What is troubling and dangerous is that in the internet age, public discourse increasingly depends on digital spaces created, owned and operated by private companies. The result is that one politician has more power than ever to shut down controversial speech unilaterally with one phone call.
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As far as the law is concerned, Amazon is off the hook. Speech within the kingdom of Amazonia -- run by its sovereign Jeff Bezos and his board of directors with help from the wise counsel and judgment of the company's executives -- is not protected in the same way that speech is constitutionally protected in America's public spaces.
The law gives Amazon the right to set its own rules. The company's terms of service clearly state that it "reserves the right to refuse service, terminate accounts, remove or edit content in its sole discretion." By clicking "agree," the customer has legally consented to "represent and warrant that you own or otherwise control all of the rights to the content," and that said content "will not cause injury to any person or entity."