Proof-of-Work as a Handicap

Daniel Krawisz, Chief Scientist at MatterPool, Inc.

Introduction

I discuss the use of proof-of-work as a handicap that can be incorporated into Internet protocols and fallacies concerning proof-of-work and handicaps that I have seen in the Bitcoin world. I will show that proof-of-work is a handicap and consequently can be used as a part of signals of fitness that are demonstrated over the Internet. Furthermore, protocols involving signals of fitness which do not begin by verifying proof-of-work are sub-optimal and waste time evaluating unqualified candidates that proof of work would have eliminated.

The Handicap Principle

Statement of The Handicap Principle

A handicap is easily assessed waste[^1] and it is used by candidates to communicate with evaluators. The Handicap Principle says that every optimal signal of fitness uses a handicap. Handicaps are costly on the candidate who bears it, cheap on the evaluator.

The cost of the handicap incentivizes the bearer to make a strategic choice[^2] about how much cost to demonstrate. Too much and he hurts himself too much, too little and he doesn't get enough attention. Thus, the information provided by handicaps is expected to be relevant. Handicaps are for gaining the attention of rational actors and for cheaply rejecting candidates who are unlikely to be qualified if given a closer look. The paradigmatic example of a handicap is the peacock’s tail. The Handicap Principle was proposed by Zahavi, who suggested that it has many applications in biology.[^3]

Not every signal of fitness is entirely a handicap.[^4] Rather, a handicap is an essential component of a signal of fitness because without it the signal is not optimal. This is because a handicap is the best possible first step in an evaluation process. Handicaps are for reducing the number of candidates down to a reasonable number, not for ignoring all other relevant information. Everybody needs to save on evaluation resources because everyone experiences information overload. Thus everybody can benefit from relying on handicaps to assess candidates.

Handicaps are optimizers of searches for relevant information. They are not the only information that is relevant nor are they a substitute for judgement, although it is in the best interest of the signaller to provide the best possible information. In a perfect world, handicaps would provide perfect information about fitness because that is what handicappers would want to do if they could. In the real world, handicaps are merely correlated with fitness because the strategic choice is not easy to make correctly. It is a complex game of self-assessment in relation to everyone else. Candidates will make mistakes. Thus, something with a big handicap is not necessarily important; rather it is worth a closer evaluation than something with a small handicap, not knowing anything else. More qualified candidates are likely to be found among more handicapped individuals, although unqualified candidates will still be among the more handicapped.

Why Handicaps Work

There are two aspects to handicaps, which, together, make them competitive with other signals of fitness: that of being costly and that of being easily assessed. The cost of handicaps is the cause of their honesty. The ease by which they can be assessed is why evaluators can require them among all candidates. Evaluators benefit so much from being able to use handicaps to limit information that they can ignore candidates without handicaps and still be successful.

Handicaps enforce honesty because attention is worth more to honest actors than to dishonest actors. Thus, honest actors can spend more on handicaps. They can do this because they are stronger and can thus can be hurt more and because they are more likely to make offers that will be accepted. Deceivers must gain more attention to gain the same number of accepted offers as honest actors.

Handicaps are preferred by evaluators of fitness due to the cheapness of the information provided in relation to its expected relevance. This does not mean that other information is not relevant. Rather, other relevant information is more costly to obtain. Not that it is never worthwhile to spend extra to get that other relevant information; rather, we save on the cost of relevant information by looking at handicaps first. In other words, those who have good handicaps are worth a closer look.

Without handicaps, evaluators suffer from information overload and candidates rely on chance to get noticed. With handicaps, evaluators find good candidates without wasting time and candidates can compete fairly and can expect attention if they do well.

Handicaps are a repeated game. Those who handicap too much do not lose immediately. They lose over time. Handicaps are a voluntary risk for the bearer. Someone who can think farther ahead can risk more. Thus, Handicaps bring far-off futures into the present. Someone who is more viable long-term can afford a bigger handicap today.

Other Reliable Information Concerning Fitness

As Számadó points out, the reason for honesty is the cost of cheating.[^5] Handicaps are not the only way of imposing costs on cheaters, thus not the only reason for honesty. For example, the size of another animal may provide reliable information on fitness. That is what biologists call a cue rather than a signal; a signal is something that exists for the purpose of communication whereas a cue is something that incidentally provides information. In this case the cost of cheating is simply an inability of animals to grow bigger. However if the size of an animal became a very important cue to look at, the animal might just make it easier on its companions by evolving a handicap that emphasized size.

In addition, there are costly signals which are not handicaps. This is an important distinction which has resulted in confusion in the scientific literature by not being understood properly. All costly signals impose a strategic choice on the signaller, but not all costly signals are easy to assess. Graffen did not model his signals as being easily assessed. Graffen’s model has been understood by later writers as a statement of the Handicap Principle but it is really a model of strategic choice, and thus applies to all costly signals. Spence’s[^6] work provides an example of the problem with Graffen’s model as a model of the Handicap Principle. Spence came up with a model that is mathematically identical to Graffen’s but which was intended to model university degrees as signals of fitness to employers. Degrees are not handicaps, although they do demonstrate cost and thus are signals of fitness. However, degrees are not easy to assess because the meaning of a degree varies a lot with the university that granted it, and the work that was done to achieve it.

