion of them receiving scholarships by around a third.

Pension Defaults 

Based on European data, every $1 of subsidies spent to encourage people to save more in their pensions led to a 1 cent increase in savings by workers. As an alternative approach, UK employers were required to start automatically enrolling their workers into a pension programs that they could opt-out of, starting with the largest UK employers (250 or more workers) in 2012 and extending it to all employers in 2018. The results from the initial phase show that the overall participation rate rose from 61% to 83% and 400,000 more people now have a pension.

Placing Roadblocks in Front of Suicide 

In the 1960s, the suicide rate in England and Wales fell by about 30%, due almost entirely due to a reduction in suicides by carbon monoxide poisoning which declined rapidly when the source of gas for ovens changed and people could no longer effectively commit suicide by ‘putting their head in the oven.’ Additionally, restrictions on how many paracetamol tablets can be bought at once were followed by a 42% reduction in deaths from paracetamol ingestion and a 61% reduction in liver transplants needed as a result of damage from paracetamol. Even requiring containers in which pills must be removed one at a time seemed to result in a reduction in suicide rates.

Preventing Theft

In 1980, the Federal Republic of Germany (West Germany) introduced spot fines for driving a motorcycle without a helmet in order to reduce head injuries. However, the policy had a surprising side effect because after its implementation motorcycle thefts fell by 60% and stayed down. Apparently, having to buy a helmet in advance was enough of an obstacle to deter a majority of thefts.

2. Attractiveness and Salience

Licensing Vehicles 

In Britain, people need to license their vehicles with the DVLA in order for them to be taxed, and it is estimated that there are around 250,000 unlicensed vehicles, representing around £40,000,000 in lost revenue annually. The BIT tried changing the wording of the letter that the DVLA sent out to people reminding them to get a license in order to make it clearer that failing to get a license could result in them losing their car. While changing the letter’s wording alone did not seem to change people’s behavior, additionally adding an image of the owner’s type of car increased the effectiveness of the letter from 40% to 49%.

Charitable Giving

In a large investment bank, people were encouraged to donate a day’s salary
to charity. People were randomly assigned to either receive generic emails and leaflets encouraging participation or more personalized emails and leaflets. Additionally, some people were randomly assigned to receive sweets with their message. Both the sweets and personalization increased people’s willingness to donate with the investors who received both being more than three times as likely to donate as investors who just received the generic letter.

Giving Feedback to Drivers

In the U.S. alone, around 100,000 people die every year in speed-related car accidents, with an associated economic cost of about $40 billion. Signs that tell drivers how fast they are going have been found to reduce their average speed by 10 to 15 percent. Although their speed tends to gradually creep back up afterwards, adding a salient reason why they should be going slower, such as being near a school, helps to improve the duration of the effect.

Personalizing Tax Letters

The BIT ran a trial with HMRC to test the effectiveness of different letters aimed at encouraging doctors to pay any outstanding tax liabilities. One group received a generic HMRC letter and another group was sent a simplified version of the letter that emphasized that this was a campaign focusing on doctors. While the response rate of the first group was only 3.8%, the response rate of the second group was 35.3%, more than nine times larger.

Financial Incentives Backfiring

Residents of a small Swiss town were asked if they would agree to a nuclear waste facility being built nearby and 50.8% agreed (This is despite a third of them believing that at least some residents would die from contamination as a result!). A study was conducted that asked the same question but also said that they would be compensated for accepting the facility (the amount offered varied between $2,175 and $6,525), which led to only 24.6% agreeing. Attaching a price to the agreement likely not only caused people to update their beliefs about how dangerous the facility would be but also changed the nature of the agreement from a matter of civic duty to a financial transaction.

Salience in Charitable Giving

People gave on average twice as much to emergency appeals when it mentioned a specific affected child as opposed to statistics about the millions who were affected.

Personalizing Court Fines

When people were sent letters telling them to pay court fines, they were three times as likely to pay if the letters were simplified and used personalized text.

3. Social

Paying Taxes

When letters that were sent to Self-Assessment tax debtors reminding them to pay were modified to mention that most people who lived in their local area paid their taxes and that most people who had possessed a debt like theirs had already paid it, the number of people who paid after 23 days rose from 33.6% to 38.6%. Overall, the use of these messages and similar ones brought in an additional £210,000,000 in revenue for the UK government in the 2012/2013 fiscal year alone.


If people are given a flyer, they are eight times as likely to litter by tossing it on the ground if there are already other flyers on the ground.

Charitable Giving

When people who work at a company where someone had already donated to a charity were asked to donate to that same charity, they were seven times more likely to if they were first informed about the colleague donating there.

4. Timeliness

Charitable Giving in Wills

In Britain, usually only 5% of people give to charity in their wills but when people were asked during the process of writing their will if they would like to donate to charity 10.4% did. If they were told about other people donating to charity and asked if there were any causes they were passionate about then 15.4% did. Among the people who did donate, those who were given the second version of the prompt gave twice as much on average (£6,661) as those who did not receive a prompt (£3,300), meaning the second version resulted in a more than six fold increase in the amount of money people were giving to charity in their wills.

Signing at the Top

When car insurance customers have to sign their name at the top of a form before they fill it out rather than at the bottom afterwards, they reported having driven around 10% more miles on average (in other words they were more honest since insurance is more expensive the more miles you drive). On average, the difference amounted to 2,428 miles per car which is estimated to translate to a minimum of a $97 average difference in annual insurance premiums per car between customers depending on whether they signed at the top or bottom of the insurance form.

