Correction
Voting matters, Issue 22, July 2006
Developing STV Rules for manual counting to give effect to the Weighted Inclusive Gregory Method of transferring surpluses, with candidates’ votes recorded as integer values
James Gilmour
e-mail: jgilmour@globalnet.co.uk
Vote fraction not transferred
Since this article was published Chris Jerdonek has pointed out that under the proposed rules, the ‘Vote fraction not transferred’ (VFNT) can be negative when one candidate is excluded alone and not just when a multiple exclusion occurs as stated in the last paragraph of section 5 of the paper (page 24). In both cases, the VFNT can be negative when the sum of the values of all the ballot papers, including all the fractional parts , held by the excluded candidate(s) exceeds the sum of the integer votes credited to the excluded candidate(s), as the following examples show (all unnecessary decimal places suppressed for clarity).
Single exclusion
Candidate A has 100 first preference votes and receives transferred votes from B’s surplus at stage 2 and from C’s surplus at stage 3. Candidate A is then excluded at stage 4 with all votes transferred to candidate D.
Stage 2: B’s surplus to A
30 papers @ 0.33 = 9.9
Votes transferred to A = 9
A’s total vote = 100 + 9 = 109
Stage 3: C’s surplus to A
20 papers @ 0.17 = 3.4
Votes transferred to A = 3
A’s total vote = 100 + 9 + 3 = 112
Stage 4: A excluded; all papers transferable to D
100 first preference papers @ 1.0 = 100
30 papers @ 0.33 = 9.9
20 papers @ 0.17 = 3.4
Total value of transferable papers = 100 + 9.9 + 3.4 = 113.3
Votes transferred to D = 113
Total vote credited to A was 112, so VFNT = 112 – 113 = -1
Multiple exclusion
Candidates A, B and C, with 50, 40 and 30 first preference votes respectively, all receive transferred votes from the surplus of candidate D at Stage 2. Candidates A, B and C are excluded together at stage 3 with all votes transferred to candidate E.
Stage 2: transfer of D’s surplus
to A: 30 papers @ 0.33 = 9.9
A’s total vote = 50 + 9 = 59
to B: 20 papers @ 0.33 = 6.6
B’s total vote = 40 + 6 = 46
to C: 10 papers @ 0.33 = 3.3
C’s total vote = 30 + 3 = 33
Stage 3: A, B and C excluded together; all papers transferable to E
50 + 40 + 30 = 120 first preference papers @ 1.0 = 120
30 + 20 + 10 = 60 papers @ 0.33 = 19.8
Total value of transferable papers = 120 + 19.9 = 139.9
Votes transferred to E = 139
Total vote credited to A, B and C was 59 + 46 + 33 = 138
So VFNT = 138 – 139 = -1
I am grateful to Chris Jerdonek for bringing this to my attention.
James Gilmour
2 August 2006