Other information which may form a part of an honest signal of fitness may involve the legal system or reputation. Each of these provides for punishments, should a candidate be dishonest. A candidate who lies may be fined or go to jail, or he may lose face. In these cases, the cost of cheating is imposed after-the-fact. By contrast, handicaps require candidates to pre-emptively punish themselves before being evaluated. This enables many bad offers to be eliminated before anything can go wrong. This does not mean that handicaps are the only way for good offers to be identified. The best reason for honesty may be a combination of costs that are imposed on cheaters.

Thus, the Boost protocol[^7] is not intended to be a replacement for the legal system or for reputation. Proof-of-work is not the only valid way to signal fitness over the Internet. Rather, a signal of fitness which does not use it can be optimized by incorporating it. A signal that only relied on reputation or law would waste resources unnecessarily on evaluating reputations or on court costs. Resources can be conserved by evaluating proof-of-work first. Candidates who meet the desired difficulty are more likely to have good reputations and less likely to require taking to court.

Although identity is not inherently a part of the Boost protocol, identity works naturally with handicaps. A proof-of-work string can be associated with an identity in a way that prevents sybil attacks. An honest actor can use one identity and can continue to let the total proof-of-work pile up. A dishonest actor will need to discard identities and start new ones more often. This is an application of the general principle that deceivers cannot compete when we rely on handicaps because they receive fewer acceptances per offer yet must handicap the same amount.

The Strategic Choice

The strategic choice refers to the choice of candidates about how much to handicap. Costly signals are correlated with fitness due to the choice which is imposed on candidates about how much cost to demonstrate. Handicaps are honest signals of fitness because candidates optimize the use of handicaps by telling the truth with them. If a candidate knows he will be rejected for not being sufficiently handicapped, he must make a strategic choice about how much to handicap. He must balance the cost of the handicap against the potential benefit of gaining attention with it.

If a peacock knew that he was a relatively more fit male it would be reasonable for him to handicap a lot because he could still survive easily and look favorable among other distinguished candidates. On the other hand, if he knew that he was less fit, then it wouldn’t make much sense to handicap because he would look scrawny next to the other distinguished candidates while simultaneously risking more than they were. As Graffen has said, “better males do better by advertising more” and as Getty put it “more fit males are better at converting advertisement into fitness.”[^8]

The difficulty of the strategic choice has to do with the fact that rank matters more than absolute amounts. The only way the potential benefit of a handicap can be known is by knowing about the other candidates and about what the evaluators want. A greater handicap will impose costs on him with certainty but it does not benefit him with certainty. He can still be rejected despite being more handicapped. The handicap will only benefit him if he can still be seen as better than the other candidates with similar handicaps.

A candidate would want to achieve the rank that makes him competitive with other individuals who are similarly ranked. This is not an easy task because one cannot know how much attention one is losing out on by not handicapping enough without understanding both the competition and the audience. One wins a handicap game by correctly assessing one’s own value and handicapping in proportion to it.

In handicaps that have evolved by natural selection, the strategic choice is a metaphor. Handicaps can also be involved in games that are played consciously by the participants. In this case the strategic choice is literal and very necessary to understand in order to play the game well.

Honesty as a Stable Strategy

An objection which I have received in conversations about the Handicap Principle is that a candidate can choose to signal a much higher level of fitness than he actually has. I do not understand why people think this is an objection or how to respond to it. People who make it prove that they do not understand the idea.

If you are playing chess, are you worried about your opponent making a bad move? No, you worry that he makes a good move. Bad moves on your opponent's part are good for you. An honest handicapper wants dishonest competitors because he can beat them.

The addition of a handicap changes a game from one in which deception is an optimal strategy for some candidates to one in which it is an optimal strategy for no candidates. A candidate who tries to deceive anyway is a loser. Such a candidate would be expected to be weeded out over by natural selection. That does not mean that an evaluator will never meet a candidate who is a deceiver. I have already said that handicaps do not remove the need for judgement. Rather an evaluator who relies on handicaps will find a good candidate relatively easily and one who does not will be overwhelmed by deceivers.

Over time, winning strategies win out. Handicap games work by preventing deception from being an optimal strategy. They do not absolutely prevent deception; they simply give honest actors a means of competing effectively with dishonest actors. If you do not think this is good simply because it does not absolutely prevent deception then you haven't understood the idea. Handicaps are very useful. The consequences of not using them or of ignoring them are very serious.

People who do not want to reveal reliable information about themselves do not like handicaps. This might be because they are afraid to think about how good they really are or because they may know the answer and don’t want anyone else to know. Not everyone who doesn’t like handicaps is bad but either they fail to understand the benefit of rapidly elimining inferior candidates or they are an inferior candidate who doesn’t want to be eliminated rapidly. Someone who is like this will lie about handicaps or willfully misunderstand them. He will know instinctively that his power is being taken away even if he doesn't know how.

Today we live in a world where people do not know about handicaps. That means we are overwhelmed by deception. Our world is so full of lies that many people have been manipulated to believe that truth tellers are liars and to act against them. Handicaps will not win out by winning arguments because in our world today narratives are controlled by people who cannot win a handicap game. Handicaps will only win out because of the real benefit. Thus they must be built and used. People who don't use them must be ignored. That is how the benefit is obtained.

Proof-of-Work

Proof-of-work is a Handicap

Proof-of-work[^9] is a message that both specifies and satisfies a constraint that is to be satisfied by the output of some cryptographic hash function which is applied to it. A cryptographic hash function cannot, by definition, be easily inverted. Consequently, proof-of-work is associated with a self-evident expected number of hash operations required before finding a message that satisfies the constraint.

