How do investors prefer to save for their pensions: the 1/N heuristic.

How do investors prefer to save for their pensions: the 1/N heuristic.

Mark and Harvey were sat having coffee in their regular café that they visited every Thursday for breakfast before work. They discussed the latest football results and eventually ended up on the subjects of retirement. Harvey had never got around to starting an investment for his retirement so wanted to ask Mark for advice. Mark simply suggested that Harvey allocate his retirement investments equally across several funds, explaining that this reduce risk.

Saving or investing for retirement is one of the most important decisions that a person can make in their lifetime. Picking the right pension plan and / or allocating resources to the right fund(s) is crucial for enjoying their retirement years. Pension plans and retirement schemes differ from country-to-country. In some pension schemes investors have the choice of how to allocate their funds. When planning for their retirement individuals with a pension plan that allows them to allocate resources to different funds must choose how to invest their money. One popular strategy for making decisions about how to allocated resources is to use the 1/N heuristic (Benartzi & Thaler, 2001). The 1/N heuristic removes the confusion and stress of weighing up the pros and cons of how to invest resources and simply states that a given amount of resources should be divided equally between ‘x’ funds, for example, when a sum of £100,000 is to be invested this would be distributed into £20,000 into 5 different funds.

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In the Swedish pension system investors have the option of deciding how to invest 2.5% of their income. They can allocate 2.5% of their income to either a stock or interest fund (Hedesstrom et al., 2007). Once an individual makes the decision to invest part of their income they receive a brochure with 655 potential funds, they are then required to decide which of the funds they’d like to invest in. In 2004 researchers at Goteborg University analysed 392 investment decisions. The researchers found that investors used at least 5 different heuristics and biases to make their decisions. Investors had a tendency to avoid funds with extreme high and low risks (extremeness aversion – Simonson & Tversky, 1992), a tendency to select the default option (default bias – Johnson et al., 1992), to choose many funds in an attempt to seek maximal variety (diversification heuristic – Read & Loewenstein, 1995), to select domestic funds (home bias – Kilka & Weber, 2000), and to use the 1/N heuristic (Benartzi & Thaler, 2001).

A larger study of more than half a million pension plan participants in Defined Contribution pension plans from the records of the Vanguard Group investigated the use of the 1/N heuristic (Huberman & Jiang, 2004). They found that when deciding how to allocate pension funds participants tended to use the 1/N to divide their funds over 3 or 4 funds.

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A third study of 1000 people examined how Dutch citizens planned for their retirement (Van Rooij et al., 2007). After analysing retirement decisions the results of this study revealed that Dutch citizens are risk-averse and considered themselves to be financially unsophisticated. When given the option these investors used one three strategies (i) the default bias, (ii) the 1/N heuristic, or were susceptible to (iii) framing.

So, depending on what country you work in and decide to retire to there are many different ways to prepare for your retirement. Since most of us, like Harvey, are not financial experts when given complex important decisions to make for our retirement we choose to avoid risk by allocating our money equally across several funds by using the 1/N strategy. When planning for retirement the 1/N heuristic can be an effective and useful way to decrease risk and ensure a substantial retirement fund.

So, depending on what country you work in and decide to retire to there are many different ways to prepare for your retirement. Since most of us, like Harvey, are not financial experts when given complex important decisions to make for our retirement we choose to avoid risk by allocating our money equally across several funds by using the 1/N strategy. When planning for retirement the 1/N heuristic can be an effective and useful way to decrease risk and ensure a substantial retirement fund.

The framing effect on climate change communication and policy making.

The framing effect on climate change communication and policy making.

Hannah and Thomas had both recently become interested in the environment and the politics of climate change after seeing a few news articles on the topic. Last week Hannah watched a very convincing documentary by a leading politician about the dangers of climate change and how humans are contributing to it. Thomas’ father worked in manufacturing and was skeptical about the contributions of humans to the change in environment, his father had always said that humans could not change the environment. Both Hannah and Thomas agreed that although they had different views on climate change there are mixed messages in the press.

Many controversial topics in the media are framed in such a way that benefit the person or company that is responsible for placing the message. The framing effect is one of the major heuristics (short-cuts in decision-making) that is used in the media. Framing works by wording a message in a persuasive way to influence the thinking of the reader (Kuhn, 1997). Communicators can make a choice to present the possible outcomes of a medical interventions as either (a) 80% chance of surviving (i.e., positively framed) or (b) 20% chance of death (i.e., negatively framed). On the topic of climate change communication researchers have found that a negatively framed (highlighting losses) message decreases individual intentions to behave environmentally whilst positively framed messages (highlighting the possibility of losses not materializing) produce a stronger intention to act in a pro-environmental way (Morton et al., 2011).

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One important factor for policy makers is that in the United States the public do not think that climate change is a concern, compared to other policies. Every January the Pew Research Centre for The People and The Press conduct a large poll of the public’s belief in which of 20 policies are of most important.  Between 2007 and 2009 the policy of “dealing with global warming” was consistently ranked at the bottom of 20 priorities (see the table below).

