2019-12 Indicative Votes - Preferential
The full paper can also be found here.
INDICATIVE VOTES, ROUND TWO – MONDAY 1ST APRIL
The aim of this paper is to hazard a guess at how the indicative votes cast in the House of Commons on Monday 1st April might have produced a different outcome if the voting methodology had been different. As it was, the MPs used a form of approval voting, each having the opportunity to vote ‘for’ or ‘against’ – that or abstain – on four separate options. As happened in the first round of indicative voting on 27th March, (and as was the case in 2003 when the House voted on five different options on the question of reforming the House of Lords), none of the options received a majority.
Table 1 records what actually happened, with the additional data of the result of the so-called ‘meaningful vote 3’ on May’s withdrawal deal.
Table 1 The Indicative Votes
Motions: |
|
E |
C |
D |
G |
||||||
Options: |
May’s Deal |
May’s Deal + People’s Vote |
Customs Union |
Common Market 2.0 |
no deal v revoke |
||||||
Sponsor: |
Theresa May |
Peter Kyle Phil Wilson |
Ken Clarke |
Nick Boles |
Joanna Cherry |
||||||
MPs |
‘for’ |
‘against’ |
‘for’ |
‘against’ |
‘for’ |
‘against’ |
‘for’ |
‘against’ |
‘for’ |
‘against’ |
|
Tory |
313 |
277 |
34 |
15 |
253 |
37 |
236 |
33 |
228 |
10 |
260 |
Lab |
245 |
5 |
234 |
203 |
24 |
230 |
10 |
185 |
25 |
121 |
18 |
SNP |
35 |
|
34 |
31 |
|
|
|
32 |
|
32 |
|
L-D |
11 |
|
11 |
11 |
|
1 |
5 |
2 |
4 |
10 |
|
TIG |
11 |
|
11 |
11 |
|
|
11 |
|
11 |
11 |
|
DUP |
10 |
|
10 |
|
10 |
|
10 |
|
10 |
|
10 |
Ind |
11 |
4 |
5 |
4 |
5 |
5 |
3 |
5 |
3 |
2 |
4 |
PC |
4 |
|
4 |
4 |
|
|
|
4 |
|
4 |
|
GP |
1 |
|
1 |
1 |
|
|
1 |
|
1 |
1 |
|
Totals* |
641 |
286 |
344 |
280 |
292 |
273 |
276 |
261 |
282 |
191 |
292 |
Total voting♯ |
630 |
572 |
549 |
543 |
483 |
* 7 SF members are absent; the Speaker doesn’t vote; and there’s one vacant seat; so to make the total of 650 MPs altogether.
♯ More MPs voted on May’s deal, in part because the 28 cabinet members abstained from the indicative votes.
________________
In Table 2, the author estimates how these MPs might have voted if they had been able to cast their preferences, bearing in mind a number of factors:
a) Some parties sometimes use whips although within parties, some MPs sometimes rebel.
b) The Tory party is split, and the ERG, of which there are/were about 95 members, is itself split. The Labour Party also has its various factions.
c) Sometimes, and especially in majority voting, MPs voting ‘for’ do not necessarily vote in favour of the option concerned or even ‘against’ the perceived opposite, but because of other considerations, even the more remote possibilities of a general election, the resignation of the premier, or whatever.
So now, the analysis. In Table 2, the right-hand side of each column – E, C, D and G – are running totals which culminate in the bold italicised figures, which coincide with all the various totals given in Table 1. The author has had to speculate as to how different MPs might have cast their preferences, and given that the data available – the MPs’ indicative votes – showed only their approvals, the data below must be taken as his best estimates.
The "May's deal" column is not included in the analysis of the indicative votes shown in Table 3. It would have been at least interesting to have included the withdrawal deal in the indicative vote, but it wasn’t; so it is not included in this analysis either except, as for example in the four Tories in the third row, where it is then assumed that the four voted for option E as a 2nd preference.
