Its a non-issue. The SC and I have already had this discussion with Sleazy. I implemented Broda counts as the constitution requires, using the published definition from seven different sources. Borda counts typically start with one. And it did not matter one bit in this election. (See http://en.wikipedia.org/wiki/Borda_count .)
1. The difference between 1 and 0 based Borda counts is to add a constant to every count for every faction.
2. In this election, I programmed both methods to make sure, and there was no difference in outcome.
3. The scores published were the consistent with the published definition, and there is unlikley to be a difference, but I would prefer we use zero-based counts in future elections. However, the constitution will have to be changed to allow this.
Here is more on each point:
1. The difference between 1 and 0 based Borda counts is to add a constant to every count.
Lets compare some votes for factions A, B, C, D. A 1-based vote, and a 0-based vote. See how they add up:
Vote: ABCD
1-based: A add: 4, B add: 3, C add: 2, D add: 1
0-based: A add: 3, B add: 2, C add: 1
Difference: A add: 1, B add: 1, C add: 1, D add: 1
Vote: ABC_ (note that excluded are counted at the lowest point level, 1 or 0)
1-based: A add: 4, B add: 2, C add: 2, D add: 1
0-based: A add: 3, B add: 2, C add: 1
Difference: A add: 1, B add: 1, C add: 1, D add: 1
Vote: AB_ _
1-based: A add: 4, B add: 2, C add: 1, D add: 1
0-based: A add: 3, B add: 2
Difference: A add: 1, B add: 1, C add: 1, D add: 1
Vote: A_ _ _
1-based: A add: 4, B add: 1, C add: 1, D add: 1
0-based: A add: 3
Difference: A add: 1, B add: 1, C add: 1, D add: 1
In other words: The difference between the 0-based and 1-based systems is to add one point to each faction, equally for each voter.
2. In this election, I programmed both methods to make sure, and there was no difference in outcome.
Output from the program:
Code: Select all
Unmodified 0-based Borda count election with 0 point added for each unranked faction.
7 seats will be allocated to parties CSDF, DPU, NuCARE, SP.
Final Borda counts: CSDF = 84, DPU = 48, NuCARE = 54, SP = 59
Sainte Lague Process for 7 Seats
Final seat allocation:
CSDF = 2, DPU = 1, NuCARE = 2, SP = 2
3. The scores published were the consistent with the published definition, and there is unlikley to be a difference, but I would prefer we use zero-based counts in future elections. However, the constitution will have to be changed to allow this
In general I favor a zero based way of counting, (the math is simpler) but there are trade offs that have to be considered. The total number of Borda points available in a zero-based election p depends on the number of voters v, and the number of factions f:
p = v * f * (v - 1) / 2
This is constant for any one election. We can write the results of an election as s(i) where i is the faction number where s(i) is the proportion of all available points earned by that faction. The number of Borda points faction i gets will be:
p * s(i)
The ordering of factions will never change for a one-based Borda vs a zero-based election because a constant, the number of voters, is added to the zero-based Borda counts to give the one-based counts. Likewise if s(A) > s(B) then faction A will always have equal or greater number of seats. The real question is when is the number of seats equal or greater and by how many seats.
Since we use a proportional allocation scheme for seats, seat allocation will depend on the ratio of Borda counts. The ratio of Borda counts for factions A and B in a zero-based election is:
s(A) / s(B)
The ratio between of Borda counts for A and B for the one-based election we just held is:
[s(A) + 1/6] / [s(B) + 1/6]
The difference between the two ratios decreases towards 0 as S(A) and S(B) get closer and is always positive if S(A) is greater than S(B), so there is a slight disadvantage for factions with higher scores in the one-based election. A difference that, in our election, did not change the seat allocation.
Take, in our case, an election with 264 points, and say zero-based Borda counts for faction A is 84 (S(A) = 0.32) and faction B is 59 (S(B) = 0.22). The ratio is approx 1.24 under the one-based election, but 1.42 under the zero-based election. We would have to have more than five seats per faction for this to result in an additional seat for faction A.
