# 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.