Table 2 The Indicative Votes
Motions: |
|
E |
C |
D |
G |
||||||
Options: |
May’s Deal |
May’s Deal + People’s Vote |
Customs Union |
Common Market 2.0 |
no deal v revoke |
||||||
Sponsor: |
Theresa May |
Peter Kyle Phil Wilson |
Ken Clarke |
Nick Boles |
Joanna Cherry |
||||||
Tory 313 |
258 |
1st |
258 |
|
|
|
|
|
|
|
|
10 |
1st |
268 |
|
|
|
|
|
|
2nd |
10 |
|
4 |
1st |
272 |
2nd |
4 |
|
|
|
|
|
|
|
5 |
1st |
277 |
|
|
2nd |
5 |
|
|
|
|
|
14 |
|
|
|
|
1st |
19 |
2nd |
14 |
|
|
|
2 |
|
|
|
|
1st |
21 |
|
|
|
|
|
8 |
|
|
|
|
|
|
1st |
22 |
|
|
|
5 |
|
|
|
|
2nd |
26 |
1st |
27 |
|
|
|
5 |
|
|
3rd |
9 |
1st |
31 |
2nd |
32 |
|
|
|
5 |
|
|
2nd |
14 |
1st |
36 |
|
|
|
|
|
1 |
|
|
3rd |
15 |
2nd |
37 |
1st |
33 |
|
|
|
Labour 245 |
25 |
|
|
1st |
25 |
2nd |
25 |
3rd |
25 |
|
|
25 |
|
|
1st |
50 |
2nd |
50 |
|
|
3rd |
25 |
|
60 |
|
|
1st |
110 |
2nd |
110 |
3rd |
85 |
|
|
|
30 |
|
|
|
|
1st |
140 |
2nd |
115 |
|
|
|
17 |
|
|
2nd |
127 |
1st |
157 |
|
|
3rd |
42 |
|
13 |
|
|
|
|
1st |
170 |
2nd |
128 |
3rd |
55 |
|
45 |
|
|
3rd |
172 |
2nd |
215 |
|
|
1st |
100 |
|
15 |
|
|
2nd |
187 |
1st |
230 |
3rd |
143 |
|
|
|
21 |
|
|
|
|
|
|
1st |
164 |
2nd |
121 |
|
16 |
|
|
2nd |
203 |
|
|
1st |
180 |
|
|
|
5 |
1st |
5 |
|
|
|
|
2nd |
185 |
|
|
|
SNP 35 |
27 |
|
|
1st |
27 |
|
|
2nd |
27 |
3rd |
27 |
4 |
|
|
2nd |
31 |
|
|
1st |
31 |
3rd |
31 |
|
1 |
|
|
|
|
|
|
2nd |
32 |
1st |
32 |
|
L-D 11 |
9 |
|
|
1st |
9 |
|
|
|
|
2nd |
9 |
1 |
|
|
3rd |
10 |
|
|
2nd |
1 |
1st |
10 |
|
1 |
|
|
2nd |
11 |
1st |
1 |
3rd |
2 |
|
|
|
TIG 11 |
|
|
|
1st |
11 |
|
|
|
|
2nd |
11 |
IND 11 |
4 |
1st |
4 |
|
|
|
|
|
|
|
|
3 |
|
|
2nd |
3 |
1st |
3 |
3rd |
3 |
|
|
|
2 |
|
|
|
|
2nd |
5 |
1st |
5 |
3rd |
2 |
|
1 |
|
|
1st |
4 |
|
|
|
|
|
|
|
PC 4 |
|
|
|
1st |
4 |
|
|
2nd |
4 |
3rd |
4 |
GP 1 |
|
|
|
1st |
1 |
|
|
|
|
2nd |
1 |
TOTALS |
|
286 |
|
280 |
|
273 |
|
261 |
|
191 |
Table 3 is an extract from Table 2, to show the totals of MPs’ cast preferences. The figures shown in bold italics confirm the mathematics. The important data, the numbers at the bottom of this table, will be used in Table 4, in the final analysis.
