# Using Bayes’s Rule to Think About a Bitcoin Bubble

Is there a Bitcoin bubble? Jason Kuznicki thinks so and believes that he has conclusive proof. He blogs three graphs that show more or less that there is a lot of speculation in Bitcoin. But does speculation prove that there’s a bubble? Let’s use Bayes’s rule to think about this carefully.

Bayes’s rule is a mathematical tool for thinking about the incorporation of new evidence into subjective probabilities. Let’s suppose that there is some proposition A for which you have a prior belief. Somebody offers evidence B for or against A. How much should you change your belief in A based on evidence B?

Bayes’s rule boils the answer down to a simple mathematical form:

$P(A|B) = P(B|A)\dfrac{P(A)}{P(B)}$

In English, the probability of A given B equals the probability of B given A, times the probability of A and divided by the probability of B.

So to evaluate Jason’s argument and see how much we should change our estimate of a Bitcoin bubble based on the evidence that there’s speculation, we can simply assign the proposition and the evidence to A and B. In this case, A is the proposition that there’s a bubble, and B is the evidence that there’s speculation in Bitcoin. If we figure out our subjective probabilities for B|A and B, we can use those to determine how different P(A|B) should be from P(A).

So what is B|A? Since B is the evidence that there is speculation in Bitcoin and A is the proposition that there is a bubble, B|A simply states the proposition that given that there is a bubble, there is speculation. It seems pretty much impossible to have a bubble without speculation, so I’ll go with a subjective probability of 1. Picking a different value here will only work against Jason’s argument.

So what is the probability of B, the fact that there is speculation in Bitcoin? The Bitcoin ecosystem isn’t built out yet. Most of the protocol’s most exciting uses haven’t even seen the light of day yet. As I blogged last week, multisignature transactions are barely in use yet, but they form the foundation for a decentralized architecture of arbitration. Ed Felten at Princeton is working on decentralized prediction markets. Jerry Brito points to microtransactions, or even nearly-continuous transactions, as another exciting future use scenario.

Given that we don’t know whether this ecosystem will ever materialize, holders of bitcoin are necessarily speculating. If the ecosystem matures and is useful, bitcoins will be worth something. If none of these innovations come about, or if we decide they’re not that useful after all, then bitcoins will probably be worth nothing. There’s no way out of speculating, because we simply don’t know for sure if the ecosystem will come along. Almost the entire “fundamental value” of Bitcoin rests on future events.

So the probability of B, I think, is 1. When P(B|A) is 1, and P(B) is 1, what does Bayes’s rule reduce to?

$P(A|B) = P(A)$

B simply offers no information as to whether A is true.

A similar argument can be made when Bitcoin’s volatility is offered as evidence of a bubble. Bitcoin is a thinly-traded asset where supply does not adjust to accommodate demand. It is going to be volatile. So the fact that Bitcoin is volatile adds no new information to the question of whether it’s a bubble.

What does provide information? I think the most reliable evidence is on the maturation (or not) of the Bitcoin ecosystem. If Bitcoin seemed static right now, I would interpret that as evidence of a bubble. But it doesn’t. Every day, people are working to build businesses that leverage some of the unique features of Bitcoin’s protocol. As long as that continues, I think it’s most reasonable to be highly agnostic about the correct price of Bitcoin.

# Stop Saying Bitcoin Transactions Aren’t Reversible

One of the criticisms leveled at Bitcoin by those people determined to hate it is that Bitcoin transactions are irreversible. If I buy goods from an anonymous counterparty online, what’s to stop them from taking my bitcoins and simply not sending me the goods? When I buy goods online using Visa or American Express, if the goods never arrive, or if they aren’t what was advertised, I can complain to the credit card company. The company will do a cursory investigation, and if they find that I was indeed likely ripped off, they will refund me my money. Credit card transactions are reversible, Bitcoin transactions are not. For this service (among others), credit card companies charge merchants a few percentage points on the transaction.

