The case against loss aversion


Jason Collins


December 5, 2019

Summary: Much of the evidence for loss aversion is weak or ambiguous. The endowment effect and status quo bias are subject to multiple alternative explanations, including inertia. There is possibly better evidence for loss aversion in the response to risky bets, but what emerges does not appear to be a general principle of loss aversion. Rather, “loss aversion” is a conditional effect that most typically emerges when rejecting the bet is not the status quo and the stakes are material.

[As a postscript, a week after publishing this post, a working paper for a forthcoming Journal of Consumer Psychology article was released. That paper addresses some of the below points. A post on that paper is in the works.]

In a previous post I flagged three critiques of loss aversion that had emerged in recent years. The focus of that post was Eldad Yechiam’s analysis of the assumption of loss aversion in Kahneman and Tversky’s classic 1979 prospect theory paper.

The second critique, and the focus of this post, is an article by David Gal and Derek Rucker The Loss of Loss Aversion: Will It Loom Larger Than Its Gain (pdf). Its abstract:

Loss aversion, the principle that losses loom larger than gains, is among the most widely accepted ideas in the social sciences. The first part of this article introduces and discusses the construct of loss aversion. The second part of this article reviews evidence in support of loss aversion. The upshot of this review is that current evidence does not support that losses, on balance, tend to be any more impactful than gains. The third part of this article aims to address the question of why acceptance of loss aversion as a general principle remains pervasive and persistent among social scientists, including consumer psychologists, despite evidence to the contrary. This analysis aims to connect the persistence of a belief in loss aversion to more general ideas about belief acceptance and persistence in science. The final part of the article discusses how a more contextualized perspective of the relative impact of losses versus gains can open new areas of inquiry that are squarely in the domain of consumer psychology.

The release of Gal and Rucker’s paper was accompanied by a Scientific American article by Gal, Why the Most Important Idea in Behavioral Decision-Making Is a Fallacy. It uses somewhat stronger language. Here’s a snippet:

[T]here is no general cognitive bias that leads people to avoid losses more vigorously than to pursue gains. Contrary to claims based on loss aversion, price increases (ie, losses for consumers) do not impact consumer behavior more than price decreases (ie, gains for consumers). Messages that frame an appeal in terms of a loss (eg, “you will lose out by not buying our product”) are no more persuasive than messages that frame an appeal in terms of a gain (eg, “you will gain by buying our product”).

People do not rate the pain of losing $10 to be more intense than the pleasure of gaining $10. People do not report their favorite sports team losing a game will be more impactful than their favorite sports team winning a game. And people are not particularly likely to sell a stock they believe has even odds of going up or down in price (in fact, in one study I performed, over 80 percent of participants said they would hold on to it).

This critique of loss aversion is not completely new. David Gal has been making related arguments since 2006. In this more recent article, however, Gal and Rucker draw on a larger literature and some additional experiments to expand the critique.

To frame their argument, they describe three potential versions of loss aversion:

The strong version appears to be a straw man that few would defend, but there is some subtlety in Gal and Rucker’s definition. They write:

This strong version does not require that losses must outweigh gains in all circumstances, as factors such as measurement error and boundary conditions might obscure or reduce the fundamental propensity for losses to be weighted more than equivalent gains.

An interesting point by Gal and Rucker is that for most research on the boundaries or moderators of loss aversion, loss aversion is the general principle around which the exceptions are framed. If people don’t exhibit loss aversion, it is usually argued that the person is not enoding the transaction as a loss, so loss aversion does not apply. The alternative that the gains have equal weight to (or greater weight than) the loss is not put forward. So although few would defend a blunt reading of the strong version, many researchers take it as though people are loss averse unless certain circumstances are present.

Establishing the weak version seems difficult. Tallying studies in which losses loom larger and where gains dominate would provide evidence more on the focus of research than the presence of a general principle of loss aversion. It’s not even clear how you would compare across different contexts.

Despite this difficulty (or possibly because of it), Gal and Rucker come down firmly in favour of the contextual version. They do this not through tallying or comparing the contexts in which losses or gains loom larger, but by arguing that most evidence of loss aversion is ambiguous at best.