% considering each as a “top priority” January 2007 January 2008 January 2009
Strengthening the nation’s economy 68 75 85
Securing social security 64 64 63
Securing Medicare 63 60 60
Reducing crime 62 54 46
Reducing health care costs 68 69 59
Strengthening the military 46 42 44
Dealing with illegal immigration 55 51 41
Reducing middle class taxes 48 46 43
Dealing with global trade 34 37 31
Dealing with global warming 38 35 30

To aid in breaking through the communication barrier policy makers can tailor their messages to specific audiences by framing their messages. News reporters (e.g., news about an event), policymakers (e.g., employment statistics), advertisers (e.g. vitamin advertisements), and public speakers (e.g., conference talks) already use framing effectively.

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The framing of climate change information has been used successfully by John Kerry in 2004 and Obama in 2008. In his 2004 election campaign the Democratic party presidential candidate Senator John Kerry made strategic use of the public accountability framing (i.e., we are responsible for our environment). Senator Kerry compared the use of different frames (i.e., denial or acceptance of climate change) to the administrations use of intelligence to invade Iraq. In Obama’s 2008 presidential candidate campaign he made use of a sound bite “creating green jobs and fuelling economic recovery.” Creating green jobs in industry with alternatives to gasoline (or petrol) was heralded as a way to benefit the economy by creating more jobs and as a way to reduce greenhouse emissions. We can see here that Kerry chose to use a public accountability frame whilst Obama used an economic frame – both frames were used towards the same aim but tailored differently. Famously, Gore in his 2008 WE campaign picked a moral frame for climate change communication.

We have seen here that the framing effect can be used effectively by communicators for any message (e.g., advertising, policies etc). On the topic of climate change communication, we can put the framing effect to work by carefully considering how we would like to frame a message to our intended audience. In the cases of Hannah and Thomas they may have both seen the same information presented in different ways (i.e., the frame), the frames that they have encountered helped them come to their own decisions about climate change.

The framing effect in bonobos, chimpanzees and capuchin monkeys.

The framing effect in bonobos, chimpanzees and capuchin monkeys.

Noam Chimpsky had had a long day playing with the other chimpanzees. Noam was starting to feel hungry so headed towards the eating area of his enclosure. He had previously stored some fruit on a branch of a large tree. On the way to collect his fruit Noam noticed that one of the other chimpanzees had a new fruit that he had never seen before. Noam was determined to try some of the new fruit. He collected some of his fruit from his stash of fruit and went towards the other chimpanzee who was still carrying the new fruit. Noam wanted to trade some of his fruit for the new fruit. He stopped in front of the other chimpanzee, placed his fruit on the ground and tried to trade. The chimpanzee with the new fruit was happy to trade but wanted more fruit then Noam was willing to give. Noam decided that trading was a bad idea if he had give away too much fruit so he went off to his tree, with his fruit in hand and settled down to eat – afterall, Noam could try some of the new fruit another day.

Noam’s choice was to trade a small amount of food for the new fruit or to trade a lot of his fruit for the new fruit. In the end, Noam decided that the new fruit was not worth a lot of his fruit. Like humans Noam is susceptible to the framing effect. For Noam, his dilemma was to accept a negatively framed trade were he would lose out by giving away too much of his fruit or to broker a positively framed trade were he would give away a small amount of fruit for the new fruit.


The framing effect states that the manner in which options are presented (or framed) can influence how we evaluate choices. We evaluate the options relative to a reference point (i.e., the amount of fruit the Noam had to start with). Changes that seem to worsen the status quo (i.e., Noam giving away a lot fruit for the new fruit) are treated differently to changes that improve the status quo (i.e., Noam gaining the new fruit after trading for a small amount of fruit). The way in which we (and Noam) perceive the choice is important because we are more willing to invest in a choice that is positively framed, rather than negatively framed. The framing effect has been documented extensively in human decision-making in areas such as financial trading (Seo et al., 2010) and medical decision-making (Bornstein et a., 2001). However, as we have seen in the case of Noam other animals, other than humans also exhibit the framing effect. According to molecular-clock estimates our genus split with other primates around 23 million years ago (Schneider et al., 2001), which means that we share a common ancestor with other primates. We share some of our decision-making processes (e.g., the framing effect) with the other animals.

One study the sought to investigate the framing effect in other primates used 40 bonobos (Pan paniscus) and chimpanzees (Pan trogladytes) (Krupenye et al., 2015). The apes were required to make choices between a positively framed option that provided a preferred food item (fruit) and a negatively framed option with a different food item (peanuts). The apes completed 5 sessions of 12 trials on separate days. Both the bonobos and the chimpanzees choose the positively framed option more than the negatively framed option demonstrating that they were susceptible to the framing effect. Furthermore, male apes were more susceptible then female apes to the framing effect.