Save More Tomorrow

Workers were asked by financial advisers to start saving more for retirement and some took their advice but many did not. Those who didn’t were then asked to follow Save More Tomorrow program which involves agreeing to save more next year than you currently are. After several years, those who had refused to take the financial advisers initial advice were saving more than those who had been willing to start saving more immediately.

Helping Poor Farmers Save

Selling poor farmers a voucher which could only be used to buy fertilizer at the end of the harvest season increased the number of farmers who bought fertilizer by 50%, which was a greater increase than cutting the price of the fertilizer in half. This is because most farmers wanted to buy fertilizer but they had trouble holding on to the necessary money in the time between harvesting and planting. Similarly, saving accounts in which withdrawals could not be made until a certain date or a certain amount was reached were proposed to people living in poverty in developing countries and 25% agreed to open one. After a year, the balances were on average 81% higher than those of people with otherwise equivalent accounts. (Originally from this post).

Draining Self-Control and Decision Fatigue

A study shows that judges moved from giving favorable judgments in 65% of parole cases when they start in the morning down towards close to zero percent by lunch, and then after lunch it starts at around 65% percent again and begins declining again. Similar findings have also been found for care workers who wash their hands less frequently the longer they go without a break and doctors who become more likely to prescribe antibiotics as the day goes on. Obviously, these are the kinds of accidental nudges that we want to try to avoid and hopefully we will see some programs in the future that try to combat them.

Choosing Lunch Options

Workers were three times more likely to choose a healthy option for lunch if they made the decision a week in advance rather than on the same day.

Increasing Diversity in Policing

Despite several changes being made by the British Police Force to increase the number of recruits who are ethnic minorities, including having their entrance exam be conducted online (so it is possible to grade them without seeing any information that would identify the person’s race), there still remained significant disparities between the acceptance rates of different races. However, when the Police Force partnered with the BIT they tried adding a prompt before the exam asking for applicants to take a moment to reflect on why they wanted to join the police and why it mattered to their community but no other changes to the test were made. Astonishingly, the pass rate for ethnic minorities rose from 40% to 60%, which completely eliminated the difference in pass rates with white applicants.

Some Other Possible Nudges

  1. Charity debit cards that automatically send information to the IRS could make getting the benefits of charitable giving easier
  2. Changing organ donor rates by having an opt-out system or having people explicitly choose whether to be donor rather than having an opt-in system
  3. Spreading the results of research on what actually makes people happier and making this research salient to people when they are making decisions
  4. Allowing people to use civility checks which check for signs of being uncivil or unproductive in things they send or post online and nudge them to cool off first
  5. Reducing gender biases in the workplace
  6. Giving people feedback about their energy use compared to their more efficient neighbors can help them become more energy efficient
  7. Self-Bans for things like gambling to help people manage time-inconsistent preferences
  8. Combating decision fatigue for those in important roles, such as judges and doctors, by limiting the the amount of sequential decisions that can be made by any individual, introducing more breaks, making changes in their behavior more salient, or providing them with good anchors to help make their decisions more consistent
  9. Reducing market frictions by requiring companies to present information about their products in a way that allows for them to be easily compared to alternatives
  10. Trying to limit the extent to which policymakers are influenced by cognitive biases

Hopefully this has given you an idea of the range of possibilities that can be achieved by applying the insights of psychology and behavioral economics to public policy. I was pleasantly surprised upon learning about these findings by how many low hanging fruit there were in trying to improve people’s behavior without having to punish people, give out costly rewards, or restrict people’s freedom. Although there are likely to be diminishing returns to applying these insights to some areas, I have a feeling that these results represent only the beginning of what is possible.

The Pieces of a Science of Cities

Epistemic Status: This post contains a mishmash of well-established facts and extreme speculation. I did my best to not blur the lines between the two but be careful!

For the first time in the history of the world, a majority of people live in cities. According to the U.N. about two-thirds of the world’s population are projected to be living in cities by 2050, with the expectation of an additional 2.5 billion urban dwellers globally and 404 million more in India alone. This means that understanding how cities change as they grow is crucial for understanding our future. Cities are incredibly diverse in many ways with each having its own unique history, culture, subcultures, climate, and governance. There is no doubt that such factors play important roles in determining what the experience of living in each city is like. Despite this though, there are rather astonishingly predictive and systematic laws of how cities change as they grow. Here, I will share some surprisingly simply scaling laws of cities as well as offer up explanations for them and explore their consequences where I can.

Most of the scaling laws are what are commonly referred to as power laws and the size of cities is always being measured in terms of its population. So if X scales with the size of a city with a 1.5 power law relationship, this means all cities roughly tend to fit the equation: X = C*Population1.5 (where C is some constant)

Infrastructure and Externalities

Many core aspects of city infrastructure such as the total length of roads, electrical cables, and water pipes and even things like the number of gas stations scale sublinearly with a 0.85 power law relationship. In addition to having much more efficient infrastructure, cities also tend to become greener as they get bigger, with a 1 percent increase in population generating a 0.8 to 0.9 percent increase in total emissions. This decline in emissions per capita is the result of economies of scale that manifest themselves in a number of ways such as more efficient heating and cooling with having many people living close together and the efficiencies that come with the increased use of public transportation and mass transit.

Interestingly though, despite how the nature of transportation changes as a city grows, commute time seems to stay approximately the same with the average staying around half an hour each way. For the most part, people seem to be able to work out ways to get around faster to compensate for the increased size of the city. In fact, even people’s average walking speed systematically increases as the population increases with a 0.09 power law.

