Today is the day of the US election. Last night's internal reference 《11.4 Teaching Chain Internal Reference: US Election, New Money vs. Old Money, Who Will Win? 》 summarized some information from two aspects. Affected by the ebb tide of the "Trump Trade", BTC once stepped back to the 30-day moving average of 66.9k overnight.
The US election is a voting democracy. But can voting really achieve democracy? Unfortunately, it can't. Even if operational problems such as ballot fraud and illegal voting are excluded, it can be proved mathematically that voting cannot achieve democracy. This is exactly the research result of Kenneth J. Arrow, the 1972 Nobel Prize in Economics.
What is democracy? Democracy is a group of people who use an institutional approach to make a collective choice or collective decision, and this collective decision can meet the interests of the majority of people in the group.
It can be seen that democracy has its limits. The American democracy is only for the benefit of the Americans. Will it harm the interests of other non-Americans on the earth? Of course it is possible.
Secondly, the purpose of democracy is to make collective decisions, or to make a specific collective choice. Voting is a means and method to achieve this goal.
Finally, the goal of democracy is interests (not morality or anything else), and the final result must be in the interests of the majority.
Even if we do not consider whether the decision made by a group of people is really in the interests of the majority, just in the step of making a collective choice, Arrow has proved that no voting system design can really get a result.
At the end of Arrow's report "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice" at the Nobel Prize ceremony in Stockholm, Sweden in 1972, he cited the voting paradox proposed by the 18th-century French scholar Condorcet as a vivid example.
The example is as follows:
There are three people, Zhang San, Li Si, and Wang Wu, who make an appointment to have lunch together at noon. They have three options: braised chicken rice, Domino's pizza, and KFC hamburgers.
Zhang San's preference is: Braised Chicken > Pizza > Hamburger
Li Si's preference is: Pizza > Hamburger > Braised Chicken
Wang Wu's preference is: Hamburger > Braised Chicken > Pizza
Please design a voting system that allows the three of them to choose the best option through democratic voting.
Anyone who has passed junior high school mathematics can find that such a democratic voting system does not exist!
If the voting result is Braised Chicken: Only Zhang San is satisfied. Li Si and Wang Wu both think that braised chicken is not as good as hamburger!
If the voting result is Pizza: Only Li Si is satisfied. Zhang San and Wang Wu both think that pizza is not as good as braised chicken!
If the voting result is hamburger: only Wang Wu is satisfied. Zhang San and Li Si both think that hamburger is not as good as pizza!
It can be seen that democracy is impossible even in such a simple system. No matter how to choose, the vast majority of people are dissatisfied.
This is just three people choosing what to eat. What if 300 million people choose the president? Is there any system that guarantees that voting and elections will definitely lead to a truly democratic decision-making - that is, the president elected is in the interests of the majority of people?
More complex designs will only cover up this fundamental problem, but will never solve it. Because this is a problem of mathematics and logic, it cannot be solved through institutional design.
Arrow generalized and formalized this problem and made a rigorous mathematical proof, which is called Arrow's impossibility theorem.
In democratic decision-making and voting systems, people often hope to make collective decisions based on the personal preferences of all members. But Arrow's impossibility theorem shows that any rule that attempts to aggregate individual preferences to form social preferences cannot simultaneously meet the following five seemingly reasonable conditions:
1. Non-dictatorship: No one person can completely determine the preferences of society. In other words, social preferences should not be equal to the preferences of a certain individual, and collective decisions should reflect the opinions of multiple members.
2. Pareto Efficiency: If everyone prefers A over B, then the preference of society should also reflect that A is better than B. This is a basic rationality requirement for collective decision-making.
3. Independence of Irrelevant Alternatives (IIA): The social preference relationship between A and B should only depend on people's preferences for A and B, and should not be affected by other options. This means that adding an irrelevant option C should not change the ranking of A and B.
4. Collective rationality (Transitivity): If the social preference A is better than B, and B is better than C, then the social preference should satisfy A is better than C. That is, the collective preference must be consistent, and there should be no circular preference.
5. Unrestricted Domain: All possible combinations of personal preferences should be allowed, that is, no matter what people's preferences are, the rules should be applicable.
Arrow proved that when there are three or more candidate options, any preference aggregation mechanism cannot simultaneously meet the above five conditions. In other words, either one of the conditions needs to be abandoned, or an imperfect decision-making system needs to be accepted (for example, accepting a "dictator" to make decisions, or allowing the system to not meet conditions such as consistency).
The Arrow Impossibility Theorem shows that there are unavoidable contradictions in the pursuit of fair, reasonable and consistent collective decision-making. This theorem has a profound impact on fields such as political science, economics, social choice theory, and voting system design. It reveals the inherent limitations of democratic decision-making, that is, we may not be able to find a completely fair decision-making mechanism to aggregate individual preferences.
The Arrow Impossibility Theorem reveals the basic paradox in collective decision-making, that is, it is impossible to design a perfect social choice rule under reasonable conditions. It tells us that any collective decision-making mechanism needs to make a trade-off between fairness, consistency and rationality.
