Bitpeople

The rule is to attest only the person you have met. There will be those who attack the system instead, and the most effective attack is all of them cooperating as if they were one entity, sharing their people and their accounts. When two of their accounts are paired together they pass for free, so their people are placed only in mixed pairs, where one is needed. And since they spend every invite, they always hold more accounts than their free pairs and their people can cover; the rest are accounts with nobody behind them, paired with honest people, each passing if the honest partner gives in and attests it, and taking that partner out for the round if they hold. In every case the ideal strategy is the same: always attest, since it costs nothing and can only gain. The population can therefore be modeled as exactly two sides, the honest against the colluders, and every time an honest person gives in they can, in this idealized model, be counted as having joined the colluders.

Each round an honest participant is paired with a person with some probability — honest, or a colluder’s own, it makes no difference, a person is there and both pass — and otherwise with an empty account. When it is empty there is one thing to do: refuse, and lose the round. An honest person knows that with a given probability they will be paired with a person, and that otherwise they forgo the round’s proof-of-unique-human. The honest population wins — holds the majority of all accounts — as long as it stays above a certain percentage of the population.

Every pass earns one invite token, and c tokens admit one newcomer to the next round. Invites are meant for people one knows — everyone has one to give, so anyone real has people who can invite them — and whoever sells them to strangers counts among the colluders. The more tokens a registration costs, the larger the percentage of the population that has to collude to gain the majority of the accounts, but if it costs too much the honest side cannot re-admit its own after lost rounds. Three invite tokens per registration is a good balance.

Two colluder accounts paired together attest each other and pass with nobody there, so the colluders place their people only in mixed pairs, and the more accounts they hold, the more of them pass for free. With K people they can sustain K/(1 − X) accounts at share X, and since they spend every invite they always hold more accounts than their free pairs and their people can cover; the rest are accounts with nobody behind them, paired with honest people. At half of all accounts the colluders run three accounts per person and need a fifth of everyone. That is the 80% honest majority: eight in ten who, paired with nothing, forgo that month’s proof-of-unique-human.

Someone who registers and then does not appear fails the pair, so the partner falls too; someone who does not register harms nobody, so only unplanned absence counts. Colluders miss rounds too, but their own pairs are immune, so no-shows hurt the honest side more. Most absence is foreseeable, and if it is communicated, so that whoever is about to be stood up knows in advance, someone who cannot come can hand their key to someone they trust who was stood up; the idealized model here assumes that no-shows do not.

An honest participant abstains whenever there is no other person in the pair. The partner may be one of the colluders’ accounts with nobody behind it: of their accounts, 1/((c+1)(1 − X)) have nobody, so at colluder share X that is X/((c+1)(1 − X)). Or the partner may be an honest person who could not come, (1 − X)m at no-show rate m — indistinguishable from the other side of the pair, though they would not have attested either. Together, the probability of forgoing a round is

With c = 3 and 5% no-shows that is 7% when the colluders are 7% of the population (a tenth of the accounts), 16% at 17% (a third), and 27% at the 20% that gives them half. Nobody is lost — whoever fails is back the next round on their friends’ invites.

Two honest people connected through two colluder accounts, each seeing the other as their partner, would verify both accounts with nobody present. Registrations are mixed before the round, so no one can tell who is who. A video lock & key, done as a handshake before the event, stops it. Each partner sends the other a sealed recording of itself together with its public key, the key as data inside the sealed payload; they meet on video; then they exchange the decryption keys and verify the recordings — that the key inside is the partner’s and that the person in the recording is, in every way, the person they just met. A recording is sealed before its maker has seen the partner, so it cannot show the person the partner will meet, and no one can be met without first passing their check.

In the hypothetical that a future AI cracks the 1-on-1 video Turing test — not outright, but well enough to pass against the average partner some share q of the time — an AI-driven account passes with probability X + (1−X)q, and with c = 3 it reproduces itself once that reaches 3/4. From q = 75% a handful of invites is enough: the accounts grow with nobody behind them from the start. Below that the attack still takes people: at most 0.8% of all at q = 70%, 4% at 60%, 8% at 50%, 14% at 30%, against 20% with no AI. Short of that, a deepfake modifies an underlying actor and creates none; what the attack needs is an autonomous AI.