Although there are many ways in which cities are greener and more efficient, they can exacerbate certain environmental problems as a result of the nature of some externalities. When an activity affects third parties in a way that isn’t taken into account in that activity’s cost, those additional costs or benefits are called externalities. Since many externalities operate in a localized way where the unaccounted for positive or negative effects impact mostly those who are close to the activity, the more concentrated people are the more distorted the activity’s price will be from its optimal value. This can lead the activities that produce smog and other relatively localized forms of pollution to be performed far more than would be optimal. This is also been the case for other negative externalities such as noise pollution and traffic (Although traffic is an especially strange case because in some cities eliminating certain roads could actually reduce traffic problems as a result of Hotelling’s Law).

This happens with positive externalities as well and leads activities that create them to be even more under-represented than they would usually be. For example, scenic views, parks, and areas of nature can provide benefits to those who don’t buy or sell them both in the form of increased pleasure and higher property values and are likely to be increasingly undervalued by the market as a city grows. Because of the localized nature of these problems, the more cities grow and become increasingly densely populated, the more important it becomes to internalize these externalities.

Economies of Agglomeration and Network Effects

Some of the most important scaling laws relate to innovation and wealth. A city’s GDP, total amount of money paid in wages, and the number of patents produced all scale with a 1.15 power law. As a result of this GDP per capita, average wages, patent rates all systematically increase as a city gets larger. In economics, the idea that increases in productivity can be gained from having many firms located near one another is known as economies of agglomeration. There are a number of factors that can partially explain the phenomenon including gains from increased specialization and division of labor and more liquid markets (Increased social connectivity may also be a factor and this will be discussed more below). Another explanation is that having more firms from the same industry concentrated together increases competition and drives up wages for workers. However, this raises the question of why firms are willing to expose themselves to this increased competition in the first place.

In some cases, it can be in a firm’s own interest to move to an area that has many firms in the same industry. On the surface this may seem rather strange since firms are deliberately exposing themselves to increased competition and decreasing their market power. Why would it be in a firm’s own interest to put themselves in a situation where they have to sell their product at more competitive prices and pay more competitive wages? A significant part of why they do this is the same reason why if you were looking to sell something online probably use a site like eBay or Craigslist. In other words, you would probably go to one of the sites that has many other people trying to sell a similar good. This is because such sites are also the most likely to have many people looking to buy that good. Buyers want to use them because there are a lot of sellers on the site and sellers want to use them because there are a lot of buyers on the site. These network effects can create an equilibrium where even if someone were to create a site with a better design no individual buyer or seller would be incentivized to switch sites. These kinds of network effects can happen not only with online platforms but also with geographical locations. If a city or region has a lot of firms within a particular industry, it incentivizes workers in that industry to move there for the job opportunities and the large number of workers will incentivize firms to move there for the larger and deeper labor market. Additionally, these larger labor markets are more liquid so there is a higher probability that when a firm is looking to hire there will be at least some qualified people looking for the job and vice versa. This same reasoning applies not only to labor but to all the inputs that the firms needs for the product. When these benefits are combined with decreased transportation costs, easier communication, and increased access to ideas it is easier to see why it could be to a firm’s advantage to tolerate the increased competition within its own industry.

Implications for Housing

Thinking about the market for housing using a basic supply and demand model, zoning restrictions and other regulations that artificially reduce the supply of housing should drive up housing prices and make it harder for people who need affordable housing. However, the scaling effects that occur in cities complicate things. To see why let’s return to the metaphor of a city as an online platform. Much like online sales sites, social media platforms benefit from network effects. One of the primary appeals for most people who use sites like Facebook and Twitter is that there are many other people on them. The demand for living in a city in affected in a similar manner. For example, when a city has a large population, restaurants, shops, startups, social groups, and other organizations are able to sustain themselves even if they only appeal to a small percentage of the total population. This means that larger cities come with increased diversity and a wider range of opportunities which can in turn make them more appealing to live in. As of result of this, the demand for housing is not only a function of the price but also to some extent a function of the quantity. So the benefits of increasing the supply in terms of making housing more affordable may be at least partially offset since the demand is likely to increase as well. The relative sizes of these different effects is something I don’t know and would probably just have to be empirically estimated. If I had to guess I would think the increase in demand would not completely offset the increase in supply, especially since, as we will see, not all the scaling effects are positive.

Increasing Connectivity of Social Networks

An important aspect how cities scale comes from the social networks that exist within them and their scaling dynamics. One fairly obvious way in which social interactions change as cities become larger is that the total number of people that a person has at least some minimal amount of interaction with tends to increase. This means that we should expect things that only need a small amount of contact between people in order to spread, such as many diseases, to become more prevalent as the city grows larger.

However, the number of people that someone has regular interactions with and a stable social relationship doesn’t seem to scale much. Instead the number of people they know with different levels of intimacy roughly seem to fit with Dunbar Layers although there is very high variation from person to person. At the same time though, even if the number of people who are one step away from you in a social network does not change, the number of people who are several steps away will. So while the number of friends you have might not change, the number of friends of friends will scale up. This can have important implications because there are activities and organizations in which having someone a few steps away in a social network who participates in it can affect your own probability of getting involved. For example, many people report finding out about the job they work at through a friend of a friend.

