8. | MODEL ELECTION |
The model election is devised to illustrate the main features of an STV count. There are eleven candidates, and six places to be filled. |
8.1 | First Stage |
The total vote is 758. The voting papers are sorted according to first preferences for the eleven candidates. Three voting papers are marked with several crosses, and two have the figure '1' against more than one candidate. These five invalid papers are set aside. The vote for each candidate is entered onto the vote record forms and on the election result sheet. The total valid vote is 753. The number of places to be filled is six. The Quota is determined by dividing the total valid vote by one more than the number of places to be filled, seven, continuing the calculation to two decimal places, and rounding up. 753/7 = 107.57142 Quota = 107.58 | |
One candidate, Smith, with a vote of 134, exceeds the quota, and is deemed elected. The first line of the upper part of the Count Control form is completed. |
8.2 | Second Stage |
Smith has a surplus of 134 - 107.58 = 26.42 This exceeds the difference between the votes of the last two candidates, (24 - 23 = 1). Since the transfer of the surplus could thus change the order of the last two candidates, and thereby determine the candidate next to be excluded, the surplus must be transferred. | |
Smith has 134 papers for review, of which 123 prove to be transferable. Since the total present value of these papers, 123, exceeds the surplus of 26.42, this surplus is shared between the transferable papers, to give, for each paper, a transfer value to two decimal places of: 26.42/123 = 0.21 Each of the candidates is credited on their vote record form with the value of the papers received, at the transfer value of 0.21, and these credits, together with the non-transferable difference arising from the neglected remainder 26.42 - (123 x 0.21) = 26.42 - 25.83 = 0.59 are recorded on the result sheet, which again shows the total valid vote at 753. |
COUNTING SLIP CANDIDATE NUMBER OF PAPERS TRANSFER VALUE |
8.3 | Third stage |
Since there is now no outstanding surplus, one or more candidates must next be excluded. The total of the votes of the last two candidates exceeds the vote of the candidate next above. Therefore the last candidate only, Monk, is excluded. | |
Monk‘s papers are arranged in descending order of transfer value, |
23 @ 1 | = | 23 |
2 @ 0.21 | = | 0.42 |
23.42 |
The 23 whole value papers are transferred first, passing over any preferences for Smith, who is already elected, and are entered on the vote record forms. A second candidate, Duke, now exceeds the Quota, and is deemed elected. The second line of the upper part of the Count Control form is completed. | |
The two papers at 0.42 are then transferred, passing over any preferences for Duke as well as Smith. | |
Each candidate is credited on their vote record form with the value of the papers received at the different transfer values, and these credits, together with the value of the non-transferable papers are recorded on the election result sheet, again giving the total of 753. |
8.4 | Fourth stage |
Duke now has a surplus of 108.68 - 107.58 = 1.10. This is less than the difference between the votes of the two candidates now last, 32.25 - 30.51 = 1.74 and is also less than the difference between the total vote of the last two candidates and the candidate next above, 64.21 - (32.25 + 30.51) = 64.21 - 62.76 = 1.45 Thus, because the transfer of the surplus could not change the order of the last two candidates or of the last three candidates, on either ground the transfer of the surplus is deferred. The last two candidates are now excluded together, because their total vote, together with the untransferred surplus, is (32.25 + 30.51) + 1.10= 62.76 + 1.10 = 63.86 which is less than the vote of the candidate next above, at 64.21 while the total vote of the last three candidates, together with the untransferred surplus, is (32.25 + 30.51 + 64.21) + 1.10 = 128.07 which is much greater than the vote of the candidate next above, at 64.84. Their papers are arranged in descending order of transfer value, |
51 @ 1 | = | 51 |
56 @ 0.21 | = | 11.76 |
62.76 |
The 51 whole-value papers are transferred first, passing over any preferences for any candidate already elected or excluded, and are entered on the vote record forms. A third candidate, Carpenter, now exceeds the quota, and is deemed elected. The third line of the upper part of the Count Control form is completed. | |
The 56 papers at 0.21 are then transferred, passing over any preferences for Carpenter as well as for the other elected and excluded candidates. | |
The vote record forms and the election result sheet are completed as before. | |
There are 6.79 non-transferable votes and three candidates have been deemed elected. The reduced vote required for election is calculated on the first line of the lower part of the Count Control form, confirming that no-one else can be deemed elected yet. |
8.5 | Fifth stage |
