The Volokh Conspiracy
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Another excerpt from the First Amendment section of my Social Media as Common Carriers? article (see also this thread); recall that the key First Amendment arguments are in this post, which relies on the PruneYard, Turner, and Rumsfeld precedents, and in this one, which explains why Miami Herald, Hurley, and the various other "common theme" precedents don't apply.
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These principles apply even when the property owner disapproves of the third party's message, or when the property owner's other visitors do the same.
In Rumsfeld, for instance, the universities seriously objected to military recruiters (in particular, to the military's "Don't Ask, Don't Tell" policy), arguing that "the Solomon Amendment requires law schools to collaborate with military recruiters in an effort—discriminatory recruiting—that the schools consider fundamentally unjust." Many students were also upset at the presence of military recruiters on campus.
Yet the Court held that "[a] military recruiter's mere presence on campus does not violate a law school's right to associate, regardless of how repugnant the law school considers the recruiter's message," and that the recruiter's presence doesn't violate the law school's right to be free from compelled speech. Likewise, California courts have followed up on PruneYard by making clear that shopping malls can't block even speech they, their business partners, or many of their visitors might disapprove of, such as speech urging listeners to boycott the mall's tenants, or speech displaying gruesome images of aborted fetuses.
In PruneYard, Justices Powell and White did note that the mall owners "have not alleged that they object to the ideas contained in the appellees' petitions," and that the owners didn't claim that some likely future speakers "will express views that are so objectionable as to require a response even when listeners will not mistake their source." But the majority didn't rely on this, and thought that the possibility that PruneYard would have to respond (by "disavow[ing] any connection with the message") was perfectly acceptable.
Of course, sometimes compelled hosting can undermine the property owner's economic interests. Cable systems, for instance, would usually choose to carry those channels that are most profitable for them to include. The must-carry rule, by requiring them to drop some of their preferred channels to make room for others, would likely harm the systems financially, at least in some measure. Yet Turner upheld the must-carry rule.
Likewise, allowing leafleters and signature gatherers at a shopping mall, as in PruneYard, might impose some costs on the shopping center. Any such speakers might offend some patrons, and offended patrons are less likely to be in a shopping mood. Indeed, the California rule upheld in PruneYard protected even speech that urged boycotting stores in that very shopping center, yet this didn't stop the Court from rejecting the shopping mall's First Amendment claim.
The Ninth Circuit likewise interpreted the California PruneYard principle as invalidating a mall rule that banned handbills "naming a [mall] tenant," "speech that may adversely affect [the mall owners'] business." "In restricting such critical speech about their tenants, owners, or managers, Petitioners' rule contravenes the purpose of California free speech protections: the preservation of discussion of issues even when they are contrary to a regulating party's belief or interest." And the California Supreme Court later reaffirmed that "a privately owned shopping center must permit peaceful picketing of businesses in shopping centers, even though such picketing may harm the shopping center's business interests."
This, I think, responds to the argument that requiring platforms to host offensive material violates the First Amendment because it might cost the platforms some money, for instance through lost advertising. To begin with, if advertisers just don't want to have their material placed alongside a page that contains certain material, platforms can likely simply block advertising on that page instead of deleting the page outright. (Some platforms already do that in some situations.) That would mean that the platforms would have to host certain material without getting financial benefit from such hosting. But that sort of modest "harm [to] the [platform's] business interests" doesn't create a First Amendment right on the platform's part to remove the offensive material.
Now in theory it's possible that an advertiser would go further, and demand that a platform purge all material of some sort, or else the advertiser would stop advertising. But, first, that seems unlikely in a world where platforms are treated as common carriers, precisely because the platform can reasonably explain that it's just complying with its legal obligation (and because social media platforms are seen as important, valuable places to advertise).
And, second, this sort of advertiser threat just can't suffice to create a First Amendment objection to common carrier obligations. If a massive phone user tells Verizon, "Stop handling phone service for this unpatriotic advocacy group, or we'll switch our millions of dollars of phone service to T-Mobile instead," I doubt that would justify Verizon's canceling the unpatriotic group's phone lines.
