Note by Nicholas Whyte: This article was posted by Jim Riley to ie.politics, soc.culture.irish, and uk.politics.electoral on 3 July 2000, in response to a previous post by Ciaran Quinn which is excerpted below. I am grateful to Jim for permission to include it on this site.

Subject: Re: NI Assembly election calculations
Newsgroups: ie.politics,soc.culture.irish,uk.politics.electoral
Message-ID: <8joo0l$3nd$1@slb6.atl.mindspring.net>
From: Jim Riley
Date: 02 Jul 2000 00:00:00 GMT

[This is a revision of a post I had made roughly a month ago. It includes information on DUP and SF; some speculation on what would have happened if there were seven MLA's elected from each constituency; and some modifications on the relations between the maximum preference vote and seats won.]

On Sat, 03 Jun 2000 22:45:36 +0100, Ciaran Quinn wrote:

I have done some calculations to explain why the UUP won more seats than the SDLP at the 1998 NI Assembly elections, despite getting fewer first preference votes.

The results are at http://election.polarbears.com/art0017.htm

In addition to the differential turnout and effects due to constituency size, UUP had a much more fortuitous distribution of its votes.

UUP had 27.11 quotas on first preferences, while SDLP had 26.49. But UUP had 20 full quotas and 7.11 fractional quotas, while SDLP had 18 full quotas and 8.49 fractional quotas. Assuming 100% intraparty transfers, UUP had 2 more seats wrapped up before inter-party transfers even began.

Party	FPQ	MPQ	TrQ	WQ	FrC	AS	TE	EffF	EffM
UUP	27.11	31.78	4.67	20	.40	+8	28	1.20	1.03
SDLP	26.54	30.99	4.45	18	.47	+6	24	1.06	.90
DUP	22.97	25.30	2.33	13	.55	+7	20	1.02	.92
SF	21.36	22.71	1.35	14	.41	+4	18	.98	.92
APNI	8.80	10.50	1.70	4	.27	+2	6	.80	.67

FPQ = First Preference Quotas.
MPQ = Maximum Preference Quotas.
TrQ = Transfer Quotas (MPQ-FPQ).
WQ = Whole first preference quotas.
FrC = Average fractional quota per constituency.
AS = Additional seats: (TE-WQ).
TE = Total MLA's elected.
EffF = Efficiency of First Preferences: (FPQ/126) / (TE/108).
EffM = Efficiency of Maximum Preferences: (MPQ/126) / (TE/108).

Efficiency is the ratio of the share of quotas to the share of seats won. A value of 1.00 would mean that the number of seats won is commensurate with the share of the popular vote normalized for differential turnout and electorate size. Note that this measure shows not so much that SDLP did poorly in translating votes into seats, but rather that UUP did particularly well.

If we discard the constituencies where a party's first preferences were less than 1/2 of a quota, the difference in efficiency for parties other than UUP is less marked.

Party	CC	FPQ	MPQ	TrQ	WQ	FrC	AS	TE	EffF	EffM
UUP	17	26.84	30.97	4.13	20	.40	+8	28	1.22	1.05
SDLP	15	25.57	29.43	3.86	18	.50	+5	23	1.05	.91
DUP	16	22.26	24.17	1.91	13	.57	+7	20	1.05	.97
SF	12	20.20	21.52	1.32	14	.52	+4	18	1.04	.98
APNI	7	6.85	8.28	1.43	4	.41	+2	6	1.02	.85

CC = Contested constituencies (constituencies where first preference quotas was great than 1/2). Note, SDLP did win a seat in East Antrim starting with first preferences equal to .41 quotas.

SDLP might ordinarily be expected to pick up more seats from interparty transfers, since they averaged .47 fractional quotas per constituency, whereas UUP averaged .40 fractional quotas per constituency (i.e. the average last SDLP candidate would need fewer transfers to secure election).

One reason for UUP's particular success is that the fractional quotas were distributed in UUP's favor:

UUP		SDLP		DUP		SF
UlM 98+				FST 97+	Str 94+*
				N&A 93+	BeS 91+*
				Foy 88+		FST 88+	UlM 85+
		WTy 80+				N&A 82+	Foy 82+
BeN 76+	ELo 76+	BeW 75+*
FST 72+	BeE 70+
Foy 67		ELo 66+	UpB 66	SDo 66+	ELo 66	ELo 68
BeS 64+*		Str 63*	LaV 61+*	NAn 63+*
NAn 56+*		UlM 56		EAn 55*		NAn 57*
		BeS 52+*	FST 51	UlM 50		SAn 51*
		BeN 47	N&A 45	BeN 49	NDo 48*	BeN 49	BeS 45*
		EAn 41+*		SAn 41*
		NDo 38*	Foy 35			WTy 39
NDo 28+*						LaV 30*
BeW 27*	N&A 27			LaV 26*
		SAn 24*	NAn 19*	BeW 23*	WTy 22
LaV 16*		BeE 18	SDo 17	BeE 16		BeE 16	EAn 15*
SAn 10*	WTy 10					BeW 13*	Str 10*
EAn 7*	Str 4*			UpB 9		SDo 6
UpB 2	SDo 1					UpB 0

+ Extra MLA elected.
* Inter-factional coalition needed.