Table 3 The Estimated Preferences Cast
Motions: |
E |
C |
D |
G |
||||
Options: |
May’s Deal + People’s Vote |
Customs Union |
Common Market 2.0 |
no deal v revoke |
||||
Sponsor: |
Peter Kyle Phil Wilson |
Ken Clarke |
Nick Boles |
Joanna Cherry |
||||
Tory |
1st |
|
26 |
14 |
|
|||
2nd |
9 |
11 |
19 |
10 |
||||
3rd |
6 |
|
|
|
||||
Totals |
15 |
37 |
33 |
10 |
||||
Lab |
1st |
110 |
75 |
37 |
45 |
|||
2nd |
48 |
155 |
48 |
21 |
||||
3rd |
45 |
|
100 |
55 |
||||
Totals |
203 |
230 |
185 |
121 |
||||
SNP |
1st |
27 |
|
4 |
1 |
|||
2nd |
4 |
|
28 |
- |
||||
3rd |
|
|
|
31 |
||||
Totals |
31 |
|
32 |
32 |
||||
L-D |
1st |
9 |
1 |
|
1 |
|||
2nd |
1 |
|
1 |
9 |
||||
3rd |
1 |
|
1 |
|
||||
Totals |
11 |
1 |
2 |
10 |
||||
TIG |
1st |
11 |
|
|
|
|||
2nd |
|
|
|
11 |
||||
3rd |
|
|
|
|
||||
Totals |
11 |
|
|
11 |
||||
IND |
1st |
1 |
3 |
2 |
|
|||
2nd |
3 |
2 |
|
|
||||
3rd |
|
|
3 |
2 |
||||
Totals |
4 |
5 |
5 |
2 |
||||
PC |
1st |
4 |
|
|
|
|||
2nd |
|
|
4 |
|
||||
3rd |
|
|
|
4 |
||||
Totals |
4 |
|
4 |
4 |
||||
GP |
1st |
1 |
|
|
|
|||
2nd |
|
|
|
1 |
||||
|
Totals |
1 |
|
|
1 |
|||
|
1st |
163 |
105 |
55 |
47 |
|||
|
2nd |
65 |
168 |
102 |
51 |
|||
|
3rd |
52 |
- |
104 |
93 |
|||
Grand Totals |
280 |
273 |
261 |
191 |
||||
|
|
|
|
|
|
|
|
|
The Analysis
A preferential vote can be analysed in any one of at least four ways, and these include a Borda count, BC; an alternative vote, AV;[i] a modified Borda count, MBC; and the Condorcet rule. In many analyses, especially in those where most voters have cast all or nearly all of their preferences, so to submit a full or nearly full ballot, the MBC social choice is the same as the Condorcet winner, and even the two social rankings are similar. Accordingly, this analysis will focus on the first three methodologies: BC, AV and NBC.
It might have been possible to suggest that a vote ‘against’ was a 4th preference, and that an abstention was a 2nd and/or 3rd. The wiser course of action, however, given that so many assumptions have already been made, was to keep the number of assumptions as small as possible. So there is no account of 4th preferences; and in any case, a vote of 1st-2nd-3rd-nothing is not too different from one of 1st-2nd-3rd-4th.
It is necessary to pause a little, to explain the difference between a BC and an MBC, which is this: in a BC, the voter is not encouraged to cast more than his 1st preference; in an MBC, she is. Basically, in a vote on n-options, voters may cast as many preferences as they want – the number cast is referred to as m and, needless to say, n ≥ m ≥ 1. Now in a BC, points are awarded to (1st, 2nd … last) preferences cast according to the rule (n, n-1 … 1).[ii] So she who casts only one preference gets n points for her favourite, and thus an n point advantage over all the other options. In an MBC, in contrast, the rule is (m, m-1 … 1), so he who casts only one preference gives his favourite just 1 point, and thus gains only a 1 point advantage over the other options. But she who casts m preferences, gets m points for her favourite, m-1 points for her 2nd choice, and so on. Overall, therefore, the last-named voter gains a 1 point advantage for her favourite over her 2nd choice but, if she casts a full ballot, an n-1 point advantage over her least favourite option.
Now of course, MPs casting their preferences in an indicative vote might adjust their voting pattern if they know which methodology is to be used.
It is time, now, to analyse the data from Table 3.
The BC Analysis
Every 1st preference gets 3 points, every 2nd preference gets 2 points and every 3rd gets 1 point.
Option E gets 163 x 3 + 65 x 2 + 52 x 1§
= 489 + 130 + 52
= 671
Option C gets 105 x 3 + 168 x 2 + 0§
= 315 + 336
= 651
Option D gets 57 x 3 + 100 x 2 + 104 x 1§
= 171 + 200 + 104
= 475
Option G gets 49 x 3 + 52 x 2 + 90 x 1§
= 147 + 104 + 90
= 341
So the winner is option E on 671.
§ And 163 + 65 + 52 = 280
105 + 168 + 0 = 273
57 + 100 + 104 = 261
49 + 52 + 90 = 191
The AV Analysis
In stage (i), the scores are:
E 163 C 105 D 55 G 49
So G is eliminated, and because it has no transfers, the stage (ii) scores are:
E 163 C 105 D 55
Which means D is now eliminated, and from these 55 1st preferences, 8 votes go to C, 20 go to E, and 27 are non-transferable, so
in stage (iii), the scores are:
E 183 C 113
So the winner is again E on 183.
The MBC Analysis
An MBC analysis is best (and usually) done on a computer. When laid out on paper, it does get a bit complex. For the sake of clarity, however, that is what will be done here. The rule, then, is as follows:
The 1st of 3 preferences gets 3 points;
the 2nd of 3, or a 1st of 2 preferences, gets 2 points;
the 3rd of 3, a 2nd of 2, or a 1st and only of 1 preference, gets 1 point.
