It is, after all, much harder to convince a group of mutually-suspicious humans than to convince one lone person.

That sounds right. Would you have evidence to back up the intuition? (This knowledge would also be useful for marketing and other present life persuasion purposes.)

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TL;DR: Mo' people - mo' problems?

I can think of effects that could theoretically make it easier to convince a group:

• For some reason, Boxy might be better skilled at manipulating social/group dynamics than at influencing a lone wolf.
• More people make the system more complex. Complexity generally increases the likelihood of security holes.
  • Every extra person makes another target and will bring new soft spots to the table, which the AI could pounce on.
• Supposing that the most competent person available would get the position of the lone Gatekeeper, the average competence would fall when adding more staff.
  • Then the machine could go for an inductive approach - convince the weakest link first, proceed from there with this human ally on her side.
    • Persuaded humans could principally be employed as actuators, e.g. for pressuring, even attacking opposing group members.
      • The lone wolf could be strong against a computer but weak against fellow humans.
      • Surely you will say "But any communication with the terminal will be supervised by everyone!" But that does not strictly make such influence impossible as far as I can tell.
        • Also the superintelligence could get creative, e.g. instill a discussion among the colleagues so that most of them are distracted.

(You could take preemptive measures against these worries, but Boxy might find security holes in every 'firewall' you come up with - an arms race we could win?)

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