Proof-of-work is easily assessed waste and therefore a handicap. Crucially, proof-of-work is a handicap that can be demonstrated over the Internet, unlike a peacock’s tail. Proof-of-work can be used to incentivize people to make a strategic choice to give you their best guess about how they relate to other candidates. It is useful whenever there is more available information than you have time to look at. Proof-of-work should be seen as a prima facie case that an idea is worth examining.

In other words, proof-of-work is a spam filter, not proof that an idea is good. Proof-of-work does not replace other reliable information concerning fitness. Rather, proof-of-work is the first step in an evaluation of fitness.

Proof-of-work reduces costs at an earlier stage by incentivizing candidates to make a strategic choice. This does not mean that we do not need reputation and justice. It simply means fewer problems for reputation and the legal system to handle. Proof-of-work is a way to make ideas die out quicker. It does not eliminate bad ideas. It simply means that new ideas are more likely to be beneficial, as a result of the strategic choice that is made by those who handicap.

Example: Spam

In addition to being metaphorically a spam filter, proof-of-work can be a literal spam filter. I have already written[^10] about this so I won't go on much. Spammers are less-fit candidates because their offers are unlikely to be accepted. They must send out many messages in order to get one response. Thus, they are priced out by small amounts of proof-of-work that would be insignificant to people who sent personalized messages that would be expected to get a response with a high probability.

Example: Résumés

A résumé is a signal of fitness and it is honest as long as the cost of cheating is great enough. However, a résumé is not as easily evaluated as proof-of-work. Thus, a résumé in combination with proof-of-work can be used to find a good candidate faster and more reliably than with résumé alone.

Recruiters would necessarily need to find ways of rejecting candidates cheaply until a reasonable number remained because they would not want to avoid situations in which there were more candidates than they had time to look at properly. They could demand that all résumé arrive with proof-of-work attached and reject all candidates other those with the top n proof-of-work levels. If not they would have to choose some other way of rejecting candidates. Whatever they chose would be more arbitrary than proof-of-work because it would involve information that candidates might not think would be used to cheaply reject them.

They could reject based on years of experience, prestigiousness of university, formatting, or any number of other things. Candidates may have applied for a job expecting that their information would be evaluated as a whole. For example, a candidate may not have gone to a good university but have an exemplary work history. If he knew he was going to be rejected based on universities he could have saved his and the recruiter’s time by not applying in the first place.

On the other hand, if proof-of-work is required, all candidates know how it will be used and thus are aware of the strategic choice they must make. They know that they will not be rejected because of some unpredictable way that the recruiters looked at the résumé. Rather, if the recruiter looks past the proof-of-work, they will be evaluated holistically.

In a perfect world, the candidate with the highest proof-of-work level would be the best and the recruiters would not have to read his résumé. However, the strategic choice is not easy to make because knowledge of other candidates is required. In reality the candidates are guessing at the correct proof-of-work level using whatever knowledge they actually have. Thus they can be expected to have made mistakes. However, if the recruiters reject based on proof-of-work down to a number of résumé that they have time to look at closely, they are more likely to find a qualified candidate than if they had rejected based on other criteria.

Later on I discuss proof-of-work versus payments as signals of fitness. I go into more detail there, but here is an obvious case in which payments cannot substitute for proof-of-work. You would not want to apply to a company that expected payments to view résumés. Such a company could solicit applications as a way to earn money without any intention of offering jobs.

Example: Upvotes

Upvoting is the currently unused application of proof-of-work that I most desire to implement. An upvote system based on proof-of-work will be universal and unmanipulatable and will contain information that tells readers about how to be long-term viable. It will replace the means of curating content which we have now, all of which can be used to serve the interest of manipulators.

Everyone will see the same list of messages but they will choose how far down the list they want to read. Some people will prefer to read only the top 10 upvoted messages per day. Others will want to read the top 100. Others, the top 10,000. The ability to read more messages is worth more opportunities to upvote content, insofar as the further up the ranks one goes, the more likely one is to find incorrectly ranked content.

The content which is upvoted must benefit the upvoter as a result of more people reading it to a degree that offsets the cost of the upvote. This could be something like an advertisement, which the upvoter expects will gain him business or it could be something that simply makes the world better. In my discussions with other people about this idea, I think that people are often imagining the former case, but I actually think the latter is more important. A big company may have a lot of money to spend on advertising, but in order to upvote its advertisements, it would have to compete with ideas that have a universal appeal which many people would have an interest in upvoting, even in small amounts.

For example, Kant’s idea of the Categorical Imperative[^11] would be something that people would want to upvote because the world would be a much better place if the idea of relying on universalizable maxims was more widely understood and adopted. By contrast, someone who wanted to be a hypocrite would have to spend a lot more to tell people to “do as I say, not as I do” because fewer people would benefit from having this information viewed more.

Will capitalism or communism be upvoted more? A capitalist is more long-term viable because capitalism is a sustainable system whereas communism is a scam. Capitalists understand the real world better than communists and would therefore be better at purchasing a sustainable amount of proof-of-work. Communism depends on convincing people to go against their own interest. Thus, it is unsustainable in the short term if it was not upvoted more than capitalism. Thus, communists would live unsustainably and use Boost unsustainably, thus hastening the fall of their economies. Ultimately capitalism would be more highly ranked, even if it trailed communism initially. We could have relied on Boost instead of nuclear proliferation during the Cold War and the result would have been much better. A reader who disagrees with me and who believes that communism is more sustainable is welcome to attempt to upvote it more than capitalism. I embrace all ideologies that attempt to promote themselves using proof-of-work.