The problem with this account is that it’s not true: Baked into the Bitcoin protocol, there is support for what are known as “m-of-n” or “multisignature” transactions, transactions that require some number m out of some higher number n parties to sign off.

The simplest variant is a 2-of-3 transaction. Let’s say that I want to buy goods online from an anonymous counterparty. I transfer money to an address jointly controlled by me, the counterparty, and a third-party arbitrator (maybe even Amex). If I get the goods, they are acceptable, and I am honest, I sign the money away to the seller. The seller also signs, and since 2 out of 3 of us have signed, he receives his money. If there is a problem with the goods or if I am dishonest, I sign the bitcoins back to myself and appeal to the arbitrator. The arbitrator, like a credit card company, will do an investigation, make a ruling, and either agree to transfer the funds back to me or to the merchant; again, 2 of 3 parties must agree to transfer the funds.

This is not an escrow service; at no point can the arbitrator abscond with the funds. The arbitrator is paid a market rate in advance for his services, which are offered according to terms agreed upon by all three parties. This is better than the equivalent service using credit cards, because credit cards rely on huge network effects and consequently there are only a handful of suppliers of such transaction arbitration. Using Bitcoin, anyone can be an abitrator, including the traditional credit card companies (although they might have to lower their fees). Competition in both terms and fees is likely to result in better discovery of efficient rules for dispute resolution.

While multisignature transactions are not well understood, they are right there in the Bitcoin protocol, as much a valid Bitcoin transaction as any other. So some Bitcoin transactions are irreversible; others are reversible, exactly as reversible as credit card transactions are.

Bitrated.com is a new site (announced yesterday on Hacker News) that facilitates setting up multisignature transactions. Bitcoin client support for multisignature transactions is limited, so the site helps create addresses that conform to the m-of-n specifications. At no point does the site have access to the funds in the multisignature address.

In addition, Bitrated provides a marketplace where people can advertise their arbitration services. Users are able to set up transactions using arbitrators both from the site or from anywhere else. The entire project is open source, so if you want to set up a competing directory, go for it.

What excites me most about the decentralized arbitration afforded by multisignature transactions is that it could be the beginnings of a Common Law for the Internet. The plain, ordinary Common Law developed as the result of competing courts that issued opinions basically as advertisements of how fair and impartial they were. We could see something similar with Bitcoin arbitration. If arbitrators sign their transactions with links to and a cryptographic hash of a PDF that explains why they ruled as they did, we could see real competition in the articulation of rules. Over time, some of these articulations could come to be widely accepted and form a body of Bitcoin precedent. I look forward to reading the subsequent Restatements.

Multisignature transactions are just one of the many innovations buried deep in the Bitcoin protocol that have yet to be widely utilized. As the community matures and makes full use of the protocol, it will become more clear that Bitcoin is not just a currency but a platform for financial innovation.

# The Great Disintermediation

Yesterday at Forbes, William Pentland had an interesting piece on possible disintermediation in the electricity market.

In New York and New England, the price of electricity is a function of the cost of natural gas plus the cost of the poles and wires that carry electrons from remotely-sited power plants to end users. It is not unusual for customers to spend two dollars on poles and wires for every dollar they spend on electrons.

The poles and wires that once reduced the price of electricity for end users are now doing the opposite. To make matters worse, electricity supplied through the power grid is frequently less reliable than electricity generated onsite. In other words, rather than adding value in the form of enhanced reliability, the poles and wires diminish the reliability of electricity.

If two thirds of the cost of electricity is the distribution mechanism, then, as Pentland notes, there is a palpable opportunity to switch to at-home electricity generation. Some combination of solar power, batteries, and natural gas-fired backup generators could displace the grid entirely for some customers. And if I understand my electricity economics correctly, if a significant fraction of customers go off-grid, the fixed cost of maintaining the grid will be split over fewer remaining customers, making centrally-generated electricity even more expensive. The market for such electricity could quickly unravel.

