The Election, by Instant Runoff Voting, of UK "Labour Party leader" in late-September 2010

By Jim Riley, Ivan Ryan, Warren D. Smith

Ed Miliband won.

The purpose of this page simply is to summarize the available data about this election, since it was one of the most-important elections (perhaps even the most important) conducted with IRV (Instant Runoff Voting) up to that date. The preceding election on 21 July 1994 (after the unexpected death of leader John Smith) had been conducted using plain-plurality, not IRV, and had elected Tony Blair with 57.0% of the weighted vote, defeating John Prescott (24.1%) and Margaret Beckett (18.9%). The weightings were the same in 1994 and 2010, just the algorithm for using those weighted votes to determine the winner changed. (There also was an "election" in 2007, but not really – Gordon Brown ran unopposed since nobody else succeeded in surpassing the "nomination" hurdles.) From a voting-theory point of view both 1994 and 2010 seem to have been rather boring. In 1994, Blair got 52.3%, 58.2%, and 60.5% in the three voter sections. In 2010, it similarly appears virtually every system ever seriously proposed by mankind would also have (with the same weighted set of voters) elected Ed Miliband, except for the previous plain-plurality system, which would have elected his brother David.

There were 5 candidates, ≈338000 voters, and 4 televised debates. The winner with plain plurality would have been (Ed's older brother and former foreign secretary) David Miliband, who indeed led in every round except for the final round which was Ed 50.65% vs David 49.35%. Eliminated in this order were: Diane Abbott, Andy Burnham, Ed Balls, and David M. There were 3 classes of voters:

  1. Labour MPs and MEPs.
  2. Dues paying Labour Party members. It appears turnout was about 63% among this group of ≈200000. The best turnout was 76.6% of the 1200 Labour members in Hornsey & Wood Green and the worst was 35.5% in Luton North.
  3. Affiliated unions and societies. Roughly 10% turnout of around 3 million or so members. In particular, according to the Manchester Guardian: "Unite the Unions" (the biggest affiliate) distributed over a million ballots but only 10.5% of them voted and 15202 of those ballots were spoiled (which suggests there was about 15% spoilage in section3, an enormous rate). At least one of these unions/societies distributed the ballots accompanied by a recommendation to vote for Ed Miliband; these recommendations may have been enough to bring him his victory.

The three kinds of votes were weighted so that each section had an equal share of the total weight. This caused each of the 266 voters in section1 to be equivalent to ≈794 section3 votes. David won in both section1 and section2 alone, but Ed's win in section3 was large enough, despite the low weights of the section3 votes, to carry the day in the final IRV round.

The election appears to have been nonpathological. Ed Miliband apparently would also have won (with these weighted voters) using range or Borda or Condorcet voting, although David Miliband was the plain-plurality voting winner.

Official results published by Labour Party

Round by round Round 1 Round 2 Round 3 Round 4
ABBOTT, Diane 7.42 0 0 0
BALLS, Ed 11.79 13.23 16.02 0
BURNHAM, Andy 8.68 10.41 0 0
MILIBAND, David 37.78 38.89 42.72 49.35
MILIBAND, Ed 34.33 37.47 41.26 50.65%

 

First Preferences Section 1 % Section 2 % Section 3 % Total %
ABBOTT, Diane 7 0.877 9314 2.447 25938 4.093 7.42
BALLS, Ed 40 5.013 12831 3.371 21618 3.411 11.79
BURNHAM, Andy 24 3.008 10844 2.849 17904 2.825 8.68
MILIBAND, David 111 13.910 55905 14.688 58189 9.182 37.78
MILIBAND, Ed 84 10.526 37980 9.978 87585 13.821 34.33
Total 266 33.333 126874 33.333 211234 33.333 100

 

2nd Round Section 1 % Section 2 % Section 3 % Total %
ABBOTT, Diane 0 0 0 0 0 0 0
BALLS, Ed 41 5.177 14510 3.829 26441 4.224 13.23
BURNHAM, Andy 24 3.030 12498 3.298 25528 4.078 10.41
MILIBAND, David 111 14.015 57128 15.076 61336 9.799 38.89
MILIBAND, Ed 88 11.111 42176 11.130 95335 15.231 37.47
Total 264 33.333 126312 33.333 206640 33.333 100