The same logic can be applied to any idea about social organization. Good ideas that enable everyone to be more sustainable would be favored. Talk is cheap today, even when broadcasting to the whole world. Thus, manipulation competes effectively with good information and as a result, everyone in the world is manipulated.

Today, people rely on hubs which collect and broadcast information for their news about the world. When we use proof-of-work as an upvote system, information can come from anywhere without going through a hub. It can all be curated automatically. No single source of information will be able to compete with the list of top upvoted content and hence people will not be manipulated by their connection to some hub. Thus, proof-of-work will awaken people from the Matrix-like dream state that humanity currently lives under.

In fact, I would argue that a proof-of-work upvote system will create a shared consciousness, or egregor. I believe that consciousness is a process of abstraction that results in a stable ordering of information about a whole system. There needs to be an ordering because pieces of information need to be related to each other in some way, especially in terms of importance. The information needs to be stable because if there is not some kind of unity to the whole system that has stable properties or else there is nothing about itself to know. Proof-of-work as an upvote system creates the incentive for people to integrate information about humanity and tell it to each other. The top upvoted content will be universally shared. Thus there will be a shared consciousness.

Proof-of-Work in Bitcoin

Proof-of-Work vs Bitcoin Payments

Payments demonstrate cost but are not a handicap because they are not easily assessed waste. Thus they could be part of an honest signal of fitness but on their own are not optimal on their own. The advantage of handicaps is that they are easy to assess with a minimum amount of context.

A payment is less easy to assess as provable cost than proof-of-work because the cost of money is less meaningful than the cost of energy and because it’s harder to be certain that a given payment bought an upvote. The payment could have been refunded or it could have bought more than an upvote. There may well be a receipt which attests to the nature of the payment but proof-of-work is still easier to verify. In addition, the value of money is all the goods that will be produced in exchange for it, whereas the value of energy is that you need it to live and run machines regardless of what form of money is used.

There is another problem with payments as signals of fitness, which is that someone gets paid. Returning to the example of résumé above, it would obviously be inappropriate for a company to accept money to handicap potential job applicants. The applicant would not want to give the company anything until after he had been accepted for the job because only then can he expect to receive something in return.

Payments do not work as well as a spam filter because they result in a failure to filter spam as a means of earning payments. In other words, I can solicit messages from people who want to pay me to read their message and pocket the money without the intention of reading them. With a proof-of-work filter, the only way to benefit from a message that I receive is from its contents. If you send a message through such a filter you can expect that it will be read because you can expect that the recipient will set the difficulty so as not to be overwhelmed with information.

Payments as an upvote system suffer from the problem that it becomes the social network’s job to provide me with good content. Why would I want to look at something just because someone else paid them to show it to me? Payments turn upvoted content into advertisements and it becomes the content provider’s job to show people something they would want to see. By contrast, with proof-of-work the platform is not in the business of providing good content. It is in the business of providing content that has an expected correlation fitness. Proof-of-work is a rational reason to look more closely regardless of who is serving the content.

Proof-of-Work in Bitcoin Mining

Given a sum of money to invest in a Bitcoin mining operation, an entrepreneur has to make a strategic choice about how much to spend on ASIC machines and how much to spend ensuring that the machines are used properly to maximize earnings. That money must be put to whatever is required to ensure that nothing will stop those ASIC machines from earning Bitcoins. That could mean anything; air filters, servers, connections to other miners, developing new applications of Bitcoin, or doing whatever the economy needed to keep running.

Thus the strategic choice affects a miner’s income because if he understands information about his correct rank, in other words how he compares to the under miners, then he has a better idea about what fraction of his money can be spent on hashpower. If he is more fit than the other miners, then he can afford to spend a higher fraction of his money on ASIC machines and thus profit more.

Why is it rational for miners to join Bitcoin on the terms that income goes to whoever wins the proof-of-work contest? Because proof-of-work is a handicap, all miners know that the other miners have made a strategic choice about how to ensure that their machines will earn bitcoins. Paying miners in proportion to hashpower will reward a quantity that will be correlated with fitness, in accordance with the Handicap Principle. Fitness of Bitcoin miners depends on the whole economy as well as their rank within that economy. Thus, the network is paying for its own propagation by paying in proportion to hashpower, insofar as some of that income earned will be expected to be spent on ensuring that the network as a whole will survive irrespective of that miner’s rank in it.

The Bitcoin whitepaper says

The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote. The majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains.[^12]

This is a rationale for proof-of-work. It is not proof that miners would actually want to mine at all. An understanding of Bitcoin based on the Handicap Principle explains a lot more about why there would be a non-zero amount of present hashpower on the longest chain. Thus, what I have said about handicaps in Bitcoin does not contradict the whitepaper.

