A sistem trustless it means that the participants involved do not need to know or trust each other or a third party for the system to work. In an environment without the need for trust there is no single entity that has authority over the system, and consensus is reached without the participants having to know or trust each other if not of the system itself.
The inherent property of being trustless in a peer-to-peer (P2P) network was introduced by Bitcoin, as it allowed all transactional data to be verified and stored immutably on a blockchain public.
Trust exists in the vast majority of transactions and is a vital part of the economy. However, systems without the need for trust have the potential to redefine economic interactions by allowing people to trust abstract concepts rather than institutions or other third parties.
It is important to consider that “trustless” systems do not completely eliminate trust, but rather they distribute it in a type of economy that encourages certain behaviors. In these cases it is more correct to say that trust is minimized but not eliminated.
I centralized systems are not trustless as participants delegate power to a central point in the system and authorize it to make and enforce decisions. In a centralized system, as long as you can trust the trusted third party, the system will work as intended. But beware of the problems, even serious ones, that can arise if the trusted entity .. is not reliable. Centralized systems are prone to system failures, attacks or hacking. The data can also be altered or manipulated by the central authority without any public authorization.
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Now let's get a little philosophical, but stick with me: when it comes to money, centralized systems probably have a more widespread appeal than decentralized systems (which are trustless), as people tend to be happier directing trust towards organizations rather than systems. However, while organizations are made up of people who are easily bribed, systems without the need for trust can be governed entirely by computer code.
Bitcoin and other Proof of Work blockchains gain their ownership trustless providing economic incentives for honest behavior. There is a monetary incentive to maintain network security, and trust is distributed among many participants. This makes the blockchain mostly resistant to vulnerabilities and attacks, while eliminating single points of failure.