 

3rd Round Section 1 % Section 2 % Section 3 % Total %
ABBOTT, Diane 0 0 0 0 0 0 0
BALLS, Ed 43 5.429 18114 4.823 35512 5.766 16.02
BURNHAM, Andy 0 0 0 0 0 0 0
MILIBAND, David 125 15.783 60375 16.076 66889 10.861 42.72
MILIBAND, Ed 96 12.121 46697 12.434 102882 16.706 41.26
Total 264 33.333 125186 33.333 205283 33.333 100

 

4th Round Section 1 % Section 2 % Section 3 % Total %
ABBOTT, Diane 0 0 0 0 0 0 0
BALLS, Ed 0 0 0 0 0 0 0
BURNHAM, Andy 0 0 0 0 0 0 0
MILIBAND, David 140 17.812 66814 18.135 80266 13.400 49.35
MILIBAND, Ed 122 15.522 55992 15.198 119405 19.934 50.65%
Total 262 33.333 122806 33.333 199671 33.333 100

There definitely was "ballot truncation" (whether intentional or not) since in "section 3" the total #ballots was 

Round....total(sec3).....total(sec2)
1..........211234.........126874
2..........206640.........126312
3..........205283.........125186
4..........199671.........122806

hence at least about 6% of the voters in sec3, and similarly at least 3% of those in sec2 truncated. Actually there was considerably more truncation than these lower bounds, see below.

The election looks like it was 2 front runners and 3 minor candidates. All the minor candidates added together got 27.9% of the weighted top-preference vote, which is less than the 34.3% and 37.8% for the two Milibands.

The 266 section1 ballots, published by Manchester Guardian

The full set of the 266 rank-order ballots in section1 was made public by the Manchester Guardian. They were cast by Labour MPs and MEPs. The table below has 6 columns. Example row: 

     "4	Ms H Alexander MP 	*	*	1	2	3"
means "Ms H.Alexander MP" (who was voter #4) cast a ballot ranking Andy Burnham top, David Miliband 2nd, Ed Miliband 3rd, and leaving Diane Abbott and Ed Balls both unranked.

Note to computer geeks: the 7 entries in each row are tab-separated. 
VOTER   MP or MEP        .........RANKS FOR THE FIVE CANDIDATES.........
NUMBER  ...VOTER.........D.Abbott..E.Balls..A.Burnhm..D.Milbnd..E.Milbnd
1	Ms D Abbott MP  	1	*	*	*	*
2	RtHon B W Ainsworth MP 	5	4	3	1	2
3	RtHon D Alexander MP 	5	3	4	1	2
4	Ms H Alexander MP 	*	*	1	2	3
5	Ms R Ali MP     	5	3	4	1	2
6	Mr G Allen MP   	*	*	*	1	2
7	Mr D Anderson MP 	5	1	4	3	2
8	Mr I Austin MP   	5	1	3	2	4
9	Mr A E Bailey MP 	*	3	4	2	1
10	Mr W Bain MP    	5	3	4	1	2
11	RtHon E M Balls MP 	*	1	*	*	*
12	Mr G R Banks MP 	*	3	4	1	2
13	RtHon K J Barron MP 	5	4	1	3	2
14	Mr H Bayley MP  	5	3	4	1	2
15	RtHon M M Beckett MP 	*	*	*	*	1
16	Miss A Begg MP  	5	3	4	2	1
17	Sir S Bell MP   	*	2	*	1	*
18	RtHon H Benn MP 	*	*	*	2	1
19	Mr J E Benton MP 	*	4	1	2	3
20	Miss L Berger MP 	5	3	4	2	1

21	Mr C Betts MP   	*	*	1	*	2
22	Ms R Blackman-Woods MP 	*	*	2	*	1
23	RtHon H A Blears MP 	*	3	1	2	4
24	Mr T Blenkinsop MP 	*	1	*	2	*
25	Mr P Blomfield MP 	*	*	*	*	1
26	RtHon D Blunkett MP 	*	*	1	2	*
27	Mr B Bradshaw MP 	*	*	*	1	*
28	Mr K Brennan MP 	5	1	4	2	3
29	Ms L Brown MP   	*	1	*	3	2
30	Mr R Brown MP   	*	3	4	1	2
31	Mr C Bryant MP  	5	2	3	1	4
32	Ms K Buck MP    	*	*	*	*	1
33	Mr R H Burden MP 	*	3	*	1	2
34	RtHon A Burnham MP 	5	4	1	2	3
35	Mr L Byrne MP   	*	2	*	1	3
36	Mr D Cairns MP  	*	*	*	1	*
37	Mr A Campbell MP 	*	*	2	1	*
38	Mr R Campbell MP 	*	*	1	*	2
39	Mr M Cashman MEP	*	*	*	1	2
40	Mr M Caton MP   	2	3	*	*	1