While it remains to be seen whether electricity generation will indeed become decentralized, such disintermediation would be the continuation of a decades-long social trend. It all began (plausibly) in 1984. The Macintosh was released, and desktop computing became a thing. Desktop printers disintermediated printing departments, Kinkos, and the steno pool. The Internet has disintermediated telephone companies, music labels, television networks, newspapers, and much more. Online education is unbundling university courses.

What’s even more exciting is the next generation of disintermediating technologies. Bitcoin could displace some financial institutions—to varying degrees, banks, the Federal Reserve, Western Union, and credit card companies. Mesh networks could solve the last-mile problem of Internet service delivery, which tends to be monopolized or at least concentrated. 3D printers could disintermediate supply chains. 3D chemical printers could disintermediate drug companies and the FDA.

Delivery drones like Amazon Prime Air‘s arguably disrupt package delivery services, though not entirely because FedEx and UPS will still run drone-utilizing distribution networks. More importantly, delivery drones disintermediate the real estate market for small businesses. It will no longer be important, if you run a local business, to have a storefront in a prime location. Your customers can order online and items can be delivered to them in half an hour straight from the factory or artisanal workshop. It could be the Etsyfication of the economy.

If information, electricity, money, and production all get disintermediated, what is left? If these trends continue, the future will be one in which human interaction is unmediated, and to a surprising degree, unregulable. It will be difficult to stop a willing buyer and seller from transacting. Information about the proposed transaction might not be censorable. Payment via Bitcoin or other cryptocurrencies can’t be stopped. Production and delivery of the item may be difficult or impossible to detect and intercept.

Intermediaries are often used by governments as points of control. As we shed intermediaries, it may become possible to live one’s entire life without any particular authority even knowing that one exists. I doubt that we’ll ever get that far in the process, because using non-abusive intermediaries often makes economic sense. But for the next few decades, at least, I expect the trend to continue and the world to get a lot more interesting.

# New Dourado and Tabarrok Paper on Intellectual Property

I’m pleased to announce that Alex Tabarrok and I have a new working paper out from the Mercatus Center today, “Public Choice and Bloomington School Perspectives on Intellectual Property.” The paper will appear in Public Choice in 2014.

Here’s the abstract:

We mine two underexplored traditions for insights into intellectual property: the public choice or Virginia school, centered on James Buchanan and Gordon Tullock, and the Bloomington or Institutional Analysis and Development school, centered on Elinor Ostrom and Vincent Ostrom. We apply the perspectives of each school to issues of intellectual property and develop new insights, questions, and focuses of attention. We also explore tensions and synergies between the two schools on issues of intellectual property.

The gist of the paper is that the standard case for intellectual property—that a temporary monopoly is needed in order to recoup the sunk costs of innovation or creation—ignores issues raised by the two schools we investigate.

From a public choice perspective, a temporary monopoly provides enormous opportunities for rent seeking. Copyright and patent owners are constantly manipulating the political environment to expand either the duration of the monopoly or the scope of what can be monopolized. We document the evolution of intellectual property in the United States from its modest origins to its current strong and expansive state.

From a Bloomington perspective, the standard case for IP wrongly treats the commons as a kind of wasteland. In fact, numerous innovations and sprawling creative works occur without monopolization—just look at Wikipedia. Innovation occurs when the right institutional structures are in place, and intellectual property that is too severe can hamper the smooth operation of these institutions. Too much IP can harm as much as too little.

Read the whole thing, cite it copiously, etc.

# The Effect of Re-election on White House Petition Responses

Last week, I launched WHPetitions.info in order to bring transparency to the We The People petitions the White House has been ignoring. But after launch, I thought it might be interesting to do a bit of social science with the data I had collected, only a tiny fraction of which is displayed on the site.

