Back up an information as $n$ pieces and require exactly $n-1$ to recover it
What you describe is known as Threshold-secret-sharing, for which a good candidate is the threshold version of shamir-secret-sharing.
In particular, for your use case I would recommend implementing an &quot;n-1 out of n threshold sharing scheme&quot;.

Shamir Secret Sharing $(n,k)$-threshold scheme.
Shamir's $k$ of $n$ threshold sharing scheme is based on the observation that a $k-1$ polynomial over a field is determined by $k$ points, and yet cannot be determined with fewer than $k$ points. If we let $k=n$ then this reduces to Shamir's original sharing scheme.

Choose $q$ such that $\mathbb F_q$ be a finite field (the size of $q$ will specify how secure the scheme is).
Sample $a_1,\dots,a_{k-1}$ uniformly from $\mathbb F_q$.
Let $a_0=s$ be the secret you wish to share.
Let $f(x)=\sum_{i=0}^{k-1} a_i x^i$.
For each of the $n$ people, let share $i$ be the pair $(i,f(i))$.

To decrypt, we use polynomial interpolation to reconstruct the polynomial $f$, which requires at least $k$ shares, and then simply read off the coefficient $a_0$.
Security:
No information about the $a_0$ coefficient is leaked until the polynomial is completely recovered, the scheme is informationally secure. As such, the size of the finite field will be the same as the security margin presented, because the best attack will be to directly guess the secret. nb: This assumes that an adversary must treat the secret as if it were uniformly sampled from all possible field elements - obviously if your secret $s\in\{0,1\}$ your security is bounded by that!