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Indeed. Both can be run either a democratic or authoritarian fashion. "Ownership should mean absolute power" is a common belief (everywhere but particularly in the US where labor rights have never been strong), but is only one option, and more democratic forms are possible.
> Peasants don't optionally sign contracts to belong to their nation.
Thinking that employers "belong" to the companies they work for is quite strange language. But more to the point, employees don't "optionally" sign employment contracts - most people are forced to work to pay the bills - in other words, they are coerced into signing the contract. Most people hate their jobs and would rather not do them.