In the Bitcoin white paper published by Satoshi Nakamoto in 2008, the problem of majority decision-making was discussed. It is in Section 4 "Proof of Work". This passage reads: "Proof of work also solves the problem of determining representation in majority decisions. If the majority is determined based on one IP address one vote, then the system can be subverted by anyone who can allocate many IPs. Proof of work is essentially one CPU one vote. The majority decision is represented by the longest chain, which has the largest amount of proof of work invested in it. If the majority of CPU computing power is controlled by honest nodes, the honest chain will grow fastest and surpass any competing chains. To modify a past block, the attacker will have to redo the proof of work of the block and all subsequent blocks, and then catch up and surpass the workload of the honest nodes. We will show later that as subsequent blocks are added, the probability of a slower attacker catching up will decay exponentially." Nakamoto's "one CPU one vote" here actually refers to one share of computing power one vote. As for how much computing power this share of computing power is, it is actually the proportion of node computing power to the computing power of the entire network.
The consistency problem of distributed systems is actually also a problem of collective choice. It's just that the collective choice is made by computers automatically executing the will of their owners.
The traditional solution is logical voting, such as BFT (Byzantine Fault Tolerance). The FLP Impossibility Theorem has blocked this road.
Satoshi Nakamoto completely abandoned these old roads that have reached a dead end. The Bitcoin white paper does not mention those traditional distributed algorithms at all, nor does it cite any relevant references, as if they do not exist.
In Section 4 of the above white paper, Satoshi Nakamoto pointed out that the method of voting by "head" (IP address) will inevitably encounter the problem of fake votes. Just like this US election, international students who are not eligible to vote also voted easily. Many people even revealed that they used to vote by using the names of cats and dogs.
There is a term called "Sybil attack" in distributed systems, which is a forged identity attack. A witch is a metaphor for a doppelganger.
Can the US election system resist Sybil attacks? It seems to have loopholes.
Some people may say that the benefits of fake voting are very small, while the losses of possible crimes are very large, so no one will do such a thing. However, if a party participating in the competition organizes a fake ballot attack, it will be a huge benefit.
Some people also say that if the United States has an ID card system and votes are recorded, can this problem be solved? However, ID cards and recorded voting will bring other problems that hinder democracy. Moreover, the unified issuance and certification of ID cards means the introduction of a centralized authority.
For the Bitcoin system, it is impossible to adopt such a centralized solution if it is to be completely decentralized.
Nakamoto changed his mindset and asked everyone to vote using "proof of work".
To put it simply, whoever does more work will have more say (voting rights). Note that it is not whoever has more coins (more money) who has more say.
It is similar to what Marx and Engels said about letting the working class take power. Let the most common group representing advanced productive forces hold the greatest power.
Why? Because coin holders can sell their shares at any time. Once the miners' mining machines are deployed, they will become scrap metal when they are turned off. This is why the basic base of the country is the working people of workers and peasants, not the capitalists.
Of course, the amount of work done in real society is not easy to measure and compare due to differences in division of labor, but it is much simpler for the Bitcoin system. They are all the same hash calculations, which are easy to measure and compare.
The result of the productivity democracy, or computing power democracy, based on proof of work voting, is what Satoshi Nakamoto calls the "longest chain".
"In an email dated November 8, 2008, Satoshi Nakamoto wrote: 'The CPU computing power proof of work voting must have the final say.' Let everyone believe that the longest chain (the chain with the largest cumulative computing power) is the valid chain. This is the only way to establish a global consensus." - "Bitcoin History" Chapter 11, Chapter 51 "Computing Power Democracy"
It can be seen that the Bitcoin system is a "one-party system" - there is only one longest chain, not a "two-party system" like the United States - choosing between two equal chains. Otherwise, there will be a "brain split". The longest chain is the system's Schelling Point (Schelling Point, the default consensus, proposed by American economist Thomas Schelling).
Any node that contributes computing power to the system can obtain the right to propose new blocks and extend the longest chain. The extension of the longest chain is actually the recognition and confirmation of the longest chain.
All other nodes that contribute computing power can recognize the extended longest chain by verifying and accepting this new block.
As long as more than half of the computing power recognizes the extended longest chain, this is the new global consensus.
At the end of Chapter 11, Episode 51, "Computing Power Democracy" of "The History of Bitcoin", Jiaolian concluded:
"Miners use computing power voting to adhere to the longest chain principle for a hundred years, but miners cannot tamper with any consensus rules. The consensus rules are defined by the Bitcoin core open source code, and the power to modify them is in the hands of the development team, but the development team cannot do whatever they want and destroy the consensus rules at will, because miners and users have the right to elect a new development team to fork the code (copy a copy of the open source code and maintain it separately). The ultimate decisive force is actually the majority of coin holders. They decide which coin to sell and which coin to buy, which is voting with their feet. Water can carry a boat, but it can also overturn it. But at the same time, coin holders are a "mob". They only have the negative freedom to come and go at will, but they do not have the positive freedom or power to force the development team to modify the rules. "Let those who have freedom have no power, and those who have power have no freedom. People can come and go as they please, but no one can do whatever they want. This is Bitcoin's computing power democracy."
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