# Privacy-Preserving E-Voting System Supporting Score Voting Using Blockchain
## 3 Background
### Score Voting  
Score-based score voting is a special type of election procedure that allows voters to assign a score to each candidate. This method has started to become more widely used in various elections, such as the election for the Secretary General of the United Nations and the election of Green Party of Utah [24]. In this method, each voter has the ability to  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Definition** \\ \hline \(\mathcal{E}\mathcal{A}\) & The Election Administrator \\ \(\mathcal{V}_{i},\mathcal{C}_{j}\) & Denotes a Voter or a Candidate \\ \(V_{i,j}\) & Denotes a voter’s ballot \\ \(C_{i,j}\) & Denotes a commitment to a ballot \\ \(g\) & The generator of the elliptic curve group \(G\) of prime order \(q\) \\ \(x_{i},y_{i}\) & The private/public key pair for voter \(i\) where \(y_{i}=g^{x_{i}}\) \\ \(n_{o},n_{c}\) & The number of voters and candidates in the election \\ \([n_{o}],[n_{c}]\) & The set of all voters and all candidates \\ \(p_{i,j}\) & The score assigned to candidate \(j\) by voter \(i\) \\ \(p_{j}\) & The aggregate score for candidate \(j\) \\ \(Y_{i}\) & The composite public key \\ \(x_{i,j}\) & The private voting key for each voter \(i\) where \(j\in[n_{c}]\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Key notations.  
score each individual candidate within a specified range, such as 0 to 5. After all candidates on a ballot have been scored, the sum of the scores should be exactly equal to a number predefined by the election authority. The result is tabulated by obtaining a summation of the scores for each candidate, with the candidate receiving the highest score being declared the winner. Score voting allows the voters to express preferences of varying degrees for different candidates and has been shown to be more advantageous than plurality voting and ranked choice voting (RCV). According to Ref. [25], _score voting eliminates split votes (where no winner receives a majority) and reduces the number of spoiled ballots (ballots that have been marked or tabulated incorrectly) as compared to plurality and ranked systems_. Moreover, score voting enables a more accurate measure of support amongst losing candidates and is easy to implement on current election systems because it does not require the complex tallying algorithms that normal ranked-choice voting needs. Figure 1 gives an example of a score-based ballot in comparison with a plurality system. Each candidate receives a score from each of the three voters; the candidate who receives the highest score on a single vote is assumed to have won the point in a plurality system. It can be seen that here [PERSON] received the highest score twice, making him the winner in a traditional plurality system; however, [PERSON] aggregated the highest score, giving him the victory in a score-based election.  
Figure 1: Illustration of a score-based election with three voters and three candidates (**a**). In (**b**), the corresponding plurality vote is visible on the left of each ballot. Notice how plurality voting yields a deceptive result when compared to the score-based result. (**a**) Example of three different votes in a score-based election. The ballot includes three candidates namely [PERSON], [PERSON], and [PERSON]. The ballot includes a score of four per candidate. The voter has to select one score per each candidate. (**b**) The results of the score-based and regular elections.