PRO-V

Product Voting (PRO-V) is a Single-Winner Cardinal voting systems developed by Aldo Tragni.

The objectives of this voting system is the balance between simplicity, resistance to strategies, elect utilitarian winner and provide the voter with a good representation of interests (range with 5 ratings).

Procedure

Voter score candidates with ratings [1,2,3,4,5].

For each candidate, the multiplication is made among all the ratings received by him, and the candidate with the highest result wins.

Product

The formula used in the count is the following:

Failed to parse (unknown function "\begin{equation}"): {\displaystyle \begin{equation}  C_{i}=\prod V_{ij}  \end{equation}}

Ci  = final score of a candidate Ci.
Vij = values ​​of candidate Ci, obtained from the ballots.

However, this formula can return very large results, difficult to manage.

In computer systems the following formula can be used :

Failed to parse (unknown function "\begin{equation}"): {\displaystyle \begin{equation}  C_{i} =\prod \sqrt[n]{V_{ij}}  \end{equation}}

n = total number of votes.

If you have paper ballots then, before counting, you can eliminate ratings 1 and those ratings that appear at least once on all candidates, even in different votes.

Eg given these 3 votes:

A[1] B[2] C[3] D[3] E[5]
A[3] B[5] C[1] D[2] E[3]
A[5] B[3] C[2] D[4] E[1]

delete the ratings 1, and 3 that appears at least once on all candidates, making the votes like this:

     B[2]           E[5]
     B[5]      D[2]
A[5]      C[2] D[4]

so there is less multiplication to do.

Name derivation

PRO-nV: the PRO-V procedure works with ranges of different sizes and n indicates the amount of ratings used in the range.

• PRO-2V: uses ratings in [1,2].
• PRO-V: is the default definition, with ratings in [1,5].
• FAIR-9V: uses ratings in [1,9].

Voting systems comparison

FAIR-V

The proportional ratings of the PRO-V make the intermediate ratings more used by the voter, because eg. adding these two votes A[1] B[2] (B is worth double A) and A[4] B[2] (A is worth double B), candidates A and B are equal, unlike the methods that add up the scores. A single point can make a lot of difference. Taking this characteristic of the PRO-V into consideration, and following the analysis of the resistance to strategies in FAIR-V, it can be seen that PRO-V is also resistant to strategies, but not as strong as FAIR-V which uses a range [0,2].

However, the PRO-V procedure is easier to understand than the FAIR-V one, and also offers a wider range of ratings to the voter.