One-to-One
Everyone equally has only one vote.
However, in this way, it is simply determined by a majority vote, and there is no way to reflect an individual's aspiration because they have same voting power.
One-to-Many
To overcome these shortcomings, a one-person multi-vote method has been proposed that allows them to have as many votes as they paid,
but there is a problem here that a small number of wealthy participants can decide the result of the voting easily.
One-to-Many, Suppressed
To solve this problem, a quadratic voting method is presented in which the cost of purchasing votes increases exponentially.
However, there is a limitation that quadratic voting is vulnerable to Sybil attacks, and it is also challenging to establish a secure system that guarantees anonymity and integrity apart from the quadratic voting protocol.
One-to-Many, Suppressed, and Probabilistic
We introduce a secure voting system through Probabilistic Quadratic Voting (PQV) and show that the system can mitigate the risk of Sybil attack.
The following is an equation that proves that PQV effectively defends Sybil attacks.
- The left-hand term is the expected value without Sybil attack.
- The right-hand term is the expected value under Sybil attack.
X: The number of votes.
N: The total number of votes.
k: How many parts of the votes will be divided.
l: The number of parts reflected in the vote.
This formula always holds when k > 1 and kN/X != 0.
In conclusion, in PQV, it is always a loss when trying Sybil attack.