Using the data provided by the We The People API, it is possible to construct retrospectively a snapshot of the state of petition responses at any moment in time. So I decided to do that beginning on October 23, 2011 at 9:00am EST and every 24 hours thereafter. This gives me 669 daily observations, at 9 or 10am each day, depending on daylight savings time.

What interesting events happened between October 23, 2011 and today? One obvious one is Barack Obama’s re-election. Let’s see if it had any effect on White House petition responses!

The first thing I decided to check was the effect on the number of petitions and responses. Interestingly, there was an increase both in the number of new pending petitions and in the number of responses shortly after election day (represented by a dashed vertical line).

Next, I looked at the average number of days that pending petitions were awaiting a response. That is, for unanswered petitions, how long have they been waiting, on average?

This graph also captures the responses that occurred shortly after the election, which decreased the average waiting time of pending petitions. But note that since that big drop, there has been a steady increase in average waiting time, and the statistic is now at an all-time high.

Next, I decided to investigate whether there is a difference in White House responsiveness to a subset of petitions before and after the election. I calculated at each moment in time how many petitions had been waiting for a response for six months or more.

Using this data, it is possible to see a much greater structural break. The number of petitions waiting for six months or more has grown almost monotonically since election day, and tellingly, it increased very rapidly about six months after election day.

Finally, I constructed an abstract measure, total petition-days for pending petitions, which I think captures the overall state of White House responsiveness.

As you can clearly see, by this measure, there has been a big change in White House responsiveness to We The People petitions since election day.

Are you interested in crunching these numbers yourself? You can download a snapshot of this data here. Please let me know if you have any questions about how the data are calculated, and also if you find anything interesting.

# Announcing WHPetitions.info, a New Site to Help the White House Keep Its Petition Promises

President Obama has promised to run the most transparent presidential administration in history, and as part of that initiative, in 2011, the White House set up its We The People site. In their words:

We the People is a new, easy way for Americans to make their voice heard in our government. It is a platform on the White House website where individuals can create and sign petitions that call for action by the federal government on a range of issues facing our nation. If a petition gathers enough signatures, it will be reviewed by White House staff and receive an official response. We the People helps the White House understand the views of the American people and have a focused and civil conversation with them.

A laudable step. But the site has an interesting quirk: there is a section of the site dedicated to open petitions, and there is a section for White House responses, but there’s no similar section dedicated to petitions that have met their signature thresholds and are awaiting a response.

So I decided to fix that.

The result is WHPetitions.info, a single-serving site that simply lists petitions that the White House has promised and neglected to answer. The oldest petitions are at the top.

Speaking of oldest petitions, some of the petitions awaiting a response are pretty old! For example, there is a petition to require genetically-modified food to be labeled that has been waiting since October 23, 2011, which was the first possible day a petition could qualify for a response. Six petitions currently on the site are over a year old, and the average time that the 30 (as of this writing) pending petitions have been waiting is 240 days.

Now, the White House never specified when they would respond. In fact, they explicitly say there is no firm timeframe for a response:

We will do our best to respond to petitions that cross the signature threshold in a timely fashion, however, depending on the topic and the overall volume of petitions from We the People, responses may be delayed.

But a 240-day average for pending petitions still seems like a lot to me; they have responded to 202 petitions so far in an average of 61 days.

It’s also interesting to see which issues the White House is neglecting. At the moment, 10 of the 30 outstanding petitions deal with Asian foreign policy. There are two petitions to fire the prosecutors whose overreach caused Aaron Swartz to commit suicide, as well as a recent petition to pardon Edward Snowden. Petitioners don’t want the FDA to regulate premium cigars or e-cigarettes. And some petitions are a little offbeat: for example, here is one asking the president to spend an hour talking tax policy with Neal Boortz.

Still, on the whole, most of the unanswered petitions raise substantive policy issues that deserve a response. Here’s hoping my site nudges the White House to keep its promise to answer.