Craig Wright on Handicaps

In a recent blog post, Craig Wright wrote of handicaps

Proof-of-work has become fetishised and overly worshipped by some in the ‘cryptocurrency communities’ and when it comes to Bitcoin. Their fixation is unfortunate, because proof-of-work is little more than a tool. Using a hammer in the wrong manner will lead to destruction.[^13]

And later on

Proof-of-work does not act to demonstrate that an entity is playing by the rules or that they should be trusted. It is merely a signal in a larger game. Just as a peacock cannot maintain a large tail without fitness, Bitcoin miners cannot maintain high levels of proof-of-work without engaging in the underlying system. That is, the nodes need to process transactions and act to enforce the rules.

This I agree with. One of the ways that people have misunderstood Boost is to see it as a complete system rather than a tool. Boost enables anyone to use hashpower as a tool in a larger game without providing a larger game. Unlike with Bitcoin, the user provides the game. Boost does nothing to prevent users from leading themselves to destruction. The great thing about proof-of-work is the way that deceivers destroy themselves with it.

Wright continues

As with the peacock, the implementation of a proof-of-work mechanism, a handicap, only acts within a defined set of participants. The peacock’s tail is only of interest to the peahen and the tiger. The monkeys and the bullfinches, that also reside in the forest, do not care. It is only the nodes as the peahens and peacocks that directly care about the results of proof-of-work, and they do so only because of the tiger.

I disagree. While it may be true that the monkeys don't care about how much any individual miner signals, they do care about the sum total hashpower of all miners. This value is a measure of the productivity of the economy as a whole. It's like a version of GDP that isn't a scam and that people can't lie about.

Continuing,

In the handicap principle, it is not the peacock’s tail that sets the equilibria. The length of the tail against the fitness of the animal is a function of the external control, the tiger.

In Bitcoin, the tiger is played by law enforcement and courts. With peacocks, the peahen will always seek the most extended tail. In the same manner, nodes will try to implement the most significant proof-of-work rate that they can profitably support. The cost of doing so is compared to fitness. It is both a combination of the amounts of inputs that go towards such a process and the cost of remaining honest. In Bitcoin, a dishonest node is equivalent to an unfit peacock. Even with a long tail, such a peacock is unlikely to succeed.

Peahens do not care about peacock tales because of tigers only. There are more ways to die than being eaten by predators. For example, nodes can go out of business not by being dishonest but simply by being bad businessmen. Proof-of-work not only makes nodes discoverable by law enforcement but also brings them all closer to being in the red.

Evading predators is but one aspect of fitness. Fitness refers to prospects of survival and reproduction, and that encompasses everything about lasting a long time. Proof-of-work is just provable spent energy. Running out of energy is a risk. If you run out, you are inert. A node has to continue signaling and not run out. Thus there is always risk associated with proof-of-work regardless of whether there are governments and proof-of-work is always a signal of fitness.

Wright later reiterates his point that peahens only care about peacock tales because of tigers.

Bitcoin has grown to the point where proof-of-work, the proverbial tail, is significantly noticeable. Such demonstration is, ultimately, not made to the other nodes, but rather to the proverbial tiger: law enforcement.

However, if there are no predators, that does not mean that everyone is equally fit. Therefore it does not make sense to say that the signal is ultimately to governments only. If governments are predators, other nodes are potential mates. Nodes need to assess other nodes because they need to invest in connectivity with one another. A node does not want to waste money connecting to an unhealthy node that could go out of business soon. Nodes have to rely on one another to ensure that the network as a whole is healthy. They need to know who they can rely on. They will care about this irrespective of whether there are governments. Proof-of-work forces nodes to be healthy so as to gain more connectivity.

Birds on islands can have no predators and have more extravagant displays than their mainland counterparts do. If Bitcoin nodes were to become immune to predators somehow, they would not signal less. They would signal more because the equivalent risk would be achieved with a stronger signal. For example, if a node managed to trick governments into thinking that it was too big to fail, as banks have done, then it would be protected by governments rather than in danger from them. In this case, the node would signal with more proof-of-work, insofar as it had become more fit.

Not running out of energy is a game that ultimately encompasses everything, including legislation. Eventually nodes will want to lobby governments for favorable laws. Then proof-of-work is no longer a game of following the law but of making it. This would be a very good thing because nodes would tend to lobby for free-market policies, which would result in more total transactions. Governments can themselves become Bitcoin nodes, which will achieve the same result. This would also be good because governments could increase profitability as Bitcoin nodes by reducing central planning. Finally, a government could collapse in a particular territory. A node that was capable of continuing to operate there would have to be better at surviving, clearly, because conditions are more hostile. Each of these scenarios would be reasons for a node to be able to signal with more proof-of-work that other nodes would care about because of the knowledge that could be learned about better survivability. If a node successfully lobbied governments for more free trade or successfully operated where there was no government, the other nodes would want to know how it was accomplished

As discussed above, proof-of-work converts long-term planning into short-term benefits. The farther out a miner can plan, the smaller margins he can accept. Proof-of-work is like a grinder that rips bad ideas apart. There is no limit to this. A miner who was thinking ten years ahead would already be thinking beyond the time scale of most politicians. If he was thinking 50 or 100 years ahead, he would be operating on a time scale on which political disruption would be important to consider.

It does not really make much sense to say that the ultimate purpose of proof-of-work is to signal to governments because bitcoin is Byzantine fault-tolerant, whereas governments are not. Byzantine fault-tolerance is achieved by relying one one another to keep the network running. The Bitcoin system has the potential to outlive all empires due to its superior organization. Over long enough time spans, Bitcoiners need to think more about each other than about governments.