41	Ms J Chapman MP 	*	*	*	1	*
42	Ms K Clark MP   	1	2	4	5	3
43	RtHon T Clarke MP 	3	5	2	1	4
44	RtHon A Clwyd MP 	*	*	*	1	*
45	Mr V Coaker MP  	*	1	4	2	3
46	Ms A Coffey MP  	5	4	3	1	2
47	Mr M Connarty MP 	5	2	1	4	3
48	Ms R Cooper MP  	*	2	*	1	*
49	Ms Y Cooper MP  	*	1	*	*	*
50	Mr J Corbyn MP  	1	*	*	*	2
51	Mr D Crausby MP 	5	1	4	2	3
52	Ms M Creagh MP  	5	2	4	1	3
53	Miss S Creasy MP 	*	*	*	1	2
54	Mr J Cruddas MP 	4	2	5	1	3
55	Mr J Cryer MP   	5	2	4	3	1
56	Mr A Cunningham MP 	5	3	4	1	2
57	Mr J Cunningham MP 	5	1	4	2	3
58	Mr T Cunningham MP 	*	1	4	3	2
59	Ms M Curran MP  	5	4	3	2	1
60	Mr N Dakin MP   	5	3	4	1	2

61	Mr S Danczuk MP 	*	*	*	1	*
62	RtHon A Darling MP 	*	*	*	1	*
63	Mr W David MP   	5	3	4	2	1
64	Mr I Davidson MP 	5	1	4	3	2
65	Mr G R Davies MP 	*	3	*	2	1
66	Ms G De Piero MP 	*	*	*	1	2
67	RtHon J Y Denham MP 	*	*	*	*	1
68	Mr J Dobbin MP  	*	1	*	*	2
69	RtHon F G Dobson MP 	*	2	*	*	1
70	Mr T Docherty MP 	*	4	1	2	3
71	Mr B Donohoe MP 	5	3	4	1	2
72	Mr F Doran MP   	*	3	4	2	1
73	Mr J Dowd MP    	*	*	*	1	*
74	Miss G Doyle MP 	4	3	5	1	2
75	Mr J Dromey MP  	*	*	*	*	1
76	Mr M Dugher MP  	*	1	*	*	2
77	Ms A Eagle MP   	5	2	4	1	3
78	Ms M Eagle MP   	*	*	*	*	1
79	Mr C Efford MP   	5	3	4	2	1
80	Ms J Elliott MP 	*	*	2	1	3

81	Ms L J Ellman MP 	*	*	2	1	*
82	Ms N Engel MP   	*	*	*	*	1
83	Mr B Esterson MP 	5	4	2	3	1
84	Mr C Evans MP   	*	1	4	2	3
85	Mr P Farrelly MP 	5	4	3	2	1
86	RtHon F Field MP 	*	*	2	*	1
87	Mr J Fitzpatrick MP 	*	*	*	1	*
88	Mr R C D Flello MP 	*	*	1	2	3
89	Ms C Flint MP   	*	*	*	1	*
90	Mr P P Flynn MP 	3	4	2	1	5
91	Ms Y Fovargue MP 	*	*	1	2	*
92	Dr H Francis MP 	*	2	*	*	1
93	Mr M Gapes MP   	5	3	2	1	4
94	Mr B Gardiner MP 	*	*	*	1	2
95	Ms S Gilmore MP 	4	5	3	1	2
96	Mrs P Glass MP   	5	2	3	1	4
97	Ms M T Glindon MP 	5	4	2	1	3
98	Mr R Godsiff MP 	5	4	3	2	1
99	Mr P Goggins MP 	*	*	1	2	*
100	Ms H Goodman MP 	*	*	*	*	1

