Distributed Voting: Difference between revisions

===Candidates===

In an election between candidates (with at least 3 winners), proceed as follows:

* 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).

Result: d1{ A[40%] B[35%] C[25%] } d2{ B[40%] C[35%] D[25%] }

Seat weights: d1{ A[0.28] B[0.245] C[0.175] } d2{ B[0.12] C[0.105] D[0.075] }

Total power: A[28%] B[36.5%] C[25%] D[6%]

Result: d1{ A[2] B[1] C[1] } d2{ B[1] C[1] }