Loss aversion as evidence for loss aversion

The principle of loss aversion is descriptive. It is a label applied to an empirical phenomena. It is not an explanation. Similarly, the endowment effect, our tendency to ascribe more value to items that we have than to those we don’t, is a label applied to an empirical phenomena.

Despite being descriptive, Gal and Rucker note that loss aversion is often used as an explanation for choices. For example, loss aversion is often used as an explanation for the endowment effect. But using a descriptive label as an explanation provides no analytical value, with what appears to be an explanation simply application of a different label. (Owen Jones suggests that stating the endowment effect is due to loss aversion is no more useful than labelling human sexual behaviour as being due to abstinence aversion. I personally think it is marginally more useful, if only for the fact there is now a debate as to whether loss aversion and the endowment effect are related. The transfer of label shows that you believe these empirical phenomena have the same psychological basis.)

Gal and Rucker argue that the application of the loss aversion label to the endowment effect leads to circular arguments. The endowment effect is used as evidence for loss aversion, and, as noted above, loss aversion is commonly used to explain the endowment effect. This results in an unjustified reinforcement of the concept, and a degree of neglect of alternative explanations for the phenomena.

I have some sympathy for this claim, although am not overly concerned by it. The endowment effect has multiple explanations (as will be discussed below), so it is weak evidence of loss aversion at best. However, it is rare that the endowment effect is the sole piece of evidence presented for the existence of loss aversion. It is more often one of a series of stylised facts for which a common foundation is sought. So although there is circularity, the case for loss aversion does not rest solely on that circular argument.

Risky versus riskless choice

Much of Gal and Rucker’s examination of the evidence for loss aversion is divided between riskless and risky choice. Riskless choice involves known options and payoffs with certainty. Would you like to keep your chocolate or exchange it for a coffee mug? In risky choice, the result of the choice involves a payoff that becomes known only after the choice. Would you like to accept a 50:50 bet to win $110, lose $100?

Below is a collection of their arguments as to why loss aversion is not the best explanation for many observed empirical results sorted across those two categories.

Riskless choice - status quo bias and the endowment effect

Gal and Rucker’s examination of riskless choice centres on the closely related concepts of status quo bias and the endowment effect. Status quo bias is the propensity for someone to stick with the status quo option. The endowment effect is the propensity for someone to value an object they own over an object that they would need to acquire.

Status quo bias and the endowment effect are often examined in an exchange paradigm. You have been given a coffee mug. Would you like to exchange it for a chocolate? The propensity to retain the coffee mug (or the chocolate if that was what they were given first) is labelled as either status quo bias or the endowment effect. Loss aversion is often used to explain this decision, as the person would lose the status quo option or their current endowment when they choose an alternative.

Gal and Rucker suggests that rather than being driven by loss aversion, status quo bias in this exchange paradigm is instead due to a preference for inaction over action (call this inertia). A person needs a psychological motive for action. Gal examined this in his 2006 paper when he asked experimental subjects to imagine that they had a quarter minted in one city, and then whether they would be willing to change it for a nickel minted in another. Following speculation by Kahneman and others that people do not experience loss aversion when exchanging identical goods, Gal considered that a propensity for the status quo absent loss aversion would indicate the presence of inertia.

Gal found that despite there being no loss in the exchange of quarters, the experimental subjects preferred the status quo of keeping the coin they had. Gal and Rucker replicated this result on Amazon Turk, offering to exchange one hypothetical $20 bill for another. They took this as evidence of inertia.

Apart from the question of what weight you should give an experiment involving hypothetical coins, notes and exchanges, I don’t find this a convincing demonstration that inertia lies behind the status quo bias. Exchange does involve some transaction costs (in the form of effort, however minimal, even if you are told to assume they are insignificant). In his 2006 paper, Gal reports other research where people traded identical goods when paid a nickel to cover “transaction costs”. The token amount spurred action.

Those experiments, however, involved transactions of goods with known values. The value of a quarter is clear. In contrast, Gal’s exploration for the status quo bias in his 2006 paper involved goods without an obvious face value. This is important, as Gal argued that people have “fuzzy preferences” that are often ill-defined and constructed on an ad hoc basis. If we do not precisely judge the attractiveness of chocolate or a mug, we may not have a precise ordering of preference between the two that would justify choosing one after another. Under Gal’s concept of inertia, the lack of a psychological motive to change results in us sticking with the status quo mug.