101	Mr T J Greatrex MP 	*	4	3	2	1
102	Ms K Green MP   	5	1	3	4	2
103	Ms L R Greenwood MP 	5	3	4	2	1
104	Ms N Griffith MP 	*	1	*	3	2
105	Mr A J Gwynne MP 	5	1	4	3	2
106	RtHon P Hain MP 	*	*	*	2	1
107	The Hon D Hamilton MP 	*	2	3	4	1
108	Mr F Hamilton MP 	*	4	3	1	2
109	RtHon D Hanson MP 	5	4	2	1	3
110	Mr T Harris MP  	*	*	*	1	*
111	Mr D Havard MP   	*	2	*	*	1
112	Mr J Healey MP  	*	1	*	*	2
113	Mr M Hendrick MP 	5	4	3	1	2
114	Mr S Hepburn MP 	*	1	*	2	*
115	Mr D A Heyes MP 	5	4	1	3	2
116	Ms M Hillier MP 	*	2	3	1	*
117	Ms J A Hilling MP 	5	4	1	2	3
118	RtHon M E Hodge MP 	*	*	*	1	*
119	Mrs G Hodges MP 	*	2	*	*	1
120	Ms S Hodgson MP 	5	1	2	4	3

121	Ms K Hoey MP    	*	*	1	3	2
122	Ms M Honeyball MEP	5	3	4	1	2
123	Mr J Hood MP    	5	2	4	3	1
124	Mr K Hopkins MP 	1	3	4	5	2
125	RtHon G Howarth MP 	*	2	*	1	*
126	Mr R Howitt MEP 	*	*	*	1	2
127	Mr L Hoyle MP   	*	1	*	3	2
128	Mr S Hughes MEP 	*	*	3	2	1
129	Mr T Hunt MP    	5	2	4	1	3
130	Mr H Irranca-Davies MP 	*	4	2	1	3
131	Mrs S James MP  	*	2	*	*	1
132	Ms C Jamieson MP 	5	4	2	3	1
133	RtHon A A Johnson MP 	*	*	*	1	*
134	Ms D R Johnson MP 	*	1	*	2	*
135	Mr G Jones MP   	*	2	3	4	1
136	Ms H Jones MP   	*	1	*	3	2
137	Mr K Jones MP   	*	*	2	1	*
138	Ms S E Jones MP 	*	*	*	2	1
139	RtHon T J Jowell MP 	4	5	2	1	3
140	Mr E Joyce MP   	5	1	3	4	2

141	RtHonSir G B Kaufman MP	*	4	3	1	2
142	Ms B Keeley MP   	5	1	4	3	2
143	Mr A Keen MP    	5	4	1	3	2
144	Miss E Kendall MP 	*	*	*	1	*
145	Mr S Khan MP    	*	*	*	*	1
146	Mr D Lammy MP   	2	3	5	1	4
147	Mr I Lavery Snr MP 	*	*	2	*	1
148	Mr M Lazarowicz MP 	*	*	*	*	1
149	Mr C Leslie MP   	5	1	4	2	3
150	Mr I Lewis MP   	*	*	*	1	*
151	Mr A Love MP    	5	3	4	2	1
152	Mr I Lucas MP    	5	2	4	3	1
153	RtHon D MacShane MP 	*	*	*	1	*
154	Ms F Mactaggart MP 	*	2	*	1	*
155	Mr K Mahmood MP 	3	1	5	4	2
156	Ms S Mahmood MP 	*	*	*	*	1
157	Mr J Mann MP    	*	*	*	1	2
158	Mr G Marsden MP 	*	4	3	2	1
159	Mr D Martin MEP 	*	*	*	1	*
160	Ms L McAvan MEP 	*	*	*	*	1

