Grabbing Now Versus Later

Today and yesterday’s Democratic debates suggests a big recent bump in tastes for regulation and redistribution, in order to lower the status of big business and the rich, and to spend more on the needy and worthy causes. South Korea, which I’ve just visited, sees a similar trend, as does Europe:

Europe’s mainstream parties are going back to the 1970s. In Germany, the U.K, Denmark, France and Spain, these parties are aiming to reverse decades of pro-market policy and promising greater state control of business and the economy, more welfare benefits, bigger pensions and higher taxes for corporations and the wealthy. Some have discussed nationalizations and expropriations. It could add up to the biggest shift in economic policy on the continent in decades. (more)

While I often hear arguments on the moral and economic wisdom of redistribution of various sorts, I rarely hear about the choice of whether to redistribute now versus later. The issues here are similar to those for the related choice in charity, of whether to give now versus later:

Then Robin Hanson of Overcoming Bias got up and just started Robin Hansonning at everybody. First he gave a long list of things that people could do to improve the effectiveness of their charitable donations. Then he declared that since almost no one does any of these, people don’t really care about charity, they’re just trying to look good. … he made some genuinely unsettling points.

One of his claims that generated the most controversy was that instead of donating money to charity, you should invest the money at compound interest, then donate it to charity later after your investment has paid off – preferably just before you die. … He said that the reason people didn’t do this was that they wanted the social benefits of having given money away, which are unavailable if you wait until just before you die to do so. And darn it, he was totally right. Not about the math – there are severe complications which I’ll bring up later – but about the psychology. (more)

Others … argue that giving now to help people who are sick or under-schooled creates future benefits that grow faster than ordinary growth rates. But … if real charity needs are just as strong in the future as today, then all we really need [for waiting to be better] are positive interest rates. (more)

You may be tempted to move resources from the rich and business profits to the poor and worthy projects, because you see business exploitation, you see low value in the rich buying mansions and yachts, you see others in great need, and you see great value in many worthy projects. But big business doesn’t actually exploit much, and the rich tend less to consume real resources, and more to invest and donate real resources.

So instead of grabbing stuff from the rich and businesses today, consider the option of waiting, to grab later. If you don’t grab stuff from them today, these actors will invest much of that stuff, producing a lot more stuff later. Yes, you might think some of your favorite projects are good investments, but let’s be honest; most of the stuff you grab won’t be invested, and the investments that do happen will be driven more by political than rate-of-return considerations. Furthermore, if you grab a lot today, news of that event will discourage future folks from generating stuff, and encourage those folks to move and hide it better.

Also, the rich put much of what they don’t invest into charity. And there’s good reason to think they do a decent job with their charity efforts. Most have impressive management abilities, access to skilled associates, and a willingness to take risks. And they can more effectively resist political pressures that typically mess up government-managed projects.

Finally, when the rich do spend money on themselves, much of that goes to paying for positional and status goods that generate much less in the way of real wastes. When they bid up the price of prestigious clubs, real estate, colleges, first-class seats, vanity books and conference talks, etc., real resources are transferred to those who get less prestigious versions.

So the longer you wait to grab from the rich, the longer they will grow wealth, donate it well, and transfer via status goods. Just as it is dangerous to borrow too much, because you may face big future crises, it can be unwise to grab from the rich today, when you could grow and farm them to create a crop available to harvest tomorrow. South Korea would have been much worse off doing big grabs in 1955, relative to waiting until today to grab.

Added 29June: Some people ask “wait how long?” One strategy would be to wait for a serious crisis. This is in fact when the rich have lost most of their wealth in history, in disasters like wars, pandemics, and civilization collapse. Another strategy would be to wait until there’s so much capital that market rates of return fall to very low levels.

Libertarian Varieties

Here at GMU Econ we tend to lean libertarian, but in a wide range of ways. For example, here are two recent posts by colleagues:

Don Boudreaux:

The economy is an emergent and dynamic order that was not, and could not possibly be, designed – and, hence, that cannot possibly be successfully engineered. … the economy is not a device or an organization with a purpose. It is, instead, the result of the multitude of interactions of hundreds of millions of diverse individual entities – persons, households, firms, and governments – each pursuing its own purposes. …

Competent intro-economics professors keep their aspirations modest. In my case, these are two. The first is to impress upon my students the full weight of the fact that the economy is an inconceivably complex order of interactions that cannot possibly be engineered. The second is to inspire students always to ask questions that too often go unasked – questions such as “From where will the resources come to provide that service?” “Why should Sam’s assessment of Sally’s choices be regarded more highly than Sally’s own assessment?” “What consequences beyond the obvious ones might result from that government action?” And, most importantly of all, “As compared to what?”