So Option E gets: (25 + 25 + 60 + 27 + 4) x 3 +
(5 + 15 + 16 + 4 + 9 + 1 + 11 + 3 + 1) x 2 +
(4 + 5 + 1 + 17 + 45 + 1 + 1) x 1
= 141 x 3 + 65 x 2 + 74 x 1§§
= 423 + 130 + 74
= 691
Option C gets: (5 + 17 + 13 + 15 + 1 + 3) x 3 +
(14 + %5 + 5 + 1 + 25 + 25 + 60 + 30 + 45 + 2) x 2
(5 + 2) x 1
= 54 x 3 + 212 x 2 + 7 x 1§§
= 162 + 424 + 7
= 593
Option D gets : (1 + 4 + 2) x 3
= (5 + 5 + 13 + 21 + 16 + 27 +1 + 1 + 4) x 2 +
= (14 + 8 + 25 + 60 + 30 + 15 + 5 + 1 + 3) x 1
= 7 x 3 + 93 x 2 + 161 x 1§§
= 21 + 186 + 161
= 368
Option G gets: (45 + 1) x 3 +
(1) x 2 +
(10 + 25 + 17 + 13 + 21 + 27 + 4 + 9 + 11 + 2 + 4 + 1) x 1
= 46 x 3 + 1 x 2 + 144 x 1§§
= 138 + 2 + 144
= 284
§§ So again, 141 + 65 + 74 = 280
54 + 212 + 7 = 273
7 + 93 + 161 = 261
and 46 + 1 + 144 = 191
So the winner is yet again option E, now on 691.
All of the above results are summarised in Table 4.
Table 4 The Results
Motions: |
E |
C |
D |
G |
Social ranking |
Options: |
May’s Deal + People’s Vote |
Customs Union |
Common Market 2.0 |
no deal v revoke |
|
Sponsor: |
Peter Kyle Phil Wilson |
Ken Clarke |
Nick Boles |
Joanna Cherry |
|
BC |
671 |
651 |
475 |
341 |
E-C-D-G |
AV |
183 |
113 |
- |
- |
E-C |
MBC |
691 |
593 |
368 |
284 |
E-C-D-G |
So the social choice in each analysis is option E.
Conclusion
As was seen in the House in 2003, if and when there are more than two options ‘on the table’, taking a corresponding number of majority votes is not a suitable methodology. Indeed, to quote Lord Meghnad Desai[iii] at the time, it was “daft;” instead he recommended (but did not name) a rankings system, the BC. (Hansard, 22.1 2003.)
With preference voting, an outcome is almost guaranteed; and if that outcome has a sufficiently high score, it may then be declared the winner, just as in majority voting, a result might depend on a similarly pre-determined simple or weighted majority. Of the three methodologies analysed in this paper, it should be emphasised that the BC is not necessarily consensual; AV can be capricious; while along with Condorcet, whenever “there are more than two” options, the MBC is “the best interpretation of majority rule.” (Oxford Concise Dictionary of Politics, Iain McLean, 2003, oup, p 139.)
In a nutshell, majority voting cannot best identify the consensus or even the best possible compromise; indeed, with so many votes ‘for’ and so many ‘against’, it measures the very opposite, the degree of dissent.
In contrast, by comparing the totals each option receives with the maximum possible score, the MBC can measure the degree of consensus with a high degree of accuracy.
Postscript
As with any form of voting, additional rules can be applied viz-a-viz minimum turnout and so on. Suffice here to say that the MBC is a highly accurate and very robust counting procedure and, if used with electronic voting, very practicable.
Recommendation
Whenever there are more than two options ‘on the table’, parliament should use a form of preference voting, and ideally, either the MBC and/or the Condorcet rule.
Peter Emerson
The de Borda Institute
36 Ballysillan Road
Belfast Bt14 7QQ
02890711795
07837717979
www.deborda.org
[i] Also known as single transferable vote, STV, (the latter usually in its PR format as an electoral system, PR-STV), but also as instant run-off voting, IRV, in North America, and preference vote, PV, in Australasia.
[ii] Some prefer the rule (n-1, n-2 … 0), which makes no difference to the outcome.
[iii] For the current author’s analysis of that “daft” voting procedure, see Reforming the House of Lords: Choosing from the Options. In Representation, 2005, Vol. 41, № 4.
http://www.tandfonline.com/doi/abs/10.1080/00344890508523322