Bitcoin nodes have a short-term need to optimize intelligence. This has never existed in any human organization previously. Governments do not have this same incentive. As discussed in my video Strategy in the Core Cash Conflict, the ability to lead an opponent has to do with the ability to simulate him. At scale, the Bitcoin network will be able to simulate governments better than governments can simulate the Bitcoin network. Ultimately, legislation becomes a part of the proof-of-work game.

Response to Wehrmann

This section responds to an article by Michael Wehrmann. Although the author was supportive and I agree with him that fake news is a problem and Boost is the solution, he did not understand why it works. Wehrmann describes Boost as working by processes that all exist without.

there is an economic incentive not to boost fake news. … the economic solution works against fake news long term by requiring a higher cost to the person trying to spread it.[^14]

This is not correct because Boost cost the same for a given amount regardless of whether you are boosting true or false information. In the next paragraphs Wehrann says something closer to correct.

Truth has a value for market participants (businesses and users). With true information, recipients can perform better decision-making. Better decision-making has value, so if you boost true information, recipients profit and get back to you for more accurate information.

Lies, on the other hand, are not the same economically. Lies are false information, even market distortions, and misleading information hinders profitable decision-making. Recipients of incorrect information do not make a profit, so they will—long term—not reach out again to those who published the fake news.

The problem with this is that it is true regardless of whether Boost. With Boost, we put liars out of business rather than just giving them less repeat business. In order to catch the same number of eyes, liars must boost the same amount. However they get less business per pair of eyes. Thus the cost is not greater for liars--the profitability is less. Because the difficulty of proof-of-work can increase to any level, it can always go up to a point that is positive for truth-tellers and negative for liars. Without proof-of-work, liars can rely on cheap means of catching eyes that truth-tellers cannot, such as emotional manipulation.

Wehrmann gives examples of applications of Boost which, I think, miss the point.

You publish true information about stock trading on social media and “add energy” to it by paying a Bitcoin SV transaction processor for its computational power. This signals to others that your information about the stock trading is valuable, at least to yourself, as you have just spent money signaling. Because your information is true, the recipients benefit from it. They can make better decisions concerning their stock trading. You lost money signaling via Bitcoin SV, but your true information has found its recipients, and the recipients make use of the true information. They come back to you for more valuable information. You have got a business going now.” Au contraire, price predictions are exactly the sort of fake news that I expect Boost to eliminate. Someone who sells price predictions for money is not using his price predictions optimally if they were actually good. The optimal way to use them would be to keep quiet about them and use them to get rich.

Boost would require everyone to lose energy if they want to blab about their price predictions to everybody. Anyone who could consistently make money doing that could save money by not talking about prices and making their own bets.

Boost incentivizes people to provide information relevant to prices without making other people's investment decisions for them. People would want to inform each other on information they have already acted upon because they would want the market to react to that information. People would use Boost to talk about new inventions or new business ventures or politics. Other people would have to interpret this information and make their own price predictions and take their own risk.

Response to Brendan Lee

Finally, I respond to an article from Brendan Lee. Lee attempts to argue against proof-of-work as a handicap but only demonstrates that he has no understanding of the idea. He says,

What most people fail to understand where hash power is concerned is that it can be owned by anyone regardless of whether or not they control a node and that those owners have the ability to connect or disconnect it to any node they feel best represents their interests. These hash operators are free agents in a market for their labour and will work for the nodes who are[sic] make them the most money.[^15]

In other words, the hash power is not the costly signal, but the reward. Incentivising the most free agents to work their block templates as possible is the reason that node operators will create and display a whole array of costly signals. First, hashpower is obviously a costly signal, insofar as it is a signal that demonstrates cost. Furthermore, it is a handicap, insofar as it is easily verified expected spent energy. As to the idea that hashpower is a reward, hashpower is only good for someone who knows how to use it. An important experimental test of the Handicap Principle provided birds with artificially lengthened feathers.[^16] These birds were not better off. Although they had more attention from females, they had more trouble flying and foraging and more hostile attention from stronger males. The same would be true of nodes that got more hashpower than they could handle. Hashpower is only a reward for nodes that could afford more risk. Nodes must make a strategic choice about how much hashpower they want. Lee continues, For us to maximise the potential return of our investment, we must choose the node which we think will make the most of the work we can apply to its block template. There are a wide variety of nodes who will pay us for our attention and it’s our job to understand what the performance characteristics are that will guide us to the best node. However, nodes can differentiate on price for hashpower. Someone with hashpower does not need to assess a node to decide where to send that hashpower. He can go with whoever is offering the best price. At MatterPool, we pay for hashpower regardless of whether our block is orphaned.

Thus, miners do not need to assess nodes. However, nodes need to assess each other. They need to invest in connectivity with one another and they need to decide who is worth more. Even if things worked the way Lee envisions them outside of Matterpool, each node would not know the others by where their hashpower originally came from. They still need to assess each other. Ultimately assessment comes down to the elements that Lee has listed but costly signals are for assessing each other at a glance. Over time miners can get a better idea of each other.

Lee concludes

If I apply it to a picture or a meme, what exactly am I signalling? If you show me a meme that has had proof of work applied to it why should I care? Not only does this proof of work not build on other work, but there is no way to build upon it. So what purpose does it serve? I may be a contrarian in this space, but as far as I can tell, all it does is lines the pockets of the miners who convince people it’s important while giving everyone else a confusing indication of who was willing to burn the most money for attention.