Students who successfully complete any well-taught economics course do not have their egos inflated with delusions that they can advise Leviathan to engineer improvements in society. Quite the opposite. But these students do emerge with the too-rare humility that marks those who understand that the best service they can offer is to ask penetrating and pertinent questions that are asked by almost no others. (more)

I’m a big fan of learning to ask good questions; it is great to be able to see puzzles, and to resist the temptation to explain them away too quickly. However, I’m less enamored of teaching students to “ask questions” when they are supposed to see certain answers as obvious.

And the fact that a system is complex doesn’t imply that one cannot usefully “engineer” connections to it. For example, the human body is complex, and yet we can usefully engineer our diets, views, clothes, furniture, air input/outputs, sanitation, and medical interventions.

Yes, most students are overly prone to endorse simple-minded policies with large side effects that they do not understand. But I attribute this less to a lack of awareness of complexity, and more to an eagerness to show values; they care less about the effects of polices than about the values they signal by supporting them. After all, people are also overly prone to offer overly simple-minded advise to the individual people around them, for the same reason.

Dan Klein:

Government is a special sort of player in society; its initiations of coercion differ from those of criminals. Its coercions are overt, institutionalized, openly rationalized, even supported by a large portion of the public. They are called intervention or restriction or regulation or taxation, rather than extortion, assault, theft, or trespass. But such government interventions are still initiations of coercion. That’s important, because recognizing it helps to sustain a presumption against them, a presumption of liberty. CLs [= classical liberals] and libertarians think that many extant interventions do not, in fact, meet the burden of proof for overcoming the presumption. Many interventions should be rolled back, repealed, abolished.

Thus CLs and libertarians favor liberalizing social affairs. That goes as general presumption: For business, work, and trade, but also for guns and for “social” issues, such as drugs, sex, speech, and voluntary association.

CLs and libertarians favor smaller government. Government operations, such as schools, rely on taxes or privileges (and sometimes partially user fees). Even apart from the coercive nature of taxation, they don’t like the government’s playing such a large role in social affairs, for its unhealthy moral and cultural effects.

There are some libertarians, however, who have never seen an intervention that meets the burden of proof. They can be categorical in a way that CLs are not, believing in liberty as a sort of moral axiom. Sometimes libertarians ponder a pure-liberty destination. They can seem millenarian, radical, and rationalistic. …
But libertarian has also been used to describe a more pragmatic attitude situated in the status quo yet looking to liberalize, a directional tendency to augment liberty, even if reforms are small or moderate. (more)

Along with Dan, I only lean against government intervention; that presumption can be and is often overcome. But the concept of coercion isn’t very central to my presumption. At a basic level, I embrace the usual economists’ market failure analysis, preferring interventions that fix large market failures, relative to obvious to-be-expected government failures.

But at a meta level, I care more about having good feedback/learning/innovation processes. The main reason that I tend to be wary of government intervention is that it more often creates processes with low levels of adaptation and innovation regarding technology and individual preferences. Yes, in principle dissatisfied voters can elect politicians who promise particular reforms. But voters have quite limited spotlights of attention and must navigate long chains of accountability to detect and induce real lasting gains.

Yes, low-government mechanisms often also have big problems with adaptation and innovation, especially when customers mainly care about signaling things like loyalty, conformity, wealth, etc. Even so, the track record I see, at least for now, is that these failures have been less severe than comparable government failures. In this case, the devil we know more does in fact tend to be better that the devil we know less.

So when I try to design better social institutions, and to support the proposals of others, I’m less focused than many on assuring zero government invention, or on minimizing “coercion” however conceived, and more concerned to ensure healthy competition overall.

We Agree On So Much

In a standard Bayesian model of beliefs, an agent starts out with a prior distribution over a set of possible states, and then updates to a new distribution, in principle using all the info that agent has ever acquired. Using this new distribution over possible states, this agent can in principle calculate new beliefs on any desired topic. 

Regarding their belief on a particular topic then, an agent’s current belief is the result of applying their info to update their prior belief on that topic. And using standard info theory, one can count the (non-negative) number of info bits that it took to create this new belief, relative to the prior belief.  (The exact formula is Sumi pi ln(pi/qi), where pi is the new belief, qi is the prior, and i ranges over possible answers to this topic question.)  