On the darker side of things, this may increase the probability that someone is only a few steps in a social network away from someone involved in a gang or other criminal activity. This may help explain why the overall number of crimes committed seems to scale with the same 1.15 power law we’ve seen before (of course as with economies of agglomeration there are many other factors at play). Similarly, even if the average number of sexual partners people have doesn’t scale, the average number of people someone will be indirectly connected in a network of past sexual relationships will scale up. This can potentially help explain why the number of AIDS cases tends to increase superlinearly, following the same 1.15 power law relationship.

It is truly amazing that so many complex social and economic phenomenon with many intricate causal factors can be accurately described on a course-grain level by a simple scaling law. Perhaps equally astonishing is that so many of these phenomena follow the same 1.15 power law. Also, the ones that scale sublinearly tend to follow a 0.85 power law which is intriguingly close to being the inverse of the other scaling laws. This suggests that there may be some underlying principles of social and economic dynamics that can give a fuller and more precise explanation of these scaling laws. The interdisciplinary field of complexity science that is studying these dynamics still seems to be in its early days. The fact that so many of these findings were only recently discovered and there is clearly still so much that we don’t understand suggests that there may still be many low hanging fruit just waiting to get snatched up and move us closer to a full-fledged science of cities.

Escaping Local Maximums in Evolution

Evolution can be thought of on an abstract level as an optimization procedure. In the most basic model there is some population where each individual has its own set of characteristics which determines how fit it is in the given environment. We can call this set of traits its phenotype and in each generation the organisms with the most fit phenotypes reproduce (for simplicity we can assume the total size of the population is kept roughly constant). Additionally, random mutations occasionally occur that result in an organism producing an offspring with a phenotype that is different from its own. We can picture a network, more specifically an undirected graph where each node is a possible phenotype and all nodes are connected to each other if they can be reached from one another by mutations in a single generation. The nodes that a given node is connected to are called its neighbors. We can also imagine that the height of each node corresponds to its relative fitness in the given environment.

Using this basic model we can think about what will happen to the population over the course of many generations. Through the combination of selection pressures causing more fit phenotypes to spread through the population and random mutations introducing neighboring phenotypes, the population will gradually improve in its fitness until it reaches a local maximum. By this I mean that the population will reach an equilibrium where most of the population will be at a phenotype that is more fit than all of its neighbors. However, if there are many local maximums then it is likely that the population will get stuck at a suboptimal one.

More realistically though, instead of only the most fit organisms reproducing, every organisms would have some probability of reproducing and organisms that are more fit would have a higher probability of reproducing but the exact differences in the probabilities would depend upon how strong the selection pressures in the environment currently are. Because there is some chance of less fit organisms reproducing, there is some non-zero probability that the population will be able to able to escape from a local maximum and reach an even higher maximum if it exists. However, the more downward steps that must be taken in the network to reach the new maximum, the less likely this is to occur.

One complication that this basic view of evolution as an optimization procedure doesn’t take into account is the distinction between the roles of the genotype and the phenotype. An organism’s genotype is the level at which mutations occur and, given a specific environment, determines what its phenotype will be. We can think of an organism’s phenotype on the other hand as being the set of characteristics that result from interactions between its genotype and the environment which determine its evolutionary fitness.

One key insight that can be gained from molecular biology is that an extremely large number of genotypes can give rise to the same phenotype. To see an example of why this is the case let’s look at protein-encoding genes.

In cells, DNA is transcribed into mRNA which is translated into a set of amino acids that are connected to construct a protein. The translation process is done by treating the mRNA as chunks of three nucleotides called codons each of which either signals to start translation, stop translation, or to add a specific amino acid. There are 64 possible codons because there are four nucleotides in mRNA but there are only twenty commonly used amino acids. This means that on average there are around three different sequences of DNA that can led to a protein having a specific amino acid at a specific point in its structure. If we use this approximation then for the average-sized protein in a Eukaryote of about 438 amino acids, there are 3438 or 9.5*10208 possible DNA sequences that could have constructed it.

This example isn’t meant to provide exact numbers though but only to be an indication of the scale we’re dealing with here. Similar arguments can also be made for the regulatory circuits and the metabolic system, showing that there are vast numbers of possible genotypic traits for a given phenotypic trait. Additionally, based on the work of people like Andreas Wagnerif we can see many of the genotypes for a given phenotype can potentially reach each other through a single mutation. Returning to our network analogy, we can think of there as being a network of genotypes that contains vast webs of genotypes with the same phenotype running through it. The ultimate result of the existence of these webs is that the number of neighbors a phenotype is extremely large. In other words, the number of phenotypes an organisms lineage can reach from a given phenotype without having to go through any other phenotypes is far higher than might be initially expected. 

In general, when you have nodes connected in a undirected graph, the higher the average number of neighbors is, the lower the average path length between nodes will tend to be. Correspondingly, a higher average number of neighbors for phenotypes means that on average a smaller number of downward steps is needed to move from one local maximum to another and thus the probability of reaching new and better local maximum will be larger. This fairly interesting and important result was obtained simply by adding in a single complication to our model about the distinction between genotypes and phenotypes. You probably have noticed though that the model being used also leaves other complications out regarding things such as sexual selection, the unit at which selection occurs, population dynamics, and changes to the environment. Incorporating these things into our model also has interesting consequences but I will save discussion of those for future posts.


Can Progress be Made Internationally on Climate Change?