Carpenter and Duke now both have surpluses whose total value is 14.77 + 1.10 = 15.87 This exceeds the difference between the votes of the two candidates now last 68.26 - 67.10 = 1.16 Since the transfer of these surpluses could change the order of the last two candidates, the larger surplus is transferred. Carpenter's surplus has arisen through the exclusion of Glazier and Wright. The transfer of Carpenter's surplus is thus in effect the completion of the exclusion of these two candidates. Hence the papers for review are the 34 papers last received, of which 8 prove to be transferable. Since the total present value of these papers, 8 does not exceed the surplus of 14.77, these papers are transferred at a transfer value equal to the value at which they were received. Each candidate is credited on his vote record form with the value of the papers received, and these credits together with the non-transferable difference: 14.77 - 8 = 6.77 are entered as before on the result sheet. A further line of the lower part of the Count Control form is completed. The reduced vote required for election is now 104.18. This is exceeded by Prince's vote of 104.31. Prince is therefore deemed elected and a fourth line of the upper part of the Count Control form is now completed. A third line of the lower part of the Count Control form calculates the new reduced vote required for election, confirming that no-one else can be deemed elected yet. |
8.6 | Sixth stage |
Duke still has a surplus of 1.10. This is less than the difference between the votes of the last two candidates, 70.26 - 68.10 = 2.16 Because the transfer of the surplus could not change the order of the last two candidates, the transfer of the surplus is again deferred. The candidate now last, Abbot, is excluded. Abbot‘s papers are arranged in descending order of transfer value, |
66 @ 1.00 | = | 66 |
10 @ 0.21 | = | 2.10 |
68.10 |
The 66 whole value papers are transferred first. Vicar now exceeds the quota and is the fifth candidate to be deemed elected. A fifth line of the upper part of the Count Control form is completed, followed by a fourth line in the lower part of that form. This calculates that the vote now required for election is 96.41. | |
This is exceeded by Freeman's vote of 101.62. Freeman is therefore deemed elected to fill the last place. | |
No further transfers of papers are made. The ten papers value 0.21 each remain with Abbot, the vote record forms and the election result sheet are completed, and the remaining candidate, Baron, is formally excluded. | |
Smith, Duke, Carpenter, Prince, Vicar and Freeman are declared elected, and the count is concluded. |
VOTE RECORD FORM | VOTE RECORD OF CANDIDATE Abbot |
QUOTA 107.58 |
Stage |
From |
Number of papers |
Transfer value |
Value received |
Present vote |
First |
First preferences |
59 |
1.00 |
59.00 |
59 |
Second |
Smith |
4 |
0.21 |
0.84 |
59.84 |
Third |
Monk |
5 |
1.00 |
5.00 |
64.84 |
Fourth |
Glazier & Wright |
1 |
1.00 |
1.00 |
65.84 |
ditto |
do |
6 |
0.21 |
1.26 |
67.10 |
Fifth |
Carpenter |
1 |
1.00 |
1.00 |
68.10 |
ERS2 |
COUNT CONTROL FORM | ||
Election for Model election |
Date | |
Number of seats to be filled 6 |
Total Valid Vote 753 |
Quota 107.58 |
Calculation of total votes attributed to elected candidates |
No. |
|
Votes |
Surplus |
|
Total vote less votes of elected candidates (f) |
Seats remaining to be filled + 1 (g) |
1 |
Smith |
134.00 |
26.42 |
107.58 |
645.42 |
6 |
2 |
Duke |
108.68 |
1.10 |
107.58 |
537.84 |
5 |
3 |
Carpenter |
122.35 |
14.77 |
107.58 |
430.26 |
4 |
4 |
Prince |
104.31 |
104.31 |
325.95 |
3 |
|
5 |
Vicar |
113.31 |
5.73 |
107.58 |
218.37 |
2 |
6 |
Freeman |
101.62 |
101.62 |
116.75 |
||
Calculation of Vote Required for Election
|
Total vote less votes of elected candidates (from col. f) |
LESS: Non-transferable votes |
EQUALS: Total free votes |
DIVIDE BY: |
EQUALS: Vote now required for election |
4 |
430.26 |
6.79 |
423.47 |
4 |
105.87 |
5 |
430.26 |
13.56 |
416.70 |
4 |
104.18 |
5 |
325.95 |
13.56 |
312.39 |
3 |
104.13 |
6 |
218.37 |
25.56 |
192.81 |
2 |
96.41 |
ERS 6 | Electoral Reform Society |
8.7 | Observations on model election |
8.7.1 | Proportional representation |
The transfers at successive stages of the count reveal three groups or 'parties'. The first preferences for candidates of these parties is shown at the first stage: |
Artisans |
Nobles |
Clerics |
Independent |
||||
Smith |
134 |
Duke |
105 |
Abbot |
59 |
Freeman |
90 |
Carpenter |
81 |
Prince |
91 |
Vicar |
55 |
||
Wright |
27 |
Baron |
64 |
Monk |
23 |
||
Glazier |
24 |
|
|
|
|||
266 |
260 |
137 |
90 |
At the first stage, of the six leading candidates, two are artisans, three nobles and one independent. At the end of the count, however, consequent upon the successive transfers of votes, of the six elected candidates, two are artisans, two nobles, one cleric and one independent, which is proportional to the support for the 'parties'. Thus proportional representation of opinion, as represented by the 'parties' has been achieved. | |
The term 'parties' is used here in the very general sense to indicate any criterion which significantly motivates electors when they vote. In some elections, parties may not be discernible. |