First, Lee is not a contrarian. I have been arguing with many people about proof-of-work who have accepted the idea that it's not useful outside of Bitcoin mining. There are many reasons to signal fitness, obviously! Second, a meme that has proof-of-work attached to it is simply more likely to be worth reading than one which does not. The purpose is to filter information, given that there are more memes than any one person can read. As to wanting to line my pockets, yes I do. Bitcoin miners need to invent ways of earning more revenue. Moreover, Lee also wants to line his pockets. In private conversation, he informed me that he wants to be paid to receive messages, which is not a legitimate service, rather than filter them with proof-of-work! I want to line my pockets by providing real services. Furthermore, Boost is designed so that any miner can provide it. I designed it that way because I want to be a customer and I want good service.

Conclusion

Handicaps are extraordinarily useful but poorly understood. Relying more on handicaps will shift the messages that we are likely to read from tricks to try to make you kill yourself to genuine information on how to survive. Other means of ensuring honesty do not work as well when there is information overload. Proof-of-work has more applications than just Bitcoin mining. It is a handicap that can be demonstrated over the internet. Everyone who wants to pretend to be fit without demonstrating it will hate proof-of-work. This includes almost everyone with political power. Anyone who uses proof-of-work will be a target. I am terrified of the attention I will receive from promoting proof-of-work but it is the only way to save the world from manipulators. Please learn how to use proof-of-work as well as possible as quickly as possible so that we can derive the benefit of having better ideas. Better ideas are our best defense. We can ensure that generally accepted ideas are better by not only understanding proof-of-work in theory, but by getting good at it as a game. Please learn to make the strategic choice wisely. All you have to do is put yourself in the correct rank. The better people get at doing this, the better we will be at conserving energy by transmitting the best information.

Acknowledgements

I thank Logan Hanson for reading an early draft of this article and providing helpful comments and clarifications.

Notes

[^1] Zahavi discovered the Handicap Principle and described it using examples and informal reasoning. In Zahavi, handicaps are costly on the bearer but cheap to assess. They are expected to be honest because of the strategic choice and preferred by evaluators because of their cheapness to evaluate. Unfortunately, later discussions concerning the Handicap Principle have focused on later mathematical models that have missed important things in Zahavi. In particular, Graffen’s model treats strategic choice, but not cheap assessment. Cheap assessment is crucial for understanding the sense in which handicaps are required in a signal of fitness. They are required because an evaluator wastes time by not looking at a handicap first.

[^2] The strategic choice was originally described by Zahavi and modeled by Graffen. Unfortunately, Graffen believed that he was modeling handicaps and later scientific discussions have treated his paper as a statement of the Handicap Principle. However, although Graffen’s work greatly extends Zahavi’s in some ways, it misses an important property of handicaps, that of being easy to assess. Thus Graffen’s model is of strategic choice, not handicaps. This point has not been made clear in later discussions of the Handicap Principle in the scientific literature. Graffen has a way of explaining why handicaps are honest signals but not why they are required. Later biologists have taken Graffen’s model as a statement of the Handicap Principle, which it is not. Thus, later biologists have understood why handicaps are honest signals but not why they are required. They are required because they are more easily assessed than other signals of fitness and are competitive with other signals because of that. Zahavi himself does not seem to have noticed that Graffen’s model does not account for everything he was talking about in his work.

See Getty and Johnstone for important clarifications of Graffen. Getty's clarification has to do with Graffen's conclusion that handicaps are "costlier for worse males". Getty shows that this results from an unrealistic assumption introduced part way through Graffen's derivation. Getty's conclusion is that "better males are better at converting advertisement into fitness". Thus Graffen made the same mistake as Wehrmann 2020.

Johnstone's has to do with the difference between a costly signal and a handicap. Johnstone shows that Graffen's work applies to a much greater range of situations than Graffen had believed. When we think of cost in terms of opportunity cost, it is evident that many situations impose strategic choices on candidates that do not involve handicaps. Handicaps are not just cost, but waste.

[^3] Zahavi 1997.

[^4] My phrasing. Zahavi never described the Handicap Principle quite this way but it is evidently what he meant from his examples. Arguments against the Handicap Principle in more recent scientific papers such as Számadó 2011 and Penn and Számadó 2019 interpret it as meaning that no honest signals of fitness other than handicaps are possible. This is not a true statement nor does it describe Zahavi's idea. Rather, a signal of fitness that does not use a handicap is not optimal, insofar as time could be saved and good candidates could be identified more reliably if a handicap was added to it.

As an example of how Zahavi thought about the Handicap Principle, here is a thought experiment from his book:

Let’s say we are going to the marketplace to find a handmade round plate. The plates are not identical. Some were made by skilled craftsmen and are perfectly round; some are less skillfully made and are slightly elliptical, or their edges are a bit malformed. A small circle in the middle of the plate would make it easier for us to tell the most perfectly round plates from the less perfect ones. A line around the edge of a plate would make it easy to spot imperfect edges. If we want to select perfectly round plates with neat, perfect edges it would make sense to select from among plates with a circle in the middle and a line around the edge, even if we had to pay a somewhat higher price for them. (Zahavi 1997).

Thus, Zahavi does not say that it is impossible to learn which plate is better without the use of handicaps. Handicaps make it easier. A customer is still able to look at other aspects of the plate as he considers buying it and would still be able to notice if a plate was fatally flawed despite having a perfectly round ring around the edge.