How much info an agent acquires on a topic is closely related to how confident they become on that topic. Unless a prior starts out very confident, high confidence later can only come via updating on a great many info bits. 

Humans typically acquire vast numbers of info bits over their lifetime. By one estimate, we are exposed to 34GB per day. Yes, as a practical matter we can’t remotely make full use of all this info, but we do use a lot of it, and so our beliefs do over time embody a lot of info. And even if our beliefs don’t reflect all our available info, we can still talk about the number of bits are embodied in any given level of confidence an agent has on a particular topic. 

On many topics of great interest to us, we acquire a huge volume of info, and so become very confident. For example, consider how confident you are at the moment about whether you are alive, whether the sun is shining, that you have ten fingers, etc. You are typically VERY confident about such things, because have access to a great many relevant bits.

On a great many other topics, however, we hardly know anything. Consider, for example, many details about the nearest alien species. Or even about the life of your ancestors ten generations back. On such topics, if we put in sufficient effort we may be able to muster many very weak clues, clues that can push our beliefs in one direction or another. But being weak, these clues don’t add up to much; our beliefs after considering such info aren’t that different from our previous beliefs. That is, on these topics we have less than one bit of info. 

Let us now collect a large broad set of such topics, and ask: what distribution should we expect to see over the number of bits per topic? This number must be positive, for many familiar topics it is much much larger than one, while for other large sets of topics, it is less than one. 

The distribution most commonly observed for numbers that must be positive yet range over many orders of magnitude is: lognormal. And so I suggest that we tentatively assume a (large-sigma) lognormal distribution over the number of info bits that an agent learns per topic. This may not be exactly right, but it should be qualitatively in the ballpark.  

One obvious implication of this assumption is: few topics have nearly one bit of info. That is, most topics are ones where either we hardly know anything, or where we know so much that we are very confident. 

Note that these typical topics are not worth much thought, discussion, or work to cut biases. For example, when making decisions to maximize expected utility, or when refining the contribution that probabilities on one topic make to other topic probabilities, getting 10% of one’s bits wrong just won’t make much of difference here. Changing 10% of 0.01 bit makes still leaves one’s probabilities very close to one’s prior. And changing 10% of a million bits still leaves one with very confident probabilities.  

Only when the number of bits on a topic is of order unity do one’s probabilities vary substantially with each bit, or with 10% of one’s bits. These are the topics where it can be worth paying a fixed cost per topic to refine one’s probabilities, either to help make a decision or to help update other probability estimates. And these are the topics where we tend to think, talk, argue, and worry about our biases.

It makes sense that we tend to focus on pondering such “talkable topics”, where such thought can most improve our estimates and decisions. But don’t let this fool you into thinking we hardly agree on anything. For the vast majority of topics, we agree either that we hardly know anything, or that we quite confidently know the answer. We only meaningfully disagree on the narrow range of topics where our info is on the order of one bit, topics where it is in fact worth the bother to explore our disagreements. 

Note also that for these key talkable topics, making an analysis mistake on just one bit of relevant info is typically sufficient to induce large probability changes, and thus large apparent disagreements. And for most topics it is quite hard to think and talk without making at least one bit’s worth of error. Especially if we consume 34GB per day! So its completely to be expected that we will often find ourselves disagreeing on talkable topics at the level of few bits.

So maybe cut yourself and others a bit more slack about your disagreements? And maybe you should be more okay with our using mechanisms like betting markets to average out these errors. You really can’t be that confident that it is you who has made the fewest analysis errors. 

Range

A wide-ranging review of research … rocked psychology because it showed experience simply did not create skill in a wide range of real-world scenarios, from college administrators assessing student potential to psychiatrists predicting patient performance to human resources professionals deciding who will succeed in job training. In those domains, which involved human behavior and where patterns did not clearly repeat, repetition did not cause learning. Chess, golf, and firefighting are exceptions, not the rule. …

In wicked domains, the rules of the game are often unclear or incomplete, there may or may not be repetitive patterns and they may not be obvious, and feedback is often delayed, inaccurate, or both. In the most devilishly wicked learning environments, experience will reinforce the exact wrong lessons. (more)

David Epstein’s book Range is a needed correction to other advice often heard lately, that the secret of life success is to specialize as early as possible. While early specializing works in some areas, more commonly one learns more by ranging more widely, collecting analogies and tools which can be applied too many new problems, and better learning which specialties fits you best.

