Today is the US election day, and last night's internal reference 《11.4 Blockchain Internal Reference: US Election, New Money vs. Old Money, Who Will Win?》 summarized some information on both sides. Affected by the "Trump trade" recession, overnight BTC once fell back to around the 30-day moving average of 66.9k.
The US election is a form of voting democracy. But does voting really achieve democracy? Unfortunately, it does not. Even excluding issues like ballot fraud and illegal voting, mathematically, it can be proven that voting cannot achieve democracy. This is the result of Kenneth J. Arrow's research, who won the Nobel Prize in Economics in 1972.
What is democracy? Democracy is a group of people using a system to make a collective choice or collective decision, and that collective decision should serve the interests of the majority in that group.
It can be seen that democracy first has boundaries. The democracy of Americans is only to serve the interests of Americans. But will it harm the interests of non-Americans on 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 purpose.
Finally, the goal of democracy is interests (not morals or anything else), and the final result must be beneficial to the interests of the majority.
Even if we do not consider whether the collective decision made by a group of people is truly in the interests of the majority, just in the step of making a collective choice, Arrow has proven that there is no voting system design that can truly obtain a result.
In the conclusion of his 1972 Nobel Prize acceptance speech in Stockholm, "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice", 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 have agreed to have lunch together at noon. Their options are three restaurants: Braised Chicken Rice, Domino's Pizza, and KFC Burger.
Zhang San's preference is: Braised Chicken > Pizza > Burger
Li Si's preference is: Pizza > Burger > Braised Chicken
Wang Wu's preference is: Burger > Braised Chicken > Pizza
Please design a voting system that can allow this group of three people to democratically vote to choose the best option.
Anyone who has passed junior high school math can discover that such a democratic voting system does not exist!
If the voting result is Braised Chicken: only Zhang San is satisfied. But Li Si and Wang Wu both think that choosing Braised Chicken is not as good as choosing Burger!
If the voting result is Pizza: only Li Si is satisfied. But Zhang San and Wang Wu both think that choosing Pizza is not as good as choosing Braised Chicken!
If the voting result is Burger: only Wang Wu is satisfied. But Zhang San and Li Si both think that choosing Burger is not as good as choosing Pizza!
It can be seen that even in such a simple system, democracy is impossible to achieve. No matter how you choose, the vast majority of people are dissatisfied.
This is just three people choosing what to eat. If it's three hundred million people choosing a president, can there be any system that can guarantee that the voting election can definitely achieve a truly democratic decision-making - that is, the elected president is in the interests of the majority?
More complex designs will only mask this fundamental problem, and absolutely cannot solve the problem. Because this is a problem of mathematics and logic, it cannot be solved by system design.
Arrow generalized and formalized this problem, and conducted a rigorous mathematical proof, known as the Arrow 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 the Arrow Impossibility Theorem shows that any attempt to summarize individual preferences to form social preferences will not be able to simultaneously satisfy the following five seemingly reasonable conditions:
1. Non-dictatorship: No one can completely determine the preferences of society. That is, social preferences should not be simply equal to the preferences of any individual, and collective decisions should reflect the opinions of multiple members.
2. Pareto Efficiency: If everyone prefers A over B, then the social preference should also reflect that A is superior to B. This is a basic rationality requirement for collective decision-making.
3. Independence of Irrelevant Alternatives (IIA): The social preference for 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 the addition of an irrelevant option C should not change the ranking of A and B.
4. Transitivity: If the social preference is that A is superior to B, and B is superior to C, then the social preference should satisfy that A is superior to C. That is, collective preferences must be consistent and not have cyclic preferences.
5. Unrestricted Domain: All possible combinations of individual preferences should be allowed, that is, the rule should apply regardless of how people's preferences are.
Arrow proved that when there are three or more candidates, any preference aggregation mechanism cannot simultaneously satisfy the above five conditions. In other words, either we need to give up one of the conditions, or we need to accept an imperfect decision-making system (for example, accept a "dictator" to make decisions, or allow the system to not satisfy consistency, etc.).
The Arrow Impossibility Theorem shows that there are unavoidable contradictions in pursuing 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 summarize individual preferences.
