No it isn't. It's a platform run by a private company for its own ends that offers membership under terms of service which grant it absolute, universal, irrevocable and arbitrary rights over user content and accounts. Terms of service that everyone with an account agreed to beforehand.
That it has global reach no more makes it a public forum than CNN, the BBC or the Wall Street Journal, and "akin to a government institution" is just an attempt to muddy the waters between the definitions of public and private enterprise.
If you or anyone wants to make this a free speech issue, don't misrepresent the nature of the problem. State that you want the government to take over social media platforms, restrict their free speech rights and force them to publish content against their will. Even if it's racist, even if it's false, even if they're not a general purpose forum, the men with guns should force them to.
People who claim, for instance, that it should be a crime for websites to moderate any content, in any way, that isn't strictly illegal, or that all moderation should be subject to judicial review (both positions I've seen repeatedly here) should realize just how radical and potentially authoritarian such moves would be, particularly given their correlation with the current atmosphere of anti-leftist panic.
People who advocate that Twitter should not exercise editorial control over content are hypocrites for using HN's community editorial control tools to suppress, or remove, content that they don't agree with on HN.
People who value free speech as an absolute right in virtually all contexts have no business curtailing what they argue is an absolute right when it is exercised by people who have views they disagree with.
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As a substantive question, I agree that Twitter is large enough that it should be regarded as an infrastructure platform, akin to the phone carriers, and should not be expected to unilaterally decide on the fair bounds of political speech. That much power does not belong in the hands of any one CEO. Absent a more suitable long-term legal framework to combat propaganda, however, unilateral action is the best of a set of very bad choices. The political situation in America is far too dangerous for potential disinformation to spread unchecked.
If there is truth to the NY Post story, it will be corroborated by other news outlets and will eventually find its way to Twitter via that route. Until that happens, however, October surprises of potentially dubious validity should not be allowed to spread unchecked.
It's refusing to spread likely BS propoganda. And he is correctly implying that many people who claim to be free speech advocates are in no way free speech advocates and merely are upset that racist and conspiratorial speech is being censored and are fine censoring viewpoints they disagree with