Comments (2)
@riastradh-brave - thanks. it would be more helpful, to make this issue a PR adding text to https://github.com/brave-intl/bat-ledger/blob/master/documentation/Ledger-Principles.md#ad-free-statistical-voting ...
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Additional notes from Rafael Pass passed on by @bridriver (with TeX tidied up by me; \let\eps\varepsilon
in preamble):
Let X be the number of ``daily-rewards'' (of \$5/30) that some site
gets in a month.
If we go for the \$100 cut-off as discussed above (i.e., only sites
that make more than \$100 per month need to get a reliable payment),
think of $\mu = E[X] > 600$.
Let's assume that users are independent.
The multiplicative Chernoff bound then says that $\Pr[X < (1-\eps)
\mu] < e^{-\eps^2 \mu/2}$.
So, if we set $\eps = 0.1$, we get that except with probability
$e^{-(1/200) \cdot 600} = e^{-3} < 0.05$, the webpage will get 90\%
of what it is supposed to get.
(And webpages that are supposed to get \$1000 will get at least 97\%
of that.)
The Chernoff bound says: $\Pr[X < (1-\eps) \mu] < e^{-\eps^2 \mu/2}$,
where $X = \sum_i X_i$ and $X_i$ are 0/1 r.v.
So you actually don't care about the \# of samples $X_i$, but rather
the expectation of the sum: you need the expectation $\mu$ to be
larger than $\eps^2$.
If you want to be within 10\% of the ideal payment, we need the
expectation to be ${>}600$.
And thus if you just do 1 submission/month this would only kick in for
websites making 3K.
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