I’ve done a lot of wide ranging in my life, so I naturally like this advice. However, as one can obviously take this advice too far, the hard question is how widely to range for how long, and then how quickly to narrow when.

Alas, Epstein seems less useful on this hard tradeoff question. He does make it plausible that your chance of achieving the very highest success in creative areas like art or research is maximized by a wider range than is typical. But as most people have little chance of reaching such heights, this doesn’t say much to them.

I’m struck by the fact that all of his concrete examples of wide rangers who succeeded are people who at some point specialized to enough gain status within a particular speciality area. He gives stats which suggest that wide rangers continue to be productive and useful to society even if they never specialize so much, but those people are apparently not seen as personal successes.

For example, Epstein cites a study showing that innovative academic papers which cite journals never before cited in the same paper are published at first in less prestigious journals, but eventually get more citations. Yet in fields like economics, status depends much more on journal prestige than eventual citations.

So while you might contribute more to the world by continuing to range widely, you often succeed more personally by ranging somewhat widely at first, and then specializing enough to make specialists see you as one of them.

The hard problem then is how to get specialists to credit you for advancing their field when they don’t see you as a high status one of them. Epstein quotes people who say we should just fund all research topics even if they don’t seem promising, but that obviously just won’t work.

Stephenson’s Em Fantasy

Neal Stephenson’s Snow Crash (’92) and Diamond Age (’95) were once some of my favorite science fiction novels. And his Anathem (’08) is the very favorite of a friend. So hearing that his new book Fall; or, Dodge in Hell (’19) is about ems, I had to read it. And given that I’m author of Age of Em and care much for science fiction realism, I had to evaluate this story in those terms. (Other reviews don’t seem to care: 1 2 3 4 5)

Alas, in terms of em realism, this book disappoints. To explain, I’m going to have to give spoilers; you are warned.

Here’s the book’s em scenario. A tech star gets a video game tech star to sign up for cryonics, and later when that guy dies early as a billionaire, his estate freezes him. This estate and this still-living associate, now also a billionaire, spend many billions funding research to develop an advanced brain scanning tech, and then on figuring out how to run that scan as an emulation.

Decades later, access to big enough quantum computers finally allows the creation of a real running em, except that this em is disconnected from the outside world, and has no memories of a prior life. Since as a human he once designed video game worlds, he eventually makes up his own fantasy physical world and rules. Then others who were scanned are added to this world, first thousands, then millions, then billions. Eventually most all humans go there, and able robots are invented that go to space to supply enough computing and energy and cooling to run it all.

Even though all these humans and orgs who build all this are supposedly deeply immersed in the tech world, none of them imagines any other use for ems than creating an immortal heaven, initially for rich folks. The possibility of making trillions selling access to em workers doesn’t interest them. So while they make tools to try to watch what happens in this heaven, they never let its residents see or talk out, or remember their prior lives. Ems never do any useful work.

The first em who set the rules of this world becomes a relative god with vast powers. He anoints demi-gods, and grand mythical adventures, dramas, etc. play out. The ems, who can’t remember their prior lives, live as primitives in a pseudo-nature fantasy-like low-tech world with very simple tools, boring jobs, pain, wars, etc. But they are mostly immortal there and have magic spells and auras on their heads that let them share feelings when they touch.

There is only one em system on Earth. No one ever makes another competing system; we never even hear of anyone trying. Apparently everyone is eager to go to the standard heaven where they don’t remember their past and live as immortal magical primitives with boring jobs. Because deep down we all really crave living as primitives ruled by tech gods?

This system starts out as an opaque hack and stays that way forever. The orgs spending billions to run it supposedly can’t support the usual controls that one might have over computer processes. While they can control an overall budget, they can’t control any relative spending, or even where that spending happens, and they can’t save the system state to pause it. The rules imagined by the first em control everything, and no one later, human or em, can resist them. Ems must all run at exactly the same speed, each has a single spatial location, they can’t make copies of themselves, and they must all obey the first em’s rules for this world.

The actual physical location and limits of the computers supporting all this are assumed to have no effects visible to the residents of this fantasy world. All they see is this fantasy world according to its rules. When this other tech star dies and enters this world, however, he somehow has system privileges to give himself more power and control, and he seems to remember more. He is somehow the bad guy to the first em as good guy, and good vs evil wars ensue.