P. S. — WHPetitions.info couldn’t have been made without the great API offered by the White House web team. Kudos to them.

# Some Points on Betting

• As I told Kevin Grier a few days ago, I usually lose arguments with Tyler, and even with my model of “Tyler” in my head. I would not be very meta-rational, therefore, for me to “attack Tyler” as Bryan wants GMU bloggers to do. Even writing this post, I have moved somewhat in Tyler’s direction.
• Everyone takes Noah’s point that an individual bet does not necessarily reveal beliefs, because through clever hedging strategies, it is possible to engineer a portfolio that has a different exposure to the original proposition than the individual bet. Everyone also takes Tyler’s point that a big part of your “portfolio” is always going to be non-traded assets.
• One reading of Tyler is that to a considerable extent, we are all a (mostly) non-tradeable part of our own portfolios. I am betting on my own success, because what choice do I have? What portfolio theory would suggest is that in terms of optimal risk allocation we are all too exposed to ourselves. We should try to find ways to hedge against ourselves that don’t undermine alpha. Which is hard to do. Ideally, we would simply “bet against ourselves” to reduce aggregate risk, but psychologically it is difficult to bet on your own failure without reducing your probability of success. Instead, we need to self-deceive to some extent, to find ways to hedge against ourselves without realizing that that’s what we’re doing. Betting on one’s beliefs is therefore counterproductive in two ways. First, it actually increases portfolio variance because we are already exposed to ourselves. Second, precisely because of the qualities that Alex, Bryan, and Robin laud, betting one’s beliefs makes self-deception, and therefore optimal portfolio allocation, harder.
• Nevertheless, these drawbacks of betting should often be outweighed by the expectation of actually winning the bet. Therefore, refusing to bet still has informational content for those who observe the refusal.
• Furthermore, Tyler says that he disagrees with “virtually every sentence in the second paragraph” of Alex’s post, but that still does not follow from my reading of Tyler. As Alex says, because the number of possible states of the world exceeds linear combinations of assets, portfolios cannot reveal a complete set of beliefs. In the presence of non-tradeable assets and psychological limitations on hedging, portfolios a fortiori don’t reveal beliefs. Bets are new assets that are difficult or costly to otherwise synthesize, and therefore add to a portfolio’s capacity to express beliefs. This is true even if we accept that bets have implications for bettor psychology; as long as bets covary with the rest of the portfolio in a unique way, they increase the information content of portfolios.
• Internal mental accounting” is simply not consistent with truth-seeking plus meta-rationality. Tyler knows this, which is why we need to do some creative reading of Tyler. He is nevertheless right that betting does pay off in terms of pride in betting.
• Tyler says to Bryan: “You seek arrangements which maximize your glee.” In my view, this is both true and an argument in favor of betting. Bryan’s glee brings me joy and amusement. If it is relatively cheap to make Bryan gleeful, why not do it?
• Tyler’s fame relative to the other participants in this discussion provides some escape. Tyler has more than 20 times as many Twitter followers as I do, and of course that metric probably overstates my relative influence. Nevertheless, I am frequently bombarded with belligerent or offbeat challenges to my claims. I imagine that for Tyler, receiving many times more than I do, this is somewhat exhausting.
• Alex says “a bet is a tax on bullshit.” Despite some concessions to Tyler, I still think that’s basically right. However, for the sake of completeness, someone should consider whether bullshit is all bad. Maybe society advances through the adjudication of competing bullshit claims. I call this dynamic the bullshit dialectic. Bullshit claims slow down our convergence to a reflective equilibrium because they present more (poorly founded) possibilities that we must consider, but they might speed up our convergence to the truth because, simply in virtue of there being so many of them, some bullshit claims end up being true. A betting norm probably cows people into parroting conventional views so that they will not be asked to bet, and that chilling effect is bad to the extent that truth-seeking is not merely an activity for atomistic elites.