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Mathematical Proof
Voting Method | Ballots | Ballots in Sybil Attack | Max Ballots | Sybil Resistancy |
---|---|---|---|---|
QV | | | | ❌ |
PQV | or 0, | | | ⭕ |
Ballots
meansReflected votes
PQV can prove its quality as a new voting system by mathematically proving its Sybil resistancy without (less) harming the result of existing QV.
Assume that total number of votes is
and the number of votes a user has is
. The expected value of votes when
votes are honestly voted at once from one account can be expressed as [Equation 1].
[Equation 2] is expected value of votes in a situation when
votes are divided into
to do Sybil attack.
is the number of groups reflected in the vote out of
.
when
In order for a Sybil attack to always less beneficial than an honest vote, the condition of [Equation 3] needs to be satisfied. This condition is always satisfied because
,
are not
and
is always bigger than
to do Sybil attack.
PQV makes it always a loss to do sybil attack by applying probabilistic element on quadratic voting. Splitting voting power makes the expected value of voting power lower that executing 1 voting power. Therefore, rational users who want to maximize their voting influence will honestly exercise their votes at once by using one account. This means PQV can prevent Sybil attacks.
Last modified 11mo ago