For example, "BeS 64+*" under the UUP column indicates that in Belfast South, UUP had (1).64 quotas, they were able to win an extra (2nd) seat, and an inter-factional coalition was needed.

Where a party had a fractional quota of more than .70 they secured an additional seat in all 16 cases. If the fractional quota was in the .60 to .70 range, 50% were converted to an additional seat:

	UUP	SDLP	DUP	SF	Top4
.70-1.00	5/5	2/2	5/5	4/4	16/16	100%
.60-.70	1/2	2/4	2/3	0/1	5/10	50%
.50-.60	1/1	1/3	0/2	0/2	2/8	25%
.40-.50		1/3	0/3	0/2	1/8	12%
.00-.40	1/10	0/6	0/5	0/9	1/29	3%
Total	8/18	6/18	7/18	4/18	25/71	35%

That UUP had 5 seats where conversion is almost automatic, to only 2 for SDLP, is all the more remarkable considering that the average fractional quota for UUP was .40, compared to .47 for SDLP. This anomaly is explained by UUP also having 10 constituencies with a fraction less 0.27, compared to only 6 for SDLP. A larger fractional quota means fewer transfers are needed to secure an additional seat. A smaller fraction means fewer votes are wasted in a vain attempt to gain an extra seat.

In 7 of 9 cases where the fractional quota was less than 0.70 and an extra seat was secured, there was an additional factor at work. If you divide 7 quotas among 3 factions (nationalist, unionist, and other), there will be either be (a) 6 whole quotas and 1 quota split 3 ways; or (b) 5 whole quotas and 2 quotas split 3 ways. (e.g. Upper Bann: 2.70-4.01-0.28 results in a 2-4-0 seat distribution, South Antrim: 1.75-0.80-4.44 results in a 1-0-4 seat distribution, with the final seat available to the faction that can attract inter-factional transfers, or at least avoid losing ground from non-transferable ballots. In South Antrim, APNI won the final seat, with SDLP the best loser).

If the vote is split such that there are 6 full quotas, then there are essentially 3 intra-factional contests for seats. Thus in Upper Bann, Fermanagh&South Tyrone, and Mid Ulster, SDLP was battling Sinn Fein for their share of 2, 3, and 4 nationalist seats respectively. In such a situation, there is less opportunity for both intra-factional and inter-factional transfers. UUP faced a similar situation in Foyle for a single unionist seat. Initial support in the range of 0.5 to 0.7 quotas was not enough of a start to gain an extra seat.

SDLP was able to overcome this handicap in Londonderry East because they had a fairly large lead over SF to start with. If the initial quotas are restated in terms of an inter-factional contest, it is clearer why SDLP was able to expand their initial fractional quota into a full seat in Londonderry East.

	6-st quota		nat. seats	nat.quota		MLA's
Const.	SDLP	SF		SDLP	SF	SDLP	SF
Mid Ulster	1.56	2.89	4	1.75	3.25	1	3
Ferm.&S Tyr.	1.51	1.88	3	1.78	2.22	1	2
Upper Bann	1.66	1.04	2	1.84	1.15	1	1
Lond. East	1.66	0.68	2	2.13	0.87	2	0

The two cases where a party was able to secure an extra seat despite an initial fractional quota less than 0.5 were Antrim East (for SDLP) and Down North (for UUP). In both cases, only 5 whole quotas were initially allocable to the 3 factions. In Antrim East, the SDLP candidate was able to accumulate transfers first from Sinn Fein, then an eliminated APNI candidate, and finally enough from a UUP surplus to gain a 49-vote margin for the final seat. North Down was UUP's strongest constituency, with 2.28 initial quotas. This gave them an initial average quota of 0.76 for their three candidates, which allowed them to avoid early exclusion. With 19 candidates, there were plenty of opportunities for transfers to accumulate to the UUP candidates (42% of the final UUP candidate who was elected were from transfers).

In Strangford, SDLP was unable to convert a 0.63 initial fraction into a seat, despite there being only 5 seats initially allocated to the 3 factions. But Strangford was the strongest unionist constituency, with 5 full unionist quotas. In this case, it was simply a matter of APNI defeating SDLP for the single non-unionist seat.

A closer look at the pattern of transfers may help explain why transfers and maximum preference votes do not necessarily convert into extra seats. Transfers to a particular party tended to be concentrated in a very few constituencies, and don't always produce any difference in the results. An extreme example is SDLP in Londonderry East. In first preferences, SDLP had a 1.66 to 0.68 lead over SF. The only question was whether the SDLP vote would be balanced enough to secure both nationalist seats, or whether they would be split. As it turned out, the SDLP vote was well balanced. The SF candidate was the last to be excluded, and roughly 2/3rds transferred to the SDLP. This resulted in a maximum preference for SDLP of 2.38 quotas, but still only 2 elected. If SF had a couple 100 more votes, they would not have been excluded, but rather simply finished 7th. SDLP would still have secured the two seats, but their transfers would have been much less.