161	Mr S J McCabe MP 	*	1	*	3	2
162	Mr M McCann MP  	*	*	*	1	*
163	Ms A McCarthy MEP	*	*	3	2	1
164	Ms K McCarthy MP 	*	1	*	2	*
165	Mr G McClymont MP 	5	3	4	1	2
166	Ms S McDonagh MP 	*	*	*	1	*
167	Mr J McDonnell MP 	1	*	*	*	*
168	Mr P McFadden MP 	*	*	*	1	*
169	Ms A McGovern MP 	5	4	2	1	3
170	Mr J McGovern MP 	*	*	*	*	1
171	Mrs A McGuire MP 	5	2	4	1	3
172	Ms A McKechin MP 	*	2	*	*	1
173	Mrs C McKinnell MP 	*	*	*	*	1
174	RtHon M Meacher MP 	2	*	*	*	1
175	Mr A Meale MP   	5	3	4	2	1
176	Mr I Mearns MP   	5	2	4	1	3
177	RtHon A Michael MP 	5	2	4	1	3
178	RtHon D Miliband MP 	*	*	*	1	2
179	RtHon E Miliband MP 	*	*	*	2	1
180	Mr A P Miller MP 	*	4	1	2	3

181	Mr A Mitchell MP 	4	3	5	2	1
182	Mrs M Moon MP   	*	2	*	*	1
183	Mr C Moraes MEP 	*	*	*	1	*
184	Ms J Morden MP   	5	4	3	1	2
185	Mr G Morrice MP 	*	*	*	*	1
186	Mr G M Morris MP 	4	3	2	5	1
187	Mr G Mudie MP   	*	1	*	*	2
188	Ms M Munn MP    	*	*	*	1	*
189	Mr J Murphy MP  	*	*	*	1	*
190	RtHon P Murphy MP 	*	*	*	2	1
191	Mr I Murray MP   	5	3	4	1	2
192	Ms L Nandy MP   	*	2	*	*	1
193	Miss P Nash MP  	*	*	*	1	*
194	Mrs F O'Donnell MP 	5	4	3	1	2
195	Ms C Onwurah MP 	3	*	*	2	1
196	Ms S Osborne MP 	*	*	*	*	1
197	Mr A Owen MP    	*	4	2	3	1
198	Ms T Pearce MP   	*	1	*	3	2
199	Mr M T Perkins MP 	5	2	4	1	3
200	Ms B M Phillipson MP 	*	*	*	1	*

201	Mr S Pound MP   	*	4	2	3	1
202	RtHon D Primarolo MP 	*	*	*	*	1
203	Ms Y Qureshi MP 	*	*	*	1	*
204	RtHon N Raynsford MP 	*	*	*	1	*
205	Mr J R Reed MP   	*	4	3	1	2
206	Ms R J Reeves MP 	5	3	4	2	1
207	Ms E Reynolds MP 	5	3	4	2	1
208	Mr J N Reynolds MP 	*	*	*	1	2
209	Ms L Riordan MP 	1	*	*	*	2
210	Mr J Robertson MP 	5	1	4	3	2
211	Mr G Robinson MP 	5	1	4	2	3
212	Mr S P Rotheram MP 	*	*	1	*	2
213	Mr F Roy MP     	*	*	*	1	*
214	Mr L A Roy MP   	*	2	*	3	1
215	Mr C Ruane MP   	5	3	4	1	2
216	Ms J Ruddock MP 	*	*	*	*	1
217	Mr A Sarwar MP  	*	*	*	1	2
218	Ms A Seabeck MP 	*	*	*	*	1
219	Mr V K Sharma MP 	5	3	4	1	2
220	Mr B Sheerman MP 	*	*	*	1	*

221	Mr J Sheridan MP 	*	*	*	*	1
222	Mr G Shuker MP  	*	2	*	*	1
223	Mr B Simpson MEP	*	*	1	*	2
224	Mr M Singh MP   	*	3	*	2	1
225	Mr D E Skinner MP 	*	*	*	1	*
226	Mr P Skinner MEP	*	*	*	1	*
227	Mr A F Slaughter MP 	*	*	*	*	1
228	RtHon A Smith MP 	5	1	4	2	3
229	Ms A C Smith MP 	*	*	2	1	*
230	Mr N Smith MP   	5	2	4	1	3
231	Mr O Smith MP   	5	2	4	3	1
232	Sir P Soulsby KBE MP 	5	4	3	1	2
233	RtHon J F Spellar MP 	*	1	4	2	3
234	Ms C Stihler MEP	5	4	3	2	1
235	RtHon J W Straw MP 	*	3	2	1	*
236	Mr G Stringer MP 	*	*	2	1	*
237	Ms G Stuart MP  	*	*	*	1	*
238	Mr G Sutcliffe MP 	5	3	1	2	4
239	Mr M R Tami MP   	5	2	3	1	4
240	Mr G Thomas MP  	*	*	*	1	*