Contrasting this with the exchange of quarters, there the addition of a nickel to cover trading expenses allows for a precise ordering of the two options, as they are easily comparable monetary sums. In the case of a mug and chocolate, addition of a nickel is unlikely to make the choice any easier as the degree of fuzziness extends over a much larger range.

The other paradigm under which the endowment effect is explored is the valuation paradigm. The valuation paradigm involves asking someone what they would be willing to pay to purchase or acquire an item, or how much they would require to be paid to accept an offer to purchase an item in their possession. The gap between this willingness to pay and the typically larger willingness to accept is the additional value given to the endowed good. (For some people this is how status quo bias and the endowment effect are differentiated. Status quo bias is the maintenance of the status quo in an exchange paradigm, the endowment effect is the higher valuation of endowed goods in the valuation paradigm. However, many also label the exchange paradigm outcome as being due to the endowment effect. Across the literature they are often used interchangeably.)

This difference between willingness to pay and accept in the valuation paradigm is often cited as evidence of loss aversion. But as Gal and Rucker argue, this difference has alternative explanations. Fundamentally different questions are asked when seeking an individual’s willingness to accept (what is the market value?) and their willingness to pay (what is their personal utility?). Only willingness to pay is affected by budget constraints.

Although not mentioned in the 2018 paper, Gal’s 2006 paper suggests this gap may also be due to fuzzy preferences, with the willingness to pay and willingness to accept representing the two end points of the fuzzy range of valuation. Willingness to pay is the lower bound. For any higher amount, they are either indifferent (the range of fuzzy preferences) or would prefer the monetary sum in their hand. Willingness to accept is the upper bound. For any lower amount they are either indifferent (the range of fuzzy preferences) or would prefer to keep the good.

There are plenty of experiments in the broader literature seeking to tease out whether the endowment effect is due to loss aversion or alternative explanations of the type above. Gal and Rucker report their own (unpublished) set of experiments where they seek to isolate inertia as the driver of the difference between willingness to pay and willingness to accept. They asked for experimental subjects’ willingness to pay to obtain a good, versus their willingness to retain a good. For example, they compared subjects’ willingness to pay to fix a phone versus their willingness to pay to get a repaired phone. They asked about their willingness to expend time to drive to get a new notebook they left behind versus their willingness to drive to get a brand new notebook. They asked about their willingness to pay for fibre optic internet versus their willingness to pay to retain fibre optic internet that they already had. For each choices the subject needs to act to get the good, so inertia is removed as a possible explanation of a preference to retain an endowed good.

With fuzzy preferences under this experimental set up, both willingness to pay and willingness to retain would be the lower bound, as any higher payment would lead to indifference or preference of the monetary sum. Here Gal and Rucker found little difference between willingness to pay and willingnes to accept.

Gal and Rucker characterise each of the options as involving choices between losses and gains, and survey questions put to the experimental subjects confirmed that most were framing the choices in that way. This allowed them to point to this experiment as evidence against loss aversion driving the endowment effect. Remove inertia but leave the loss/gain framing, and the effect disappears.

However, the experimental implementation of this idea is artificial. Importantly, the decisions are hypothetical and unincentivised. Whether coded as a loss or gain, the experimental subjects were never endowed with the good and weren’t experiencing a loss.

More convincing evidence, however, came from Gal and Rucker’s application of this idea in an exchange paradigm. In one scenario, people were endowed with a pen or chocolate bar. They were then asked to choose between keeping the pen or swapping for the chocolate bar, so an active choice was required for either option. Gal and Rucker found that regardless of the starting point, roughly the same proportion chose the pen or chocolate bar. This constrasts with a more typical endowment effect experimental setup that they also ran, in which they simply asked people given a pen or chocolate bar whether they would like to exchange. Here the usual endowment effect pattern emerged, with people more likely to keep the endowed good.

Like the endowment effect experiments they critique, this result is subject to alternative explanations, the simplest (although not necessarily convincing) being that the reference point has been changed by the framing of the question. By changing the status quo, you also change the reference point. (I should say this type of argument involving ad hoc stories about changes in reference points is one of the least satisfactory elements of prospect theory.)