The Arrow Impossibility Theorem reveals the fundamental paradox in collective decision-making, that is, under the condition of satisfying reasonable conditions, it is impossible to design a perfect social choice rule. It tells us that any collective decision-making mechanism requires 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 written in Section 4 "Proof-of-Work":
"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. To modify a past block, an attacker would have to redo the proof-of-work of that block and all blocks after it, and then catch up with and surpass the work of the honest nodes. We will show later that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added."
What Satoshi Nakamoto meant by "one-CPU-one-vote" is actually one share of computing power one vote. As for how much computing power this one share is, it is actually the proportion of the node's computing power to the entire network's computing power.
The consistency problem of distributed systems is also a collective choice problem. The only difference is 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) algorithms. The FLP Impossibility Theorem has blocked this path.
Satoshi Nakamoto completely abandoned these dead-end old paths. The Bitcoin white paper did not mention a single word about traditional distributed algorithms, nor did it cite any relevant references, as if they did not exist.
In the above Section 4 of the white paper, Satoshi Nakamoto pointed out that the method of voting by "head" (IP address) will inevitably encounter the problem of casting fake votes. Just like in this US election, international students without voting rights easily voted. Even many people have openly admitted to voting using the names of cats or dogs.
In distributed systems, this is called a "Sybil attack", which is an attack by forging identities.
Can the US election system withstand witch attacks? It seems to have vulnerabilities. Some may say that the payoff from counterfeit voting is extremely small, while the potential criminal losses are extremely large, so no one would do such a thing. However, if it is one of the competing parties, organized fake ballot attacks would be a huge gain. Some also say that if we have a nationwide ID system and name-based voting, won't that solve the problem? But ID cards and name-based voting will also bring other problems that hinder democracy. Moreover, the centralized issuance and authentication of ID cards means introducing a centralized power department. Compared to the Bitcoin system, to be truly decentralized, it is impossible to adopt such a centralized solution. Satoshi Nakamoto changed the thinking, he let everyone vote by "proof of work". Simply put, the more work you do, the greater your voice (voting power). Note, it's not who has more coins (money), who has more say. This is similar to what Marx and Engels said about letting the working class take power. Let the group that represents the most advanced productive forces have the greatest power. Why? Because coin holders can always sell and run. But once miners' mining machines are deployed, turning them off will turn them into scrap metal. This is also why the foundation of the state is the working masses, not the capitalists. Of course, in real society, the amount of work done is not easy to measure and compare due to differences in division of labor, but for the Bitcoin system it is much simpler, as it is all the same hash calculation, very easy to measure and compare. The result of voting by proof of work, or what can be called "computing power democracy", is what Satoshi Nakamoto called the "longest chain". "In the November 8, 2008 email, Satoshi Nakamoto wrote: 'Proof of work voting by CPU power must have the final say.' Making everyone believe that the longest chain (the chain with the most accumulated computing power) is the valid chain is the only way to establish global consensus." - "A History of Bitcoin", Chapter 11, Section 51, "Computing Power Democracy" As can be seen, the Bitcoin system is a "one-party system" - there is only one longest chain, not the "two-party system" of the US - where you have to choose between two equivalent chains. Otherwise, it would result in a "brain split". The longest chain is the Schelling point of the system (the default consensus, proposed by American economist Thomas Schelling). Any node that contributes computing power to the system can gain the right to propose new blocks and extend the longest chain. The extension of the longest chain is also a recognition and confirmation of the longest chain. All other nodes that contribute computing power can then validate and accept this new block to realize their recognition of the extended longest chain. 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, Section 51, "Computing Power Democracy" of "A History of Bitcoin", the author summarizes: "Miners achieve unwavering adherence to the longest chain principle through computing power voting, but miners cannot alter any consensus rules. The consensus rules are defined by the open source Bitcoin core code, and the power to modify them lies with the development team, but the development team cannot do whatever they want and arbitrarily destroy the consensus rules, because miners and users have the right to elect a new development team to fork the open source code (copy the open source code and maintain it separately). The ultimate decisive power is actually the vast majority of coin holders, who decide which coin to sell and which coin to buy, which is voting with their feet. Water can carry a boat, and it can also capsize a boat. But at the same time, coin holders are a "mob", they only have the passive freedom to come and go at will, and do not have the active freedom or power to force the development team to modify the rules. "Let those who are free have no power, and those who have power have no freedom. Come and go at will, but no one can do whatever they want. This is the computing power democracy of Bitcoin."
