What role do miners play in determining a fork?


As I understand it, blockchains are governed by smart-contracts. These set out valid transactions. Miners then determine whether the transactions in blocks are valid or not. Changes to smart-contracts may be made according to an ‘articles of association’ style democratic process. If a minority chooses a different validity protocol, how do they achieve a fork? Surely they are simply invalid blocks and would be rejected. If this is not the case, then do miners have a determining role in forking?
This is probably a very basic question, but when searching for it, documents tend to describe what a fork is rather than the process by which it occurs. Thanks for any clarification.

    Many thanks Daniel,
    The link is a good overview. The example offered for forking is that of China and Canada, and it’s this that has still left me with uncertainty regarding the independence of blockchains.
    Forking can, as I understand it, have either a technical or a political cause. Technical causes such as lags may quickly disappear as soft forks, that is they are unintentional artifacts of the chain and it’s technology.
    The other, such as the Bitcoin fork seem very much more political. A change is made in the hope of attracting new users, by migrating their tokens to the new chain.
    The page highlights the complex political interests of stakeholders, and so an extension of my question would be whether political control of one stakeholder, say miners, would be enough to control the block by ensuring the increased likelihood of forked blocks being validated.
    If not, could you advise on the political conditions under which a crypto-currency or other block chain would become ‘owned’ by one cartel either within a stakeholder class or between them, or political entity, and whether there are any cases of this.
    Or, are the implicit transaction costs of blockchains low enough to ensure that network effects and cartels are nunable to dominate any one chain, and therefore mitigate against ownership by any one group?
    Thanks for your thoughts.