Despite the potential for alternative explanations, these experiments are the beginning of a body of evidence for inertia driving some results currently attributed to loss aversion. Gal and Rucker’s argument against use of the endowment effect as evidence of loss aversion is even stronger. There are many alternative explanations to loss aversion for the status quo bias and endowment effect. The evidence for loss aversion is better found elsewhere.

Risky choice

Gal and Rucker’s argument concerning risky bets resembles that for riskless choice. Many experiments in the literature involve an offer of a bet, such as a 50:50 chance to win $100 or lose $100, which the experimental subject can accept or reject. Rejection is the status quo, so inertia could be an explanation for the decision to reject.

Gal and Rucker describe an alternative experiment in which people can choose between a certain return of 3% or a risky bet with expected value of zero. As they must make a choice, there is not a status quo option. 80% of people allocate at least some money to the risky bet, suggesting an absence of loss aversion. This type of finding is reflected across a broader literature.

They also report a body of research where the risky bet is not the sole option to opt into, but rather one of two options for which an active choice must be made. For example, would you like $0 with certainty, or a 50:50 bet to win $10, lose $10. In this case, little evidence for loss aversion emerges unless the stakes are large.

This framing of the safe option as the status quo is one of many conditions under which loss aversion tends to emerge. Gal and Rucker reference a paper by Eyal Ert and Ido Erev, who identified that in addition to emerging when the safe option is the status quo, loss aversion also tends to emerge with:

  • high nominal payoffs
  • when the stakes are large
  • when there are bets present in the choice list that create a contrast effect, and
  • in long experiments without feedback where the computation of the expected payoff is difficult.

Ert and Erev described a series of experiments where they remove these features and eliminate loss aversion.

Gal and Rucker also reference a paper by Yechiam and Hochman pdf, who surveyed the loss aversion literature involving balanced 50:50 bets. For experiential tasks, where decision makers are required to repeatedly select between options with no prior description of the outcomes of probabilities (effectively learning the probabilities with experience), there is no evidence of loss aversion. For descriptive tasks, where a choice is made between fully-described options, loss aversion most typically arises for “high-stakes” hypothetical amounts, and is often absent for lower sums (which are also generally hypothetical).

For the higher stakes bets, Yechiam and Hochman suggest risk aversion may explain the choices. However, what Yechiam and Hochman call high stakes aren’t that high; for example $600 versus $500. As I described in my previous post on the Rabin Paradox, risk aversion at stakes of that size can only be shoehorned into the traditional expected utility model with severe contortions (although it can be done). Rejecting that bet is a high level of risk aversion for anyone with more than minimal wealth (although these experimental subjects may have low wealth as they are generally students). Loss aversion is one alternative explanation.

Regardless, under the concept of loss aversion as presented in prospect theory, we should see loss aversion for low stakes bets. Once you are arguing that “loss aversion” will emerge if the bet is large enough, this is a different conception of loss aversion to that in the academic literature.

Other phenomena that may not involve loss aversion

At the end of the paper, Gal and Rucker mention a couple of other phenomena incorrectly attributed to or not necessarily caused by loss aversion.

The first of these is the Asian disease problem. In this problem, experimental subjects are asked:

Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows:

If Program A is adopted, 200 people will be saved.

If Program B is adopted, there is 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved.

Which of the two programs would you favor?

Most people tend to prefer program A.

Then ask another set of people the following:

If Program C is adopted 400 people will die.

If Program D is adopted there is 1/3 probability that nobody will die, and 2/3 probability that 600 people will die.

Which of the two programs would you favor?

Most people prefer program D, despite C and D being a reframed version of programs A and B. The reason for this change is usually attributed to the second set of options being a loss frame, with people preferring to gamble to avoid the loss.

This, however, is not loss aversion. There is, after all, no potential for gain in the second set of questions against which the strength of the losses can be compared. Rather, this is the “reflection effect”.

Tversky and Kahneman recognised this when they presented the Asian disease problem in their 1981 Science article pdf, but the translation into public discourse has missed this difference, with the Asian disease problem often presented as an example of loss aversion.

Gal and Rucker point out some other examples of phenomena that may be incorrectly attributed to loss aversion. The disposition effect - people tend to sell winning investment and retain losing investments - could also be explained by the reflection effect, or by lay beliefs about mean reversion. The sunk cost effect involves a refusal to recognise losses rather than a greater impact of losses relative to gains, as no comparison to a gain is made.