No scientist who has written on the Handicap Principle since Zahavi has understood it even those who have supported the idea. Zahavi himself has not appeared to notice that Graffen’s model is not the same as his idea. He was apparently not very good at math. Other scientists are math fetishists and have taken Graffen 1990’s model to be the statement of the Handicap Principle, which it is not.

[^5] Számadó 2011’s and Penn and Számadó 2019’s argument against the Handicap Principle is to enumerate everything that can impose costs on cheaters, since all are reasons for honest signals. They define the Handicap Principle as meaning that honest signals which are not handicaps are impossible and think that they have refuted it by showing that honest signals can exist that are not handicaps. This only proves that he has failed to comprehend Zahavi's idea. There are many reasons for honest signals of fitness that do not rely on handicaps. They are all less efficient than if a handicap were added to the front.

A big problem with communicating the Handicap Principle is that less-fit males instinctively misunderstand it and spread confusion about it as a result of the way that it threatens their use of cognitive bias to continue believing that they are superior when they really are not. If they could understand the Handicap Principle, they would realize that they have no choice but to evaluate themselves next to other males objectively. This they cannot do without interfering with their own self-deception. They can only succeed in contexts in which handicaps are not being used properly and must therefore prevent them from being understood.

Penn and Számadó 2019 are classic examples. They also argue for the Fisher theory of sexual selection, which says that female preference can drive male ornaments to maladaptive levels via a runaway positive feedback process. In their words:

Fisherian and good‐genes models are not mutually exclusive, but nevertheless it is useful to distinguish between traits that affect reproductive success versus those that influence viability. Indeed, trade‐offs between these two traits are central to evolutionary life‐history theory, and Grafen's strategic signalling model is better understood as a life‐history model in which individuals differ in quality and optimally allocate resources into traits for survival versus sexual signalling due to their fitness trade‐offs.

Thus Penn and Számadó agree that in Graffen's model, males are more successful at mating with females when they demonstrate more cost but not necessarily because females have any rational reason to prefer more demonstrated cost. It could be that females are just irrational. I'm sorry but that is not a valid theory. Everyone is always trying to optimize. Although Graffen did not address the issue in his paper, Zahavi already had in his works: females prefer handicaps because they are easy to assess. Someone throwing stuff away in front of you is obvious, or at least it is to peahens.

Maladaptive ornaments cannot exist in equilibrium. As soon as the most fit males figure out how to signal with something that is actually correlated to fitness, both they and females benefit from using it. Handicaps persist in equilibrium because if females didn’t look at them they would waste time evaluating less-fit males.

This footnote is not a complete refutation of everything in this paper. It just addresses one thing I noticed in it that I think is absurd. This paper is one of the top ranks google for “handicap principle” and they can’t even understand the idea. This would never have happened if we were using proof-of-work to rank content. Google ranks are suitable to less-fit males because it is easier for them to compete with more-fit males to achieve top ranks using cheap talk. That’s what their paper is.

[^6] Stein 1973.

[^7] Krawisz 2020 (a). A protocol for buying proof-of-work from Bitcoin miners using a Bitcoin transaction.

[^8] Grafen1990 and Getty 1998.

[^9] See Adam Back 2002 (a) and 2002 (b). Adam Back was not the first person to propose the use of work puzzles. However, he described them in a way that was simpler and more general than earlier writers. The name HashCash does not make sense because HashCash is not cash.

[^10] Krawisz 2020 (b).

[^11] Kant 1996. The categorical imperative is Kant's attempt to rationalize Jesus’s principle of “do unto others as you would have them do unto you.” Similar ideas have appeared in many ethical frameworks. Kant’s formulation is different in that it is not a command but rather a constraint which all valid ethics must satisfy. The same idea is the foundation of Hayek’s politics. People who apply the categorical imperative will have a better idea of what content is worthwhile to upvote with proof-of-work and will therefore be able to conserve energy better than hypocrites.

[^12] Nakamoto, 2009.

[^13] Wright, 2020.

[^14] Wehrmann, 2020.

[^15] Lee, 2020.

[^16] See Moeller 1994 and Smith and Montgomerie 1991. As Zahavi describes it,

Barn swallows have long, forked tails; the outer feathers are longer in adult males than in females or in young males. When Moller added extra pieces of tail feather to the tails of some males and shortened the tail feathers of others, he discovered that those with the longer tails, whether natural or artificially enhanced, found mates more easily than those with the shorter or shortened tails and that they got to copulate with additional females as well (extrapair copulation). But the inadvertent cheaters--the males with artificially lengthened tails--paid a heavy price. The added length apparently ampaired their ability to fly. They could not hunt large insects, and their physical condition deteriorated: they did not molt well after the breeding seasons, and none of them returned from their winter migration the next spring, while many of the other males did return to bered in the same area.

Smith and Montgomerie repeated Moller’s experiments and found that males with either naturally long or artificially lengthened tails found mates earlier and started breeding earlier than other swallows. But when they tested for paternity among the nestlings by DNA fingerprinting, they found that only half of the nestlings in the nest of the inadvertent “cheaters”--the males with enhanced tails--were in fact the offspring of those males, compared with 95 percent in the nests of males whose tales were either naturally long or artificially shortened. Smith and Montgomerie suggested that the glued-on tails were too much of a burden for males who were not fit to carry them, and that such males could not prevent their females from consorting with other males.

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