|
The Distributed Voting indicates the method for obtaining single or multiple winners. The Distributed Voting System also describes how seats should be handled.
* The state is divided into districts (at least 2, and possibly of similar size).
===Candidates===
* Each district must have at least 2 seats (at least 3, for a good representation). To satisfy this constraint you can increase the number of total seats or join the districts into groups.
* In each district, the worstDV candidatesis areused eliminated,to leavingobtain a quantitynumber of winners equal to the number of seats in the district. The sum of the points for each winning candidate iswill used to deriveindicate the % of victory of the candidates. ▼In an election between candidates (with at least 3 winners), proceed as follows:
* If P is the power assigned to the district, then the weight of each seat will be: P • "% of victory of the candidate".
* the value S (threshold) is obtained, using the following formula: <math>\begin{equation} S=\frac{50\%+\frac{100\%}{\#seats}}{2} \end{equation}</math>
▲* the worst candidates are eliminated, leaving a quantity of winners equal to the seats. The sum of points for each winning candidate is used to derive the % of victory.
* starting from the best candidate, the [[Surplus Handling]] is applied using S as threshold, that is the points that exceed the threshold are redistributed among other winning candidates, based on the interests expressed in the votes.
* the seats will have a fractional weight equal to the % of victory of the candidates.
Example - 3 winners
Result: A[51%] B[27%] C[22%] S = 41,7% ≈ 40% (rounded for simplicity)
Redistribute A points that exceed 40%
Result: A[40%] B[35%] C[25%]
Seats weight: A[0.4] B[0.35] C[0.25]
Fractional seats offer better proportionality than unit seats, but there is a risk that a candidate alone will gain more than 50% of the power. The formula indicated for S serves to ensure that a single candidate cannot have a majority on his own, while maintaining the benefits of fractional seats. The effectiveness of these properties is noted with increasing seats.
Example - 10 winners
Result: A[30%] B[20%] ... L[1%] S = 30%
Seats weight: A[0.3] B[0.2] ... L[0.01]
A's seat is worth 30 times that of L, in respect of the % of victory obtained by the candidates.
Assigning A and L a seat with the same weight would be unfair.
The difference between the % of victory is reduced in a fair way, through the procedure indicated in the [[Distributed_Voting#All_0_points| All 0 points]] section.
===Parties===
In an election between parties, proceed as follows:
* the value S (threshold) is obtained, using the following formula: <math>\begin{equation} S=\frac{100\%}{\#seats\cdot 2} \end{equation}</math>
* the worst parties are eliminated until both of the following 2 conditions are met:
# the number of winners is less than or equal to the number of seats (if a party has more than 50%, then the number is considered "seats-1").
# all candidates have a % of victory greater than or equal to S.
* 1 seat is assigned to each party (if there is a party that has obtained more than 50%, it will receive 2 seats).
* If seats remain to be filled, they distribute according to % of the party victory, using a method of your choice (as [[D'Hondt method]]).
* dividing the % of victory of the parties by the number of seats they have, the fractional weight of each seat is obtained.
Example - 5 seats
Result: A[39%] B[25%] C[15%] D[9%] E[2%] S = 10% exclude E
Result: A[40%] B[25%] C[15%] D[10%] S = 10%
Seats: A[2] B[1] C[1] D[1]
Seats weight: A[0.2] B[0.25] C[0.15] D[0.1]
if had been used unit seats and S = 20%:
Unit seats: A[2] B[2] C[1]
The fractional seats, through the formula of S, allow for greater proportionality and representation than the unit seats.
A certain party will always have total power equal to the % of victory in the elections, regardless of how many seats are divided by that power. This property solves problems related to the [[Alabama paradox]].
===Districts===
The winning candidates and the fractional weight of the seats are obtained using the methods described above. To ensure representation, the district must be large enough to have at least 2 seats available (at least 3 for a good representation).
Example - 2 districts, 6 seats
Districts: d1{70%} d2{30%}
Seats: d1{3} d2{3}
Result: d1{ AA1[40%] BB1[35%] CC1[25%] } d2{ BB2[40%] CC2[35%] DD2[25%] }
Seat weights: d1{ AA1[0.28] BB1[0.245] CC1[0.175] } d2{ BB2[0.12] CC2[0.105] DD2[0.075] }
Total power: A[28%] B[36.5%] C[25%] D[6%]
If I had unit seats:
Seats: d1{4} d2{2}
Result: d1{ AA1[2] BB1[1] CC1[1] } d2{ BB2[1] CC2[1] }
Total power: A[33.3%] B[33.3%] C[33.3%] D[0]
|