If you’ve read Age of Em, you can see these are pretty arbitrary and unrealistic assumptions apparently made to put ems in a typical fantasy-like world, so the author can tell a typical fantasy story. In reality, I say, ems will most likely remember their past, be easily connected to our world, and have local budget-based control over their running speed and copy making. They will do useful work, and they’ll often notice the locations and limits of their physical computing infrastructure. They will often coordinate on shared virtual worlds, but those wouldn’t usually be primitive fantasy worlds with all rules set by one super-god. Many such worlds would be created, with rules supporting advanced lifestyles.

The saddest thing here, from my view, is the low interest in what an em world would really look like. Even if he didn’t come across my book, I’m sure Stephenson has access to many computer savvy folks who could have explained many real computing system issues. But he apparently didn’t bother, probably because he doesn’t care much and guesses that most of his readers feel similarly. Alas, he’s probably right.

Decision Markets for Monetary Policy

The goals of monetary policy are to promote maximum employment, stable prices and moderate long-term interest rates. By implementing effective monetary policy, the Fed can maintain stable prices, thereby supporting conditions for long-term economic growth and maximum employment. (more)

Caltech, where I got my PhD in social science, doesn’t have specialists in macroeconomics, and they don’t teach the subject to grad students. They just don’t respect the area enough, they told me. And I haven’t gone out of my way to make up this deficit in my background; other areas have seemed more interesting. So I mostly try not to have or express opinions on macroeconomics

I periodically hear arguments for NGDP Targeting, such as from Scott Sumner, who at one point titles his argument “How Prediction Markets Can Improve Monetary Policy: A Case Study.” But as far as I can tell, while this proposal does use market prices in some ways, it depends more on specific macroeconomic beliefs than a prediction markets approach needs to. 

These specific beliefs may be well supported beliefs, I don’t know. But, I think it is worth pointing out that if we are willing to consider radical changes, we could instead switch to an approach that depends less on particular macroeconomic beliefs: decision markets. Monetary policy seems an especially good case to apply decision markets because they clearly have two required features: 1) A clear set of discrete decision options, where it is clear afterward which option was taken, 2) A reasonably strong consensus on measurable outcomes that such decisions are trying to increase. 

That is, monetary policy consists of clear public and discrete choices, such as on short term interest rates. Call each discrete choice option C. And it is widely agreed that the point of this policy is to promote long term growth, in part via moderating the business cycle. So some weighted average of real growth, inflation, unemployment, and perhaps a few more after-the-fact business cycle indicators, over the next decade or two seems a sufficient summary of the desired outcome. Let’s call this summary outcome O.  

So monetary policy just needs to pick a standard metric O that will be known in a decade or two, estimate E[O|C] for each choice C under consideration, and compare these estimates. And this is exactly the sort of thing that decisions markets can do well. There are some subtitles about how exactly to do it best. But many variations should work pretty well. 

For example, I doubt it matters that much how exactly we weight the contributions to O. And to cut off skepticism on causality, we could use a 1% chance of making each discrete choice randomly, and have decision market estimates be conditional on that random choice. Suffering a 1% randomness seems a pretty low cost to cut off skepticism.

Our Prestige Obsession

Long ago our distant ancestors lived through both good times and bad. In bad times, they did their best to survive, while in good times they asked themselves, “What can I invest in now to help me in coming bad times?” The obvious answer was: good relations and reputations. So they had kids, worked to raise their personal status, and worked to collect and maintain good allies.

This has long been my favored explanation for why we now invest so much in medicine and education, and why those investment have risen so much over the last century. We subconsciously treat medicine as a way to show that we care about others, and to let others show they care about us. As we get richer, we devote a larger fraction of our resources to this plan, and to other ways of showing off.

I’d never thought about it until yesterday, but this theory also predicts that, as we get rich, we put an increasing priority on associating with prestigious doctors and teachers. In better times, we focus more on gaining prestige via closer associations with more prestigious people. So as we get rich, we not only spend more on medicine, we more want that spending to connect us to especially prestigious medical professionals.

This increasing-focus-on-prestige effect can also help us to understand some larger economic patterns. Over the last half century, rising wage inequality has been driven to a large extent by a limited number of unusual services, such as medicine, education, law, firm management, management consulting, and investment management. And these services tend to share a common pattern.

As a fraction of the economy, spending on these services has increased greatly over the last half century or so. The public face of each service tends to be key high status individuals, e.g., doctors, teachers, lawyers, managers, who are seen as driving key service choices for customers. Customers often interact directly with these faces, and develop personal relations with them. There are an increasing number of these key face individuals, their pay is high, and it has been rising faster than has average pay, contributing to rising wage inequality.