Half of the transfers to UUP occurred in just 5 constituencies.

	FPQ		MPQ	Result
North Down	2.28	+0.61	2.89	3rd seat gained.
Belfast West	0.27	+0.54	0.81	No seats.
North Antrim	1.56	+0.51	2.07	2nd seat gained.
East Antrim	2.07	+0.47	2.54	No 3rd seat gained.
Belfast South	1.64	+0.38	2.02	2nd seat gained.

Half of the transfers to SDLP occurred in 5 constituencies:

	FPQ		MPQ	Result
Londonderry E	1.66	+0.72	2.38	2nd seat, most transfers superfluous.
South Antrim	1.24	+0.56	1.80	No 2nd seat gained.
East Antrim	0.41	+0.41	0.82	1st seat gained.
South Down	3.17	+0.38	3.55	No 4th seat gained.
Belfast South	1.52	+0.34	1.86	2nd seat gained.

Half of the transfers to DUP occurred in just 3 constituencies:

	FPQ		MPQ	Result
South Down	0.66	+0.45	1.11	1st seat gained.
Belfast South	0.91	+0.44	1.35	1st seat, most transfers superfluous.
North Down	0.48	+0.35	0.83	No seat gained.

Half of the transfers to SF occurred in just 3 constituencies:

	FPQ		MPQ	Result
Ferm&S.Tyrone	1.88	+0.29	2.17	2nd seat, most transfers superfluous.
Newry&Armagh	1.82	+0.24	2.06	2nd seat, most transfers superfluous.
Foyle	1.82	+0.22	2.04	2nd seat, most transfers superfluous.

The 6.91 quotas in 16 constituencies represented by the above transfers converted to 11 additional seats. The other 5.89 quotas in 45 constituencies converted to 14 additional seats. Alternatively, it wasn't so much the transfers, but rather the starting position after the first preferences were counted that largely determined whether additional seats were gained.

It is interesting to see what would have happened if there had been a different number of candidates elected from each constituency. Assuming no change in party strategy, nor voter preferences, I would project the parties to have gained seats in the following constituencies if there had been 7 elected per constituency.

Belfast East	APNI
Belfast North	SDLP
Belfast South	APNI
Belfast West	UUP
East Antrim	DUP, APNI gain; SDLP loss
East Londonderry	DUP
Ferm.&S.Tyrone	SDLP
Foyle	UUP (or SDLP)
Lagan Valley	UUP (or UDP)
Mid Ulster	SDLP
Newry&Armagh	SDLP (or UUP or SF)
North Antrim	SF
North Down	DUP (or UKUP)
South Antrim	SDLP (or UUP or DUP)
South Down	SDLP
Strangford	SDLP (or INDU) or (SDLP, UUP; UKUP loss)
Upper Bann	SDLP
West Tyrone	SF

.

	6/const	eff.6	change	7/const	eff.7	most	eff.ml
UUP	28	1.20	1-6	29-34	1.07-1.25	31	1.14
SDLP	24	1.06	4-8	28-32	1.06-1.21	31	1.17
DUP	20	1.02	2-4	22-24	0.96-1.04	23	1.00
SF	18	0.98	2-3	20-21	0.94-0.98	20	0.98
APNI	6	0.80	3-3	9- 9	1.02-1.02	9	1.02

6/const = MLA's if 6 elected per constituency.
eff.6 = efficiency converting first preferences to MLA's.
change = Range in MLA gains if 7 elected per constituency.
eff.7 = Range in efficiency, 7 elected per constituency.
most = Most likely number of MLA's, 7 per constituency.
eff.ml = Most likely efficiency.

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See also: The Boundary Commission's Provisional Recommendations | Boundary Commission 2003 | 1998 Assembly | The Jenkins Report

Full 1998 results for each seat: East Belfast | North Belfast | South Belfast | West Belfast | East Antrim | North Antrim | South Antrim | North Down | South Down | Fermanagh and South Tyrone | Foyle | Lagan Valley | East Londonderry | Mid Ulster | Newry and Armagh | Strangford | West Tyrone | Upper Bann

Other sites based at ARK: ORB (Online Research Bank) | CAIN (Conflict Archive on the INternet) | Northern Ireland Life and Times Survey

Your comments, please! Send an email to me at nicholas.whyte@gmail.com.

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Your comments, please! Send an email to me at nicholas.whyte@gmail.com..

Other sites based at ARK: ORB (Online Research Bank) | CAIN (Conflict Archive on the INternet) | Northern Ireland Life and Times Survey

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Jim Riley, 2 July 2000; last modified by Nicholas Whyte, 17 February 2002