What is a soft fork?
A soft fork is an update to the protocol software, however it is backward compatible. Unlike a hard fork whereby every user must upgrade, only the majority of the miners must upgrade so as to enforce the new rules. Because the old nodes (nodes which have not upgrade) still recognize the new blocks as valid, this type of upgrade only requires the majority of miners to upgrade their software so they can enforce the new rules.
Detailed description of a soft fork
The reason a soft fork does not require users to upgrade is because the transactions follow the old rules set our in the protocol as well as the new rules. This means that any user who has not upgrade their software would still have a verifiable transactions as long as it follows the old rules and does not violate any of the new rules.
In order for a soft fork to work the majority of miners need to upgrade to the new protocol, the more miners that upgrade their software the more secure the network will be. If a percentage of miners do not upgrade their software then this could mean that any blocks validated by them run the risk of violating the new rules. While these blocks would be valid to the old nodes/nodes which have not upgraded, they would not be recognized by the new nodes/nodes which have upgraded.
An example of a soft fork is segregated witness, this is just an addition to the software which means that it will work with both the old and new versions of the blockchain.
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