For each of these services, we see customers knowing and caring more about the prestige of key service faces, relative to their service track records. Customers seem surprisingly disinterested in big ways in which these services are inefficient and could be greatly improved, such as via tech. And these services tend to be more highly regulated.

For example, since 1960, the US has roughly doubled its number of doctors and nurses, and their pay has roughly tripled, a far larger increase seen in median pay. As a result, the fraction of total income spent on medicine has risen greatly. Randomized trials comparing paramedics and nurse practitioners to general practice doctors find that they all produce similar results, even though doctors cost far more. While student health centers often save by having one doctor supervise many nurses who do most of the care, most people dislike this and insist on direct doctor care.

We see very little correlation between having more medicine and more health, suggesting that there is much excess care and inefficiency. Patients prefer expensive complex treatments, and are suspicious of simple cheap treatments. Patients tend to be more aware of and interested in their doctor’s prestigious schools and jobs than of their treatment track record. While medicine is highly regulated overall, the much less regulated world of animal medicine has seen spending rise a similar rate.

In education, since 1960 we’ve seen big rises in the number of students, the number of teachers and other workers per student, and in the wages of teachers relative to worker elsewhere. Teachers make relatively high wages. While most schools are government run, spending at private schools has risen at a similar rate to public schools. We see a strong push for more highly educated teachers, even though teachers with less schooling seem adequate for learning. Students don’t actually remember much of what they are taught, and most of what they do learn isn’t actually useful. Students seem to know and care more about the prestige of their teachers than about their track records at teaching. College students prefer worse teachers who have done more prestigious research.

In law, since 1960 we’ve similarly seen big increases in the number of court cases, the number of lawyers employed, and in lawyer incomes. While two centuries ago most people could go to court without a lawyer, law is now far more complex. Yet it is far from clear whether we are better off with our more complex and expensive legal system. Most customers know far more about the school and job prestige of the lawyers they consider than they do about such lawyers’ court track records.

Management consultants have greatly increased in number and wages. While it is often possible to predict what they would recommend at a lower cost, such consultants are often hired because their prestige can cow internal opponents to not resist proposed changes. Management consultants tend to hire new graduates from top schools to impress clients with their prestige.

People who manage investment funds have greatly increased in number and pay. Once their management fees are taken into account, they tend to give lower returns than simple index funds. Investors seem willing to accept such lower expected returns in trade for a chance to brag about their association should returns happen to be high. They enjoy associating with prestigious fund managers, and tend to insist that such managers take their phone calls, which credibly shows a closer than arms-length relation.

Managers in general have also increased in number and also in pay, relative to median pay. And a key function of managers may be to make firms seem more prestigious, not only to customers and investors, but also to employees. Employees are generally wary of submitting to the dominance of bosses, as such submission violates an ancient forager norm. But as admiring and following prestigious people is okay, prestigious bosses can induce more cooperative employees.

Taken together, these cases suggest that increasing wage inequality may be caused in part by an increased demand for associating with prestigious service faces. As we get rich, we become willing to spend a larger fraction of our income on showing off via medicine and schooling, and we put higher priority on connecting to more prestigious doctors, teachers, lawyers, managers, etc. This increasing demand is what pushes their wages high.

This demand for more prestigious service faces seems to not be driven by a higher productivity that more prestigious workers may be able to provide. Customers seem to pay far less attention to productivity than to prestige; they don’t ask for track records, and they seem to tolerate a great deal of inefficiency. This all suggests that it is prestige more directly that customers seek.

Note that my story is somewhat in conflict with the usual “skill-bias technical change” story, which says that tech changed to make higher-skilled w0rkers more productive relative to lower-skilled workers.

Progeny Probs: Souls, Ems, Quantum

Consider three kinds of ancestry trees: 1) souls of some odd human mothers, 2) ems and their copies, and 3) splitting quantum worlds. In each kind of tree, agents can ask themselves, “Which future version of me will I become?”

SOULS  First, let’s start with some odd human mothers. A single uber-mother can give rise to a large tree of descendants via the mother relation. Each branch in the tree is a single person. The leaves of this tree are branches that lead to no more branches. In this case, leaves are either men, or they are women who never had children. When a mother looks back on her history, she sees a single chain of branches from the uber-mother root of the tree to her. All of those branches are mothers who had at least one child.