241	Ms E Thornberry MP 	*	*	*	*	1
242	RtHon S Timms MP 	*	4	3	2	1
243	Mr J Trickett MP 	4	1	*	3	2
244	Mr K Turner MP   	5	4	1	2	3
245	Mr D Twigg MP   	5	3	1	2	4
246	Mr S Twigg MP   	*	*	*	1	2
247	Mr C Umunna MP  	*	*	*	2	1
248	Mr D Vaughan MEP	*	*	*	2	1
249	RtHon K Vaz MP   	4	3	5	1	2
250	Ms V Vaz MP     	2	*	*	1	3
251	Ms J L Walley MP 	*	*	2	*	1
252	Mr T Watson MP   	5	1	3	4	2
253	Mr D Watts MP   	4	2	1	5	3
254	Mr A Whitehead MP 	*	*	2	3	1
255	Mr M Wicks MP   	5	4	3	1	2
256	Mr C Williamson MP 	5	2	4	3	1
257	Ms G Willmott MEP	*	*	*	2	1
258	Mr P Wilson MP  	*	*	2	1	*
259	Mr D Winnick MP 	*	*	*	1	*
260	RtHon R Winterton MP 	*	*	*	*	1

261	Mr M Wood MP    	1	3	*	*	2
262	Mr J Woodcock MP 	*	4	2	1	3
263	RtHon S Woodward MP 	5	3	4	1	2
264	Mr P Woolas MP  	*	*	*	1	*
265	Mr D Wright MP  	*	1	4	2	3
266	Mr I D Wright MP 	5	1	3	4	2
Edited Comment by Rob Richie: Ed Balls and his wife Yvette Cooper both "bullet voted" for Balls; Abbott and John McDonnell both bullet-voted for Abbott; these 4 were the only voters of the 266 who left both Milibands unranked. McDonnell had actually tried to run for labour leader himself but had dropped out.

These 266 voters, since they all were MPs or MEPs and since they presumably all (or nearly) actually were personally acquainted with each of the 5 candidates, were presumably far more motivated and knowledgeable voters than an average British citizen.

There were the following numbers of preferences expressed by these 266 voters: 

        61 (gave 1 preference), 60 (gave 2 preferences), 24 (3), 26 (4), 95 (5).
      [Average number of candidates ranked=3.13; and 3.23 if count 4 ranked as "really" being 5.]

Ranking 4 candidates was equivalent to ranking all 5 as far as the IRV algorithm was concerned since it treated unranked candidates as ranked co-equal last; 26+95=121=45.5% of these 266 voters thus effectively ranked all candidates. The remaining 145=54.5% of these voters "truncated." Note that 61, i.e. 22.9%, of these voters "bullet voted," i.e. maximally truncated by ranking only a single candidate.

The ballots of 4 (1.5%) of the 266 sec1 voters had no impact on the crucial final round since these 4 ballots each left both Milibands unranked. That 1.5% compares with 5.5% among the sec3 voters (ratio 3.67) and 3.2% among the sec2 voters (ratio 2.13). This suggests that "bullet voting" and "truncation" rates both were probably substantially greater among sec3 voters (who are more representative of the average British voter) than the 22.9% and 54.5% rates among sec1 voters.

In fact, if we model the ballots as being of two types – "truncated" and "full" (and counting 4-rank ballots as "full") then if we assume the sec3 voters acted the same as the sec1 voters except for altering the relative fractions of these two ballot types – then we would find that the ballot truncation rate among sec3 voters had to be 3.67 times the 54.5% rate among the sec1 voters, i.e. this model would yield 200% and 115% ballot truncation rates for sec3 and sec2 voters! Of course, these are impossible, which means the model was incorrect or the ratios "3.67" and "2.13" were heavily contaminated by statistical noise (or, more likely, both). Still, this is enough that it seems seems safe to deduce that the truncation rate was extremely high among average British voters. Noting (as did Rob Richie above) that all 4 of the sec1 ballots that left both Milibands unranked were "bullet vote" ballots, if we model by assuming ≈100% of ballots in all sections leaving both Milibands unranked were bullet votes, and regard ballots as either "bullet" or "not" assuming ballots in sec3 were statistically identical to ballots in sec1 aside from changing the relative fractions of the two ballot types – this approximate model again would lead to the conclusion that the bullet-vote percentages in sec3 and sec2 were respectively 3.67 and 2.13 times sec1's 22.9% rate, i.e. 84% and 49% bullet-voting rates (extrapolated) among the sec3 and sec2 voters. Again, these estimates are very noisy, but still it seems safe to say the true bullet-voting rates were very large.

