> For the complete documentation index, see [llms.txt](https://shai-deshe.gitbook.io/pow-book/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://shai-deshe.gitbook.io/pow-book/part-1-blockchains-and-blockdags/chapter-2-the-block-chain-paradigm/honesty-and-rationality.md).

# Honesty and Rationality

The idiom "honest majority" is extremely common when discussing PoW. The sufficiency of an honest majority (opposed to a privileged majority of two thirds) is considered one of the greatest accomplishments of Nakamoto consensus. Another tenet of the Bitcoin ethos is *trustlessness*: the property that all sides of all interactions do not have to trust the other side to follow suit. That the protocol protects them from malfeasance.

Ostensibly, there is quite a tension between the two: how can a system be *trustless* if its security hinges on an honest majority we *trust* to exist?

The answer is that *we don't*. The term *honest* might be a bit misleading. In the world of protocol design and algorithmic game theory, labeling a player *honest* is not supposed to be a testimony to the pureness of their intention, it just means that they behave *the way we expect*. We assume honesty because it makes analysis easier. But it *does* require us to further explain *why* we should assume miners (or other types of players) would be compelled to follow behavior we branded as "honest".

Miner behavior *cannot* be enforced by the protocol. If we could *assure* that miners are "honest" we would not have needed to make assumptions. The next best thing is to *encourage* miners to behave as we need them to through *incentive alignments*. That is, we make it *worthwhile* for a miner to behave.

This, in a nutshell, is the underlying theme of the subset of *algorithmic game theory* called *mechanism design*, a beautiful field of research concerned with constructing protocols in a way that encourages participants to behave as the protocol requires.

But what *is* an incentive? How do we quantify and reason about it? A more in depth discussion will be deferred far down the line, when we analyze a blockDAG's fee market (and until that is completed, you can enjoy [this post](https://kasmedia.com/article/three-woes) instead). But a cursory explanation is that we assume there is some *utility* that a so-called *rational* miner will want to maximize. For example, we can assume that a Bitcoin miner wants to maximize the amount of coin they gain from mining. A miner that conforms to this utility (in a sense that will be made more formal when time is due) is called *rational*.

Now, much like "honest", the name *rational* is also not a judgement call. It's not that miners that are not rational are crazy, or stupid, or irrational in any other colloquial interpretation of the term. It just means that *their utility is different*. A miner that stops mining because they went into debt and are better off selling their equipment is not maximizing the utility and is therefore "not rational", despite selling her gear to cover her debts is arguably the more (colloquially) rational approach, and that's hardly the only example of a miner who has something to gain by *deviating* from the protocol.

However, if the incentive is strong enough, assuming that a majority of miners are rational (in the sense that they work toward obtaining as much coin as possible) is a very reasonable assumption. So it remains to explain why the rational behavior coincides with our idea of honesty.

## Incentive Alignment in Block Chains

When we defined the [block chain paradigm](/pow-book/part-1-blockchains-and-blockdags/chapter-2-the-block-chain-paradigm/the-paradigm.md#the-block-chain-paradigm-at-last), we only had two expectations honest of miners:

* Always mine over the **selected tip**
* When discovering a new block (via mining or a peer) **immediately transmit it and recompute the selected tip**

But now we want *rational* miners to follow suit. How shall we achieve that? Bitcoin offers a simple and powerful: **pay miners for creating blocks,** as long as the block is **within the selected chain**. The said payment has two components: block rewards, and fees.

Block rewards serve two functions: increase supply in a *gradual manner* (which is why the coins created by block rewards are often called *emissions*), and incentivize miners to behave even when fees are negligible.

Most PoW coins are *deflationary*, which means that the *total emission* *must be finite*, making fees the dominant, and finally only, incentive for good behavior in the long run. Hence, the fee market and the incentives it poses are obviously *crucial* for the long run of a deflationary proof of work. For that reason, we defer the discussion to an entire part of the book dedicated to fee market dynamics. For now, however, we treat block rewards as *fixed*.

{% hint style="info" %}
For a review and analysis of Bitcoin's emission schedule, see the [appendix](/pow-book/supplementary-material/math/stuff-you-should-know/geometric-sums-and-series.md)
{% endhint %}

So, how do block rewards affect rational miners?

One can prove that for Bitcoin's heaviest chain rule (that we did not introduce yet), not mining over the selected tip reduces the chance of creating the next block, and thus the expected gain. In essence, this is true since by not mining over the currently heaviest known chain, the miner competes *against it* from a disadvantage.

OK, but what about withholding blocks? Surely a rational miner would want to avoid that too, right? Well, not quite. We will soon discuss a phenomenon called [selfish mining](/pow-book/part-1-blockchains-and-blockdags/chapter-2-the-block-chain-paradigm/selfish-mining-in-bitcoin.md), which shows that there is in fact *some* divergence between the rational and honest strategies for bitcoin miners. But before that, we need to familiarize ourselves with some chain selection rules.