Capuchin monkeys (Cebus appella) have also shown the framing effect in several different studies (Chen et al., 2017; Lakshminarayanan et al., 2011). In their natural environments capuchins live in complex environments, they are socially sophisticated primates whose native environment requires careful management of their scarce resources. The study by Lakshminarayanan et al., (2011) found that capuchins are able to learn how to trade tokens for food. When trading tokens they are susceptible to framing effect for positively and negatively framed choices.

The results of the capuchin, bonobo and chimpanzee studies suggest that the mechanisms that drive the framing effect is evolutionarily ancient. Some of our ‘human’ economic biases are shared by Noam and the other primates throughout the primate order. These studies highlight the importance of comparative research in understanding the origins of cognitive biases and individual differences in human decision-making. To understand the human brain and decision-making we should complement of research by looking towards our distant relatives.

The gambler’s fallacy, framing, anchoring and hindsight bias in judicial decision-making.

The gambler’s fallacy, framing, anchoring and hindsight bias in judicial decision-making.

Months before William had moved into a new house with his wife, Sarah. They were excited about their move to their new home. William and Sarah unlocked the door to their new house and waited for the furniture removal staff to arrive at the end of their driveway. As the removal van drove up the driveway the van struck the side of William and Sarah’s car, writing the car off. Several months later William and Sarah headed to court to claim for the damages of their car against the removal company. Over many years their lawyer had learnt to be careful in the way that she words her cases in court. Their lawyer asked the judges “How much would you award the plaintiff in compensatory damages?” rather than “We are claiming ‘x’ amount from the defendant.” William and Sarah’s lawyer had learnt that framing a case in such away could exploit the framing bias.

The judicial system is one of the most important systems in all countries with a court of law. Judges play a significant role in society deciding on the outcome of many cases and setting precedencies for future cases. The public expect judges to decide on the outcome of each case fairly, without systematic errors or bias. However, like any instance where a person must make a judgement or decision judges are subject to systematic biases.

One of the most important aspects of law for many people is immigration law. Asylum judges must make decisions that can determine the fate of the individual in court. The United States offers asylum to foreign national who can (i) prove that they have a well-founded fear of persecution in their own countries, and (ii) that their race, religion, nationality, political opinions, or membership in a particular social group is one central reason for the threatened persecution. In 2016 a study by Harvard academics investigated the use of heuristics and biases in the asylum courts of the United States (Chen et al., 2016). Chen and colleagues accessed data through a Freedom of Information Act request of 699 decisions that were made by 357 judges in 45 courts from 1985 to 2013. All cases in the US are handled on a first-in-first-out basis with no quotas as to how many individuals are granted, or not granted asylum. On analysis of the data Chen et al found that judges were subject to the gambler’s fallacy. Judges were more likely to grant (or deny) asylum after denying (or granting) asylum to a previous applicant. The judges presiding over the fate of the asylum applications believes in a representation of randomness, as such, they were more likely to alternate between granting and denying asylum.

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There are many other heuristics and biases that play an important role in the judicial decisions of judges in the US these include framing (as demonstrated by William and Sarah’s lawyer), anchoring, and the hindsight bias. In a joint study with Cornell Law School researchers at a major conference issued questionnaires to 167 federal magistrates. The questionnaires contained examples of cases that a court judge would preside over. From the responses to the questionnaires Guthrie et al (2002) found that judges were subject to anchoring in personal injury claims, framing in copyright action cases, and the hindsight bias in cases of medical negligence.

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A retrospective study by Rachlinski et al (2000) examined the effect of the hindsight bias on decisions in real court cases. The hindsight bias is a mental shortcut that states that we have an inclination, after an event has occurred, to see that the event was predictable. The researchers found that judges failed to appreciate the problems associated with judging an event from hindsight. One example (Chase v. Pevear) from the Supreme Judicial Court of Massachusetts decided that the trustees of two high risk investments should have known the outcome of the investments with a nearly omniscient ability. In the case of First Alabama Bank v. Martin the Alabama Supreme Court held that another group of high risk, high yield equities were speculative, as shown by the fact that trustees lost money by selling ‘at the bottom of the market.’ The courts in both cases assumed that the investors should have known that the price of the equities were recovering, and hence the trustees should not have sold them. One court even held a trustee liable for failing to predict the stock market crash of 1929.

The public expects our judges to make well balanced judgements and decisions without falling for cognitive biases. As humans tasked with make important decisions the judicial system is not isolated from any of the shortcuts that we use to make decisions. For William and Sarah seeking their compensation for the damage to their car the experience that their lawyer had with the framing bias came in useful. In many of other cases, such as with the example of the gambler’s fallacy in the asylum courts these cognitive biases and mental shortcuts can become problematic. We have seen how the framing bias, anchoring heuristic and hindsight bias are all important when making decisions, even at the highest levels of decision-making in society.