Now here is the odd part: imagine that some mothers see their personal historical chain as describing a singular soul being passed down through the generations. They believe that souls can be transferred but not created, and so that when a mother has more than one child, at most one of those children gets a soul.

Yes, this is an odd perspective to have regarding souls, but bear with me. Such an odd mother might wonder which one of her children will inherit her soul. Her beliefs about the answer to this question, and about other facts about this child, might be expressed in a subjective probability distribution. I will call such a distribution a “progeny prob”.

EMS  Second, let’s consider ems, the subject of my book The Age of Em: Work, Love, and Life when Robots Rule the Earth. Ems don’t yet exist, but they might in the future. Each em is an emulation of a particular human brain, and it acts just like that human would in the same subjective situation, even though it actually runs on an artificial computer. Each em is part of an ancestry tree that starts with a root that resulted from scanning a particular human brain.

This em tree branches when copies are made of individual ems, and the leaves of this tree are copies that are erased. Ems vary in many ways, such as in how much wealth they own, how fast their minds run relative to humans, and how long they live before they end or next split into copies. Split events also differ, such as re how many copies are made, what social role each copy is planned to fill, and which copies get what part of the original’s wealth or friends.

An em who looks toward its next future split, and foresees a resulting set of copies, may ask themselves “Which one of those copies will I be?” Of course they will actually become all of those copies. But as human minds never evolved to anticipate splitting, ems may find it hard to think that way. The fact that ems remember only one chain of branches in the past can lead them to think in terms of continuing on in only one future branch. Em “progeny prob” beliefs about who they will become can also include predictions about life details of that copy, such as wealth or speed. These beliefs can also be conditional on particular plans made for this split, such as which copies plan to take which jobs.

QUANTUM  Third, let’s consider quantum states, as seen from the many worlds perspective. We start with a large system of interest, a system that can include observers like humans and ems. This system begins in some “root” quantum state, and afterward experiences many “decoherence events”, with each such event aligned to a particular key parameter, like the spatial location of a particular atom. Soon after each such decoherence event, the total system state typically becomes closely approximated by a weighted sum of component states. Each component state is associated with a different value of the key parameter. Each subsystem of such a component state, including subsystems that describe the mental states of observers, have states that match this key parameter value. For example, if these observers “measured” the location of an atom, then each observer would have a mental state corresponding to their having observed the same particular location.

These different components of a quantum state sum can thus be seen as different “worlds”, wherein observers have different and diverging mental states. Decoherence events can thus be seen as events at which each quantum world “splits” into many child worlds. The total history starting from a root quantum state can be seen as a tree of states, with each state containing observers. And so a quantum history is in part a tree of observers. Each observer in this tree can look backward and see a chain of branches back to the root, with each branch holding a version of themselves. More versions of themselves live in other branches of this tree.

After a split, different quantum worlds have almost no interaction with each other. Which is why we never notice this quantum splitting process in the world around us. So observers typically never see any concrete evidence of that there exist other versions of themselves, other than their past versions in the chain from them now back in time to the root state. That is, we never see other quantum worlds. As observers see only a sequence of past versions of themselves, they can naturally expect to see that sequence continue into the future.

That is, observers typically ask “In the future, what will be the state of the one world, including the one version of my mind?” Even though in fact there will be many worlds, holding many versions of their minds. (Quantum frameworks other than many worlds struggle to find ways, usually awkward, to make this one future version claim actually true.) Beliefs about this “who will I be?” question are thus “progeny probs”, analogous to the beliefs that an em might have about which future copy they will become, or that an odd human mother might have on which future child inherits her soul.

The standard Born rule in quantum mechanics is usually expressed as such a progeny prob. It says that if the current state splits into a weighted sum of future states, one should expect to find oneself in each component of that sum with a chance proportional to the square of that state’s weight in the sum. This is a remarkably simple and context-independent rule. Technically, quantum states are vectors, and the Born rule uses the L2 norm for relative vector size. And a key question about many worlds quantum theory, perhaps the key question, is: from where comes this rule?

IN GENERAL  These three cases, of human souls, em copies, and quantum worlds, all have a similar structure. While the real situation is a branching tree of agents, an agent who looks back to see a sequence of ancestors can be tempted to project that sequence forward, predict that they will become only one next descendant, and wonder what that descendant will be like. This temptation is especially strong in the quantum case, where agents never see any other part of the tree than their ancestor sequence, and so can fail to realize that a larger tree even exists.