Disclaimer: Please keep in mind that I am not an expert in international relations or any related area 

Although it is currently difficult to quantify what the exact consequences will be, specialists agree that an increase of 1.5 to 2 degrees Celsius in the average global temperature is the upper limit of what can be reasonably accommodated. However, in their 2014 evaluation report, the Intergovernmental Panel on Climate Change (IPCC) estimated that based on current trends the rise in temperature will be between 2.5 and 7.8 degrees Celsius before the end of the twenty-first century. Although economists are somewhat split on whether a carbon tax or a cap-and-trade policy would be better, there is a broad consensus that either of these would help significantly reduce greenhouse gas emissions efficiently (at least relative to alternative polices). The need for action seems clear and when the consensus among climate scientists and economists is combined, there is a straightforward and solid case that solutions like a carbon tax or cap-and-trade policy are the right direction to go. So why has there been so little progress internationally in the past several decades in implementing such policies?

A significant part of why to is so difficult for governments to coordinate on this issue is connected to why markets are unable to handle the problem. Simply put, climate change presents a coordination problem, meaning a situation in which every agent doing what is optimal for themselves leads to a suboptimal result for the entire group. When a company or a person emits greenhouse gases in the process of creating energy, farming animals, or some other activity they get all the benefits of doing so but the costs related to climate change and other environmental problems are distributed throughout the population and as a result end up not incorporated into the market. Because of this, the amount which they emit will be greater than the amount that would be emitted if all the costs were being taken into account. One of the things that makes climate change an especially difficult problem is that because its costs are distributed globally this coordination problem exists at the level of nations as well as at the level of individuals. The ideal scenario for any given country is for all the other nations to limit their pollution enough to prevent significant harm from climate change while they continue to gain from the economic benefits of fossil fuel use. But with all the countries facing these incentives we end up at the same suboptimal outcome as we do at an individual level.

But what if some especially altruistic country does decide to implement a policy like a carbon tax or cap-and-trade? In such a situation companies that emit significant amounts of carbon would be incentivized to move production overseas to places that don’t have such policies and then export their products back into the country. This problem is known as carbon leakage and it makes it so that any one country implementing a carbon tax would not have even the proportional effect, based on its percentage of the world’s carbon output, that you would expect it to. Additionally, the economy of the country that implements the environmental-friendly policy in this scenario is hurt more than it would be if every country implemented the same policy because there would not be the same incentives for outsourcing. This has an effect of creating an “I will if everyone else does” attitude among countries. This can create a weakest-link problem in which a small set of countries refusing to join an agreement has the risk of derailing the whole thing. This a particularly nasty side effect considering that there may be countries that economically rely heavily on fossil fuel production such as Venezuela or gulf states whose political leaders actually view the scenario where the deal fails more favorable than the one where it succeeds.

Additionally, there may be developing countries that people feel it is unjust to impose these policies on, either for fairness reasons or on the grounds of not wanting to impede their development and the reduction of extreme poverty. These concerns were attempted to be addressed in previous agreements by having rich countries promise to provide compensation to poor countries. However a significant portion of the money that was committed for this came from aid agencies such as the World Bank and the European Bank for Reconstruction and Development who had not had their budgets increased at all so there were questions about how much of this aid would actually have been additional.

There is another problem. How could the monitoring and enforcing for a policy like a global carbon tax be done? There aren’t any international organizations currently set up to handle this and if the enforcement it left up to individual nations then each country will be incentivized to be very lax in their enforcement. Even if the policy is enforced there is still a chance that countries will implement other policies that at least partly offset it such as subsiding the fossil fuel industry. According to the OECD, there is already currently 141 to 177 billion euros spent around the world every year to subsidize fossil fuel energy sources. And this is just the problem of determining whether a nation is staying true to the agreement and still leaves open the question of what is to be done to countries who are found to be violating it. Presumably in order for the policy to work there have to be some ramifications for violating the agreement but who should have the authority to decide what the proper repercussion for a given violation is?

Considering all of this, it seems remarkable that any progress has been made at all, even if it has been highly inadequate. However, there may still be some hope negotiations going forward. Despite the difficulty of the issues posed here, there may be some methods of handling them.

Experimental programs by the European Space Agency to measure global carbon dioxide emissions on the sale of each country may become a feasible solution in the long term for accurately monitoring how well each country is reducing their emissions. As for the problem of what to do if a country doesn’t follow the agreed upon policy, the World Trade Organization could be used to impose sanctions on the grounds that not respecting the climate agreement is equivalent to environmental dumping. Countries could also separately agree to impose sanctions or import taxes against countries who refuse to join or follow the agreement but it would presumably be to important to determine what is appropriate collectively to prevent countries from doing this for there own selfish reasons. Additionally to would be important for the agreement to be binding to the countries’ futures. This could possible\y be done by involving the International Monetary Fund and tying the policy to its sovereign debt. For example, if a tradable permits system were used, a countries debt could increase or decrease based on the shortage or surplus of permits they had at the end of the year and the permits’ current market price. Compensation for poorer countries will need to be part of the agreement but it will need to done in a way that makes it clear that the aid is actually additional. For example, in a cap-and-trade system this could be done by giving them disproportionately large allocations of permits. As for the problem of coordinating among countries, it may be worth trying to negotiate among a subset of the countries initially and then once they have an agreement trying to encourage others to join. The U.S., Russia, China, India, and Europe are responsible for about 65% of global greenhouse gas emissions so they might make a good starting point but it should be clear that the ultimate goal is to have every country following the policy in order to deal with carbon leakage and commitment issues. None of this would alleviate all of the difficulties that accompany a global coordination problem but they might just be enough to make an international carbon tax or cap-and-trade policy possible. And despite all of the imperfections that are bound to be associated with this, it could still be a huge piece of progress.