Losses don’t hurt more than gains

Beyond the thoughtful argument in the paper, Gal’s Scientific American article goes somewhat further. For instance, Gal writes:

People do not rate the pain of losing $10 to be more intense than the pleasure of gaining $10. People do not report their favorite sports team losing a game will be more impactful than their favorite sports team winning a game.

I find it useful to distinguish two points. The first is the question of the psychological impact of a loss. Does a loss generate a different feeling, or level of attention, to an equivalent gain? The second is how that psychological response manifests itself in a decision. Do people treat losses and gains differently, resulting in loss aversion of the type described in prospect theory?

The lack of differentiation between these two points often clouds the discussion of loss aversion. The first point accords with our instinct. We feel the pain of a loss. But that pain does not necessarily mean that we will be loss averse in our decisions.

Gal and Rucker’s article largely focuses on the second of these points through its examination of a series of choice experiments. Yet the types of claims in the Scientific American article, as in the above quote, are more about the first.

This is the point where I disagree with Gal. Although contextual (isn’t everything), the evidence of the greater psychological impact of losses appears solid. In fact, the Yechiam and Hochman article pdf, quoted by Gal and Rucker for its survey of the loss aversion literature, was an attempt to reconcile the disconnect between the evidence for the effect of losses on performance, arousal, frontal cortical activation, and behavioral consistency with the lack of evidence for loss aversion. Yechiam’s article on the assumption of loss aversion by Kahneman and Tversky (the subject of a previous post) closes with a section reconciling his argument with the evidence of the effect of small stake losses on learning and performance.

To be able to make claims that the evidence of psychological impact of losses is as weak and contextual as the evidence for loss aversion, Gal and Rucker would need to provide a much deeper review of the literature. But in the absence of that, my reading of the literature does not support those claims.

Unfortunately, these points in the Scientific American article have been the focus of the limited responses to Gal and Rucker’s article, leaving us with a somewhat unsatisfactory debate (as I discuss further below).

Hey, we’re overthrowing the old paradigm!

The third part of Gal and Rucker’s paper concerns what they call the “Sociology of Loss Aversion”. I don’t have much to say on their particular arguments in this section, except that I have a gut reaction against authors discussing Thomas Kuhn and contextualising their work as overthrowing the entrenched paradigm. Maybe it’s the lack of modesty in failing to acknowledge they could be wrong (like most outsiders complaining about their ideas being ignored and quoting Kuhn). Just build your case overthrowing the damn paradigm!

That said, the few responses to Gal and Rucker’s paper that I have seen are underwhelming. Barry Ritholtz wrote a column, labelled by Richard Thaler as a “Good takedown of recent overwrought editorial“, which basically said an extraordinary claim such as this requires extraordinary evidence, and that that standard has not been met.

Unfortunately, the lines in Gal’s Scientific American article on the psychological effect of losses were the focus of Ritholtz’s response, rather than the evidence in the Gal and Rucker article. Further, Ritholtz didn’t show much sign of having read the paper. For instance, in response to Gal’s claim that “people are not particularly likely to sell a stock they believe has even odds of going up or down in price”, Ritholtz responded that “the endowment effect easily explains why we place greater financial value on that which we already possess”. But, as noted above, (a solid) part of Gal and Rucker’s argument is that the endowment effect may not be the result of loss aversion. (It’s probably worth noting here that Gal and Rucker did effectively replicate the endowment effect many times over. The endowment effect is a solid phenomena.)

Another thread of response, linked by Ritholz, came from Albert Bridge Capital’s Drew Dickson. One part of Dickson’s 20-tweet thread runs as follows:

13| So, sure, a billionaire will not distinguish between a $100 loss and a $100 gain as much as Taleb’s at-risk baker with a child in college; but add a few zeros, and the billionaire will start caring.

4| Critics can pretend that Kahneman, Tversky and @R_Thaler haven’t considered this, but they of course have. From some starting point of wealth, there is some other number where loss aversion matters. For everyone. Even Gal. Even Rucker. Even Taleb.

15| Losses (that are significant to the one suffering the loss) feel much worse than similarly-sized gains feel good. Just do the test on yourself.