A different estimation can be based on the fact (which we can tell from the official data) that 28.5% of the 7, 6.0% of the 9314, and 17.7% of the 25938 Abbott-top voters in sec1, sec2, and sec3 respectively cast "bullet"-style ballots (i.e. ranking Abbott only). Evidently Abbott-top voters were less likely to "bullet vote" than random voters, probably because they knew she was doomed to lose, so a bullet vote for her was a wasted vote.

Roughly 70% of those ranking both (I have not computed it exactly) ranked David & Ed Miliband consecutively, i.e. they were not "clones" in the sense this was below 100%, but they were clones to a considerable degree.

David Miliband and Ed Miliband were ranked by 213 and 209, of 266 sec1 voters, with average rankings of 1.75 and 1.90 respectively. Ed Balls was 159 and 2.52; Andy Burnham was 146 and 2.95; and Diane Abbott was 150 and 4.46. Thus David Miliband was also the range/Borda voting winner (among these 266 ballots) if these ballots are treated as range-voting style. He also was the approval-voting winner, if "ranking" vs "not ranking" is regarded as "approval" vs "disapproval."

David also was the plain-plurality voting winner (in sec1) and the "Condorcet winner" defeating every rival pairwise. (E.g. in the next-closest pairwise battle, DM beat Ed Balls 166:64, namely 95:47 if exclude blank scores and 71:17 among those ranking exactly one of the two candidates.) Since we know from the official final round count that Ed Miliband beat DM pairwise among the full set of weighted votes, and considering the huge margins of pairwise victory for the Milibands versus non-Milibands in sec1, it seems clear that Ed Miliband was a "Condorcet winner."

"Strategic Nomination" manipulation attempt?

Abbott was actually nominated by David Miliband, enabling her to enter this race! What are we to infer from that move by DM? At the time some declared this a strategic masterstroke because of the theory that somehow Abbott's presence in the race would hurt Ed Miliband's vote-count, thus causing David to win. But afterward others speculated that somehow the move had backfired to actually make David lose the election! All such speculations rest on the mathematical fact that IRV has the property that if some losing candidate is removed from all IRV ballots, that can alter the IRV-winner. For example, in Burlington's 2009 mayoral election (conducted using IRV), if Wright had dropped out of the race, that would have changed the winner from Kiss to Montroll. That phenomenon happens in 12.2%, 9.2%, and 19.4% of random 3-candidate IRV elections (in 3 different probability models), and in 23.3%, 33.8%, and 22.2% of random 3-candidate IRV elections in which the plurality and IRV winner differ (as they did here; same 3 probability models). Range voting cannot exhibit that mathematical flaw – although it still can if the range votes are "rescaled" after the drop-out – hence presumably is more-immune than IRV to such "strategic nomination" manipulation attempts.

To analyse the question in this particular election: because Abbott was the first candidate IRV eliminated, her presence or absence did not affect the winner from the given vote-set – the mathematical phenomenon can only arise for later-eliminated losers. So the only way it could have affected things was by affecting who voted. If Abbott's presence attracted Abbott-voters to the polls who otherwise would not have voted, then her presence appears to have helped Ed Miliband (as we see from the vote-transfers after the first IRV round), and probably enough to tip the election (i.e. the backfire-theory is correct). Note that this is exactly the opposite of what would have happened in a plurality-voting election – then DM nominating Abbott really would have been an anti-Ed masterstroke.

But on the other hand, if Abbott's presence attracted Abbott-hating voters to the polls who otherwise would not have voted, then we don't know. It is difficult to make speculations about this sort of thing without very specialized kinds of poll data. We do not have that data, although perhaps one of the Milibands did.

Pre-election polls


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