Finance in the Developing World

Disclaimer: This post is 1 of 4 intended to summarize some findings in the field of Developmental Economics. All findings are from JPAL, Innovations for Poverty Action, and Poor Economics by Abhijit Banerjee and Esther Duflo

Quick Conceptual note: One of the main questions in Developmental Economics is whether different aspects of the lives of the poor are acting as poverty traps. A poverty trap is something preventing them from being productive and they need an initial investment to help fix it, but they cannot pay for the investments precisely because they are poor.

Risk and Insurance

Many people living in extreme poverty experience a poverty trap related to risk and stability. Because their opportunities are much less financially stable than those of people living in wealthy countries (e.g. agricultural wages in India are 21 times more variable than in the U.S.), they are forced to achieve financial stability through diversification methods. This diversification can be rather extreme. For example, the median family of poor farmers in West Bengal has 7 occupations. Unfortunately, this diversification also prevents them from being able to specialize and acquire experience in their main occupation which can keep them trapped in poverty.

One potentially cost effective way to help people escape this poverty trap could be to offer them micro-insurance programs that help them to share risk among each other. However, for many reasons including lack of trust, adverse selection, moral hazard, and time inconsistent preferences, micro-insurance programs are unlikely to become popular without government assistance, such as helping to pay the premium. If these insurance programs were subsidized though, it’s possible that they could pay for themselves through the increased income of the poor.


The existence of poverty traps would make it seem that lending to the extremely poor could not only be morally good but also profitable there have many ways in which they could increase their earnings in only they could make an initial investment. Additionally, that fact that many local banking organizations lend at rates too high for many of the poor would seem to suggest that microfinance policies could be successful but it raises the question of why the local money lending organizations refuse to lower their rates (which can oftentimes be as high as 4% compounding interest per day).

Most loans that the poor take out are not from official institutions even when they have good access to them. This is because of the high fixed cost the banks charge as a result of having to gather information about the poor. Banks want to how likely people are to pay them back, however it is difficult for them to verify relevant information about the poor such as their income and past credit history and this problem is made worse by the adverse selection and moral hazard problems that occurs when banks cannot effectively discriminate between good and bad borrowers.

Despite these challenges microfinance programs have been rather successful with 150 to 200 million borrowers have used microcredit. Many microfinance institutions try to deal with the problems caused by asymmetric information by giving money to groups of borrowers, usually from the same village, so they each have an incentive to make sure the others pay. Unfortunately, this system seems to result in less people taking advantage of microfinance. There is evidence that microfinance makes people slightly more likely to start a business, purchase durable goods, and spend less money on what they considered to be wasteful expenditures like tea. However, there was no evidence of women being able to exercise greater influence over how the household’s money was spent and there was no increase in spending on education or health. There is also evidence that social proof plays are large role in whether or not people repay their loans which means that there can be a cascade of defaults once some threshold is reach. This suggest that microfinance institutions may be justified in focusing heavily on keeping default rates low. One surprisingly cost effective way of doing this simply involved doing a better job of keeping in touch with borrowers. Borrowers who were regularly called showed much better repayment behavior and greater satisfaction with the bank services than borrowers who either received no follow up or only received follow up calls from the bank when they are delinquent.


Few of the extremely poor have formal savings accounts. In the median country of the 18 countries examined, Indonesia, only 7% of the rural poor and 8% of the urban poor have formal savings accounts. This was the case for less than 1% of people below the poverty line in Brazil, Panama, and Peru. The main more of the poor don’t have accounts is because of the fees that are required to create an account, withdrawal fees, and the cost of traveling to the bank.

However, there evidence that giving people access to better was to save can be very helpful. Selling people a voucher which they could only use to buy fertilizer at the end of the harvest season increased the number of farmers who bought fertilizer by 50%, which was a greater increase than cutting the price of the fertilizer in half. This is because most farmers wanted to buy fertilizer but they had trouble holding on to the necessary money in the time between harvesting and planting. Similarly, saving accounts in which withdrawals could not be made until a certain date or amount was reached were proposed to people and 25% agreed to open one. After a year the balances were on average 81% higher than those of people with otherwise equivalent accounts.

This suggest that there may be a savings poverty trap. Self-control can be worn down and poor people have to exercise self-control by not buying nonessential items more frequently. Additionally, poor people live with higher levels of cortisol as a result of increased stress and high cortisol levels lead to greater impulsivity. This means that the extremely poor likely have a harder time saving their money and thus improving their long term financial situation than the slightly richer.


Although it is perhaps not unexpected that many of the extremely poor run their own agricultural businesses, a surprisingly large number of them run other kinds of businesses as well. In fact, 50% of the urban poor and 20% of the rural poor in 18 developing countries run their own non-agricultural business. Almost all of these businesses have no paid employees and in places like Hyderabad only 20% have a room dedicated to them. Expanding these businesses beyond this scale usually involves paying high fixed costs so one might that their is an entrepreneurial poverty trap.

However, in Hyderabad only small percentage of small business owners took out a microcredit loan when given the chance and similar low interest in expanding their businesses has been observed elsewhere. The reason why so few of the business owners borrow or save significantly for their small businesses is likely because the marginal revenue diminishes quickly as they expand production. This suggests that there is not an entrepreneurial poverty trap giving the extremely poor opportunities to expand there own businesses won’t significantly help them. In fact, when asked about there economic hopes for the future many of them say that their hope is for their children to get a stable government job.

