The following question is extremely broad and speculative, for which I apologize, but it strikes me as exceedingly important, so I will ask it nonetheless.
Suppose an event of global significance took place, like the detection of an Earth-threatening asteroid or an alien invasion, and humanity were to need to decide collectively how to respond to it. Suppose further -- as is quite likely -- that (a) some individual nation states (US, UK, RU, CN etc) would attempt to control the global response, but (b) citizens of other states would be skeptical of whether the "leader" states' proposals were in their own best interest. In such circumstances, existing political arrangements like the United Nations probably might not suffice to achieve a mechanism for arriving at a true "consensus" that would be (approximately) universally recognised as such. Is there a plausible cryptographic mechanism for conducting a global referendum that would be (approximately) universally recognised as legitimate?
Some of the issues that I am trying to get at:
What sort of cryptographic guarantee, if satisfied to a reasonable degree of certainty, would ensure "legitimacy"? A presumably-unattainable example illustrates what I mean: if a cryptographic protocol could ensure adherence to the principle of "one person one vote", while simultaneously permitting a sufficiently large fraction of the human population to vote, I would venture to guess that the outcome of the election would enjoy a certain degree of "universal" legitimacy.
Although a layman in cryptography, I'm still well aware that when I interact on the internet I "leak" some information that would suffice to identify me uniquely to a high degree of certainty. (My persistent logins, browser cookies, ...) What fraction of the human population could be identified uniquely, with what degree of certainty, using a cryptographic protocol that could ensure anyone can vote once and only once?
Can and should ordinary, run-of-the-mill elections like those held in the United States for selecting our President, be conducted online? If not, why not? In terms of provable (albeit probabilistic) guarantees about how electoral outcomes compare to the preferences of the electorate, are there any valid reasons to prefer paper ballots to electronic ones? If so, what infrastructure changes could be adopted that would allow us to leverage the efficiencies of online voting? Do we need an international public key infrastructure with private key issuance tied to state identities? Something else?