But this idea that you will be loss averse if the stakes are high enough is not “loss aversion”, or at least not the version of loss aversion from prospect theory, which applies to even the smallest of losses. It’s closer to the concept of “minimal requirements”, whereby people avoid bets that would be ruinous, not because losses hurt more than gains.

Thaler himself threw out a tweet in response, stating that:

No minor point about terminology. Nothing of substance. WTA > WTP remains.

That willingness to accept (WTA) is greater than willingness to pay (WTP) when framed as the status quo is not a point Gal and Rucker would disagree with. But is it due to loss aversion?

Thankfully, the publication of Gal and Rucker’s article was accompanied by two responses, one of which tackled some of the substantive issues (the other response built on rather than critiqued Gal and Rucker’s work). That substantive response (pdf), by Itamar Simonson and Ran Kivetz, would best be described as supporting the weak version of loss aversion.

Simonson and Kivetz largely agreed that status quo bias and the endowment effect do not offer reliable support for loss aversion, particularly given the alternative explanations for the phenomena. However, they were less convinced of Gal and Rucker’s experiments to identify inertia as the basis of these phenomena, suggesting the experiments involved “unrealistic experimental manipulations that are susceptible to confounds and give rise to simple alternative explanations”, although they leave those simple alternative explanations unspecified.

Simonson and Kivetz also disagreed with Gal and Rucker on the evidence concerning risky bets, describing as ad hoc and unsupported the assumption that not accepting the bet is the status quo. It’s not clear to me how they could describe that assumption as unsupported given Gal and Rucker’s experimental evidence (nor the evidence Gal and Rucker cite) about the absence of loss aversion for small stakes when rejecting the bet is not framed as the status quo. Loss aversion only emerges for larger bets.

I should say, however, that I do have some sympathy for Simonson and Kivetz’s resistance to accepting Gal and Rucker’s sweeping of the risky bet premium into the status quo bucket. Even those larger bets for which loss aversion arises aren’t that large (as noted above, they’re often in the range of $500). Risk aversion is a somewhat unsatisfactory alternative explanation (a topic I discuss in my post on Rabin’s Paradox), and I sense that some form of loss aversion kicks in, although here we may again be talking about a minimal requirements type of loss aversion, not the loss aversion of prospect theory.

Despite their views on risky bets, Simonson and Kivetz were more than willing to approve of Gal and Rucker’s case that loss aversion was a contingent phenomena. They would simply argue that loss aversion occurs “on average”. As noted above, I’m not sure how you would weight the relative instances of gains or losses having greater weight, so I’ll leave that debate for now.

Funnily enough, a final comment by Simonson and Kivetz on risky bets is that “the notion that losses do tend to loom larger than gains is most likely correct; it certainly resonates and “feels” consistent with personal experience, though intuitive reactions are a weak form of evidence.” As noted above, we should distinguish feelings and a decision exhibiting loss aversion.

Unfortunately, I haven’t found anything else that attempts to pick apart Gal and Rucker’s article, so it is hard to gauge the broader reception to the article or whether it has resonated in academic circles at all.

Where does this leave us on loss aversion?

Putting this together, I would summarise the case for loss aversion as follows:

  • The conditions for loss aversion are more restrictive than is typically thought or stated in discussion outside academia
  • Some of the claimed evidence for loss aversion, such as the endowment effect, have alternative explanations. The evidence is better found elsewhere
  • There is sound evidence for the psychological impact of losses, but this does not necessarily manifest itself in loss aversion
  • Most of the loss aversion literature does a poor job of distinguishing between loss aversion in its pure sense and what might be called a “minimal requirements” effect, whereby people are avoiding the gamble due to the threat of ruin.

This is a more restricted conception of loss aversion than I held when I started writing this post.

The loss aversion series of posts

My next post will be on the topic of ergodicity, which involves the concept that people are not maximising the expected value of a series of gambles, but rather the time average (explanation on what that means to come). If people maximise the latter, not the former as many approaches assume, you don’t need risk or loss aversion to explain their decisions.

My other posts on loss aversion can be found here:

  1. Kahneman and Tversky’s debatable loss aversion assumption
  2. What can we infer about someone who rejects a 50:50 bet to win $110 or lose $100? The Rabin paradox explored
  3. The case against loss aversion (this post)
  4. Ergodicity economics - a primer