Instead of focusing on their own businesses, policies that make it easier for the poor to move to urban areas such as assistance with low income housing and improving urban land use can increase their economic opportunities. Labor regulations can also help increase job security for the poor but if they are too restrictive than they may do more harm than good by making it harder for workers to obtain jobs in the first place. Overall, most of these entrepreneurs run their own business because they can’t find any other forms of employment and the best way to assist them is by providing them will better alternatives.

Multi-Winner Voting Methods

I would recommend reading this post first unless you are already familiar with the main theorems and concepts in voting theory. Before looking at specific voting methods, let’s examine some themes in multi-winner methods:

Themes in Multi-winner Methods

Proportionality and Locality: Proportional voting methods elect multiple representatives in a way that is designed to be in proportion to voters’ actual preferences for different candidates or groups that candidates belong to. There are a number of benefits to such methods. The most obvious is that it allows voters’ preferences to be represented more accurately than a single winner voting method in which voters’ preferences must be distilled down into a single option. A related benefit is that such systems naturally reduce the harm of gerrymandering. Politicians or political parties gaining disproportionate support as the result of reshaping districts relies on the election results within districts not being proportional in the relevant manner. Most voting methods referred to as proportional don’t give perfectly proportional results, so it is still possible that some harm can be done by gerrymandering, but the distortions that can be caused by reshaping districts are far more minimal than in a voting system like First-Passed-The-Post where the candidate who gets a plurality of votes wins the whole district.

In many multi-winner election methods, multiple people are selected to represent voters from a single district. In general, the more representatives there are per district the more accurately the candidates and the proportions of candidates from different parties will reflect the voters’ preferences. This means that given a fixed number of representatives for the whole population, the larger the districts are the better the proportionality of the results will be, with the extreme case being that the entire population is a single district.  However, many voters appreciate  having elections be on a more local scale. This is because voters may prefer having a set of representatives who are specifically focused on reflecting their local preferences rather than having all the representatives be slightly concerned about their preferences. To some extent this issue is a matter of whether voters are more concerned about geographical or party proportionality. Some methods try to balance these concerns by having both regional and population-wide elections while others try to achieve both forms of proportionality simultaneously.

The Role of Political Parties:  As opposed to virtually all single winner methods, many multi-winner voting methods explicitly involve political parties in the voting process by having parties create lists of candidates that people vote on. This can make it easier to achieve a form of proportionality but some criticize such methods as giving the parties too much influence. By allowing parties to create or influence the list that determine which politician have the highest chance of being elected it gives them a greater ability to influence candidates platforms and get politicians to follow the party line. Sometimes this concern is attempted to be addressed in systems that use party list either by also having elections that aren’t based on party lists or by giving voters some control over which names appear on the different lists.

Variety and Stability: Almost all multi-winner methods do not incentivized the formation of a two-party system as much as single winner voting methods because the threshold for a party or candidate to gain some representation is so much lower. This means that voters have more realistic options to choose from when voting and they don’t have to be as concerned about getting stuck voting for the lesser of two evils. However, some worry about setting the threshold to low or including too many options. This could be for a number of reasons. One reason is that while lowering the threshold can make a greater degree of proportionality possible, it may be necessary to increase the number of representatives or the size of districts in order to achieve this proportionality. The costs of increasing district size was discussed above and some costs associated with more representatives include increasing the number of options voters have to learn about and choose from as well as making negotiations and work between the representatives more complicated.

Now with that background in mind, let’s examine some of our options for multi-winner voting methods:

Voting Methods

Party-Based Methods

  • Basic Party List Systems: In these systems people vote for lists of candidates where each list is usually submitted by a different political party although individuals are often allowed to submit their own lists. The lists are given seats in proportion to the number of votes they received and if a list received N seats then the first N people on the list will be given seats. In order to assign seats to the different lists some rounding must be done for which there are different methods. These methods have two main categories which are Highest Average methods and Largest Remainder methods. Highest Average methods involve a series of rounds in which a seat is awarded to the list with the current highest percentage of the vote and then that party’s percentage is divided by some number such as S + 1 where S is the number of seats that party already has. Using a Largest Remainder method a party’s number of seats is obtained by dividing its votes be some quota, which is obtained by dividing the total number of votes by the number of seats available. This usually leaves some extra seats left which are given to the parties with the largest remainders. Party list systems vary in terms of how much influence voters have over party lists. In a closed list system the list is completely determined by the party while in open list systems voters are allowed to influence the ordering of the candidates. Some systems are completely open where the ordering is determined entirely by the voters while others are only partly open such as in the case where the party gives an ordering but that candidates that achieve some threshold of votes are moved up in the ordering.
  • Majoritarian Bonus: This is a Party List System which gives extra seats or representation to the party or to the joined parties with the most votes. This is deliberately designed to decrease the proportionality of the election and the role of minor parties with the hope that it will result in increased government stability.
  • Parallel Voting: As in other Party List Systems, political parties each create lists of candidates for people to vote on except that these lists are for the whole population and not just a specific district or region. However, people also have a region-based vote where they vote on a candidate to represent their specific district, usually using First-Past-The-Post, and half of the seats are filled by the district specific candidates and the other half are filled using the party lists based on the whole population’s votes.
  • Additional Member System (Mixed Member Proportional Representation): This system is the same as Parallel Voting except for the way that the party list seats are filled. This is done after the winners of the district elections have been declared by comparing the proportions of members from the different parties who currently have seats to the proportions of votes received for the different party lists. The party who is currently the most underrepresented based on the voting gets to give the current top person on their list a seat and then this process is repeated until all of the seats have been filled. One potential flaw in this system is candidates or political parties being dishonest about which politicians are actually with which parties. There have been cases, such as in Italy and Wales, of this being attempted but it seems that this usually isn’t a very effective tactic, especially when most people vote for candidates from parties with established reputations. This method still tends to create better overall proportionality than Parallel Voting.
  • Biproportional methods: This is a set of list-based voting methods that tries to achieve proportionality based on two different criterion, such as political party and region, using a single vote. One example is Duel Member Proportional which operates as a version of a party list system where there are different party lists in each district. Each district has two representative so each list can only have two candidates. The list that gets the most votes in each district has the first candidate on it elected and that parties secondary candidate is assigned half of the votes the list got. Then all of the other parties secondary candidates are eliminated with the first candidate being assigned all of the party’s votes. As in the Additional Member System, the number of seats each party should have to be proportional on the population level based on the sum of the party list votes is compared to the number of candidates that have been elected from each party. This is used to determine how many of the secondary seats each party should get. These seats are then sequentially filled by each party’s remaining candidate who got the most votes with the constraint that there can only be two seats per district.