Likewise, say Robinsons-May (the boycotted business in Fashion Valley Mall, LLC v. NLRB) had told a mall owner,
We're your anchor tenant, and we demand that you stop leafleters from urging a boycott of our store, or else we won't open any more stores in malls owned by your company; instead, we'll just open stores that aren't in the large shopping malls that are governed by the PruneYard right of public access.
That can't have given the mall owner a get-out-of-the-PruneYard-doctrine-free card. The First Amendment viewpoint-neutrality rules often require the government to incur some costs and to lose some revenue because of public reaction to speech. Similarly, common-carrier rules may permissibly require common carriers (or their analogs, like shopping malls) to incur some costs and to lose some revenue because of public hostility to offensive speech.
 See, e.g., Brief for Respondents, Rumsfeld v. FAIR, 547 U.S. 47, No. 04-1152, 2005 WL 2347176, *17.
 See supra note 123 and accompanying text.
 Rumsfeld, 547 U.S. at 70.
 See supra p. 42 & notes 141–142. Similarly, it is doubtless true that content moderation policies "express the company's view that [certain] content is 'objectionable,'" and "express to users, and to the entire world, that the company maintains a certain viewpoint about an idea or topic—or even a single word." Lily A. Coad, Note, Compelling Code: A First Amendment Argument Against Requiring Political Neutrality in Online Content Moderation, 106 Cornell L. Rev. 457, 485 (2021). Yet the universities in Rumsfeld likewise argued that their policy of excluding military recruiters expressed their views that the military's discrimination against gays and lesbians was "objectionable," and "express[ed] to [students], and to the entire world, that the [university] maintains a certain viewpoint about an idea or topic"; that did not make the Solomon Amendment, the Court held, into a violation of the universities' First Amendment rights.
 Id. at 101 (Powell, J., concurring in part and concurring in the judgment).
 Id. at 87 (majority opin.).
 Robins v. Pruneyard Shopping Center, 592 P.2d 341, 346 (Cal. 1979) (quoting and describing Schwartz-Torrance Investment Corp. v. Bakery & Confectionery Workers' Union, 394 P.2d 921 (1964)).
 The Takings Clause analysis in the U.S. Supreme Court's PruneYard decision did note that the California rule wouldn't "unreasonably impair the value or use of their property as a shopping center." 447 U.S. at 83 (emphasis added). But some impairment would be tolerable, so long as it isn't "so essential to the use or economic value of their property that the state-authorized limitation of it amounted to a 'taking.'" Id. at 84.
 Glendale Assocs., Ltd. v. NLRB, 347 F.3d 1145, 1153–58 (9th Cir. 2003); see also United Bhd. of Carpenters & Joiners of Am. Local 586 v. NLRB, 540 F.3d 957, 965 (9th Cir. 2008).
 Id. at 1158.
 Fashion Valley Mall, LLC v. NLRB, 172 P.3d 742, 750 (Cal. 2007).
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Note that common carriers have historically been given some flexibility to impose "just" and "reasonable" regulations of their services. See, e.g., 47 U.S.C. § 201(a); W. Union Tel. Co. v. Bolling, 91 S.E. 154, 156 (1917). Likewise, for instance, a social media hosting mandate might except, for instance, spam pages, which the platform may define in certain content-based ways. But the legislature could well conclude that viewpoint-based exclusions are not permitted.
 See, e.g., YouTube Help, Advertiser-Friendly Content Guidelines, https://perma.cc/KNG2-WFE5.
 See Szóka & Barthold, supra note 10 (making this argument)
 "[S]ocial media advertising revenues reached $41.5 billion in 2020. That 16.3% year-over-year growth attributes social media with nearly 30% of all internet advertising revenue … ." Interactive Advertising Bureau, IAB Releases Internet Advertising Revenue Report for 2020, https://perma.cc/H9HY-RHNF.
 172 P.3d at 744.
 See, e.g., Forsyth County v. Nationalist Movement, 505 U.S. 123, 136–37 (1992) (striking down requirements that organizers of offensive parades pay for the city's security costs).