An agent’s beliefs about which next descendant will “really” be them can be described by a probability distribution, which I’ve called a “progeny prob”. This gives the chance this agent will “really” become a particular descendant, conditional on the details of a situation. For ems, this chance may be conditional on each copy’s wealth, or speed, or job role. For quantum systems, this chance is often conditional on the value of the key parameter associated with a decoherence event.

In the rest of this (long) post, I make three points about progeny probs.

IS FICTION  The first big thing to notice is that, for an agent who is a branch in some tree of agents, there is actually no truth of the matter regarding which future branch that agent will “really” be! They will become all descendant branches in that tree. So one of the most fundamental elements of quantum theory, the Born probability rule, is typically expressed in terms of an incoherent concept. Also incoherent is a big question that ems will often ask, “Who will I be next?”

However, even though progeny probs are in this sense fictional, we usually connect them to some very real data: the past sequence of ancestors we see up until today. Agents who believe that their past history was generated by the same sort of progeny prob that applies to their future should expect this history to be typical of sequences generated by such a progeny prob. This test has in fact been applied to the quantum progeny prob, which passes with high accuracy.

If one has has a detailed enough model of how a certain kind of ancestry tree of observers is generated, then one can use this tree model to predict a probability distribution over possible trees. Each such generated tree comes with a set of ancestor sequences, one for each branch in the tree. So given a distribution over trees, one can generate a distribution over ancestor sequences in these trees.

IS RELATIVE  However, in order to take a tree model and generate a distribution over ancestor sequences, one needs to pick some relative branch weights, weights which say how much each branch counts relative to others in that tree. And the progeny prob that best fits this total distribution of ancestry sequences will depend on these relative branch weights.

For example, consider all the ems that descend from some particular human, and consider a late time when there are many such descendants. There are several different ways that one could sample from these late ems to create a distribution of ems. For example, one could repeatedly sample 1) a random memory unit able to store part of the mental state of an em, 2) a random processor able to run part of an em mind, or 3) a random dollar of wealth and pick the em who owns it.

The random processor approach tends to fit better with progeny probs which say that you are more likely to be a descendant who runs faster (and who has descendants who run faster). The random memory approach tends to fit better with progeny probs that count descendants more equally, regardless of speed. And the random dollar of wealth approach tends to fit better with progeny probs that say you are more likely to become the descendants who inherit more wealth from you. Which of their descendants an em should expect to become depends on which of these methods this em thinks makes more sense for weighting future ems.

Each progeny prob predicts the existence a tiny fraction of very weird ancestors sequences, ones quite unlikely to be generated by that progeny prob. But such sequences are only actually rare if this progeny prob fits with the correct distribution. For example, few ems chosen by looking at random memories should have ancestor histories that are weird according to a memory-based progeny prob. But most of them might have ancestors histories that are weird according to processor- or wealth-based progeny probs.

For the quantum case, the standard Born rule progeny prob seems to fit well with distributions that sample from later quantum worlds in proportion to the same L2 norm that the Born rule uses. However, we lack a good widely accepted derivation of this distribution from the basic standard core of quantum mechanics. That is, we can’t explain why we should focus on later quantum worlds in proportion to this L2 norm, and mostly ignore the far larger numbers of quantum worlds that have much smaller values of this norm.

Yes, some try to derive this norm from other axioms, but none of these derivations seems a compelling explanation to me. The L2 norm is so simple that it must be implied by a great many sets of axioms. I’ve proposed a “mangled worlds” approach, and show that the Born rule can result from counting discrete worlds equally, if we ignore worlds below a size threshold that are mangled by larger worlds, and so are not hospitable to observers. But my proposal is so far mostly ignored.

IS COMPLEX  Finally, it is worth noting that the implicit assumptions of a progeny prob model are typically violated by the reality of even simple tree models. As a result, the best fit progeny prob for a simple tree model can be quite complex.

The progeny prob framework assumes that one and only one “me” travels along some path in the tree. Conditional on being in one branch, the chances that I become each of the child branches must sum to one. And it may seem natural to have those chances be independent of what would have happened had I instead gone to other branches at earlier times.

But even in simple tree models, there is not a fixed total quantity of branches. So when there is more growth in other branches of the tree, this part of the tree shrinks as a fraction of the whole. And so the sum of the weights for the children of a branch do not usually sum to the weight of that branch. And such weights do typically depend on what happens in distant branches that split off long ago.

It thus seems all the more remarkable that the mysterious Born rule progeny prog for quantum mechanics is so simple and context independent.