Other Methods

  • Plurality-at-large Voting: This methods is simply a more general version of First-Past-The-Post in which people get to vote for S different candidates where S is the number of seats available and S candidates with the most votes win. Although it isn’t as bad as First-Past-The-Post in terms of favoring a two-party system, it does still significantly incentivize strategic voting and has similar problems with spoiler effects.
  • Limited Voting: This method is the same as Plurality-at-large Voting except the number of candidates that a voter can select is limited to be some number less than the number of available seats. This may mean that candidates supported by a sizable minority have a better chance gaining some representation. The extreme version of this is Single Non-transferable Vote where voters only get to select a single candidate in a multi-member race.
  • Single Transferable Vote (Hare System): This a a multiple rounds voting method in which in each round a candidate is elected to take one of the seats for the district if the number of votes they have meets a certain threshold. The way that people vote is by providing a ranking, or partial ranking of the candidates. The threshold that is normally used is called the Droop Quota, which requires that candidates need to get more than the total number of votes divided by one more than the number of seats available in the district. So if there were 200,000 votes and 3 seats available in the district than a candidate would have to get more than 50,000 votes to win. After the first round, the excess votes from all of the candidates who have won would transfer over to the their voters’ second choice, starting with the candidate with the most excess votes. So if in the previous example a candidate got 60,000 votes, 10,000 of those would be redistributed. There is a problem here of determining what the candidates excess votes are. There are a number of different methods for determining this and they usually try to make it so the votes are redistributed in a way that is proportional to the winning candidate’s voters’ preferencesIf this transfer of votes results in more candidates crossing the threshold then this process is repeated, but if not then the candidate with the smallest number of votes is eliminated and all of their voters are transferred over to their voters’ next choices. This process is repeated until all of the seats have been filled. Although it is complicated, the Single Transferable Vote system manages to reap the benefits of a proportional voting method while limiting the influence of political parties. However, because of its elimination runoff style is it can have the same center squeeze problem that a method like Instant Runoff Voting can have. For this method it is generally considered optimal to have about 5 seats per district.
  • Weighted Representative Voting Methods: This is a set of voting methods that allows for representatives’ voting power to be weighted by how much support they received from voters. Unlike other multi-winner systems, methods that allow for weighted representative voting can potentially achieve perfect proportionality. In order for it to be perfectly proportional though every candidate who received a single vote would be elected and representatives’ votes would be weighted precisely in proportion to the number of votes that they received. Realistically there is likely to be some threshold required becoming a representative and some rounding in the weighting of representatives’ power.
  • Multi-Winner Approval Voting: The way in which voters convey information about their preferences is the same as in Single Winner Approval Voting where they either approve or disapprove of each candidate. However, there are several ways this can translated into an election result. The simplest way to decide the winners would be to select the candidates with the largest number of approvals, however because this does poorly in terms of proportionality others versions that involve reweighting voters’ approvals are used instead. In Proportional Approval Voting, for each voter the formula 1 + 1/2 + 1/3 + …  + 1/N is taken to be a measure of how satisfied they are, where N is equal to the number of candidates elected that the voter approved. Using this, the combination of candidates is elected that maximizes total voter satisfaction. This is an NP-Hard problem and if there are C candidates and S seats then their will be C!/(S!(C – S)!) combinations of candidates who could be elected. A computationally easier version of this method is Sequential Proportional Approval Voting which takes place in rounds. In each round the candidate with the highest number of approvals wins a seat but after each round voters’ approvals are reweighted by setting them equal to their original weight times 1/(N+1) where N is the number of candidates elected so far that the voter approved. A simpler method is Satisfaction Approval Voting in which voters can still approve of as many candidates as they want but their approvals will be multiplied by 1/N where N is the number candidates they approve.
  • Delegation-based Methods: This is a set of methods in which voters can either vote using some other method or delegate part or all of their ballot to someone else. Many delegation-based methods are rather complicated and can make it harder for voters to think about the consequences of their votes. For example, some delegation-based methods involve a system similar to Single Transferable Vote except that how the votes are transferred are determine by a list or categorization created by the different candidates. In such a system voters only select a single candidate and then that candidate decides how their votes are transferred if they have excess votes or are eliminated.