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EFFECTIVE NUMBER OF CANDIDATES IN UK PARTY LEADERSHIP ELECTIONS

 

The effective number of candidates (ENC) in leadership elections is a measure of the competitiveness of contests. It involves counting the absolute number of candidates and weighting them according to the proportion of votes that they win. The measurement of ENC is based on a similar measure for the effective number of parties (ENP) suggested by Laakso and Taagepera. It is the inverse of the summation of the squared proportions of the vote won by the candidates:

ENC (Laakso-Taagepera) = 1/∑Vi2

where Vi is the proportion of the vote won by candidate i. An evenly-matched three-candidate contest will have an ENC of 3.0, an evenly-matched two-candidate contest 2.0, and a contest in which there are two strong candidates and one weaker one could have an ENC of 2.5.

A rival measure of the effective number of parties, and which can also be applied to leadership elections, has been suggested by Golosov. Golosov’s measure better reflects the dominance of parties that win overall majorities and so is an appropriate measure of ENC, since leadership contests normally result in one candidate eventually passing the 50% mark. Golosov’s ENC index is given by:

ENC (Golosov) = ∑{∑Vi/[∑Vi + (V12/Vi) – Vi]}

where ∑Vi is simply the total number of votes cast, V1 is the number of votes won by the candidate with the highest number of votes and Vi is the number of votes won by the ith candidate. Each candidate’s score on the Golosov index is expressed in relation to that of the leading candidate. Performing the above calculation for the leading candidate gives a score of 1, with other candidates each having scores of between 0 and 1. These are then summed to produce the overall ENC.

Key
% win = winning candidate’s margin of victory over second-placed candidate in final round of voting
ACB = annual conference ballot
Ad hoc = ad hoc ballot or selection
EC (BV) = electoral college (block voting)
EC (OMOV) = electoral college (individual voting)
ENC(1) = effective number of candidates in first round of voting
ENC(F) = effective number of candidates in final round of voting
OMOV = one member-one vote
OMOV+ = one member-one vote including affiliated and registered supporters (Labour)
PPB = parliamentary party ballot
PPB/OMOV = parliamentary and membership ballots

References
M. Laakso and R. Taagepera, ‘“Effective” Number of Parties: A Measure with Application to West Europe’, Comparative Political Studies, 12:1 (1979), 3-27.
G. Golosov, ‘The Effective Number of Parties: A New Approach’, Party Politics, 16:2 (2010), 171-92.

 

UK major parties
UK minor parties
Scottish parties
Welsh parties
Northern Irish parties

 

Effective Number of Candidates in UK Party Leadership Elections 1960-2015

 

Contest System Candidates Laakso-Taagepera Golosov % win
      ENC (1) ENC (F) ENC (1) ENC (F)  
Labour              
1960 PPB 2 1.8 - 1.5 - 34.4
1961 PPB 2 1.6 - 1.3 - 48.7
1963 PPB 3 2.6 1.9 2.3 1.7 16.6
1976 PPB 6 4.7 2.0 4.3 1.8 12.5
1980 PPB 4 3.2 2.0 2.7 1.9 3.7
1983 EC (BV) 4 1.8 - 1.5 - 52.0
1988 EC (BV) 2 1.3 - 1.1 - 77.2
1992 EC (BV) 2 1.2 - 1.1 - 82.0
1994 EC (OMOV) 3 2.4 - 1.9 - 32.9
2007 EC (OMOV) 1 n/a - n/a - n/a
2010 EC (OMOV) 5 3.5 2.0 3.2 2.0 1.3
2015 OMOV+ 4 2.4 - 1.8 - 40.5
               
Conservative              
1965 PPB 3 2.2 - 2.1 - 5.7
1975 PPB 7* 2.2 2.6 2.1 2.1 24.5
1989 PPB 2 1.2 - 1.1 - 81.0
1990 PPB 4* 2.0 2.5 1.7 2.1 14.5
1995 PPB 2 1.7 - 1.4 - 42.0
1997 PPB 5 4.5 2.0 4.0 1.8 13.6
2001 PPB/OMOV 5 4.5 1.9 4.0 1.6 21.4
2003 PPB/OMOV 1 n/a - n/a - n/a
2005 PPB/OMOV 4 3.8 1.8 3.5 1.5 35.2
               
Liberal              
1967 PPB 3 2.7 - 2.1 - 25.0
1976 OMOV 2 1.9 - 1.6 - 28.2
               
SDP              
1982 OMOV 2 2.0 - 1.8 - 11.4
1983 OMOV 1 n/a - n/a - n/a
1987 OMOV 1 n/a - n/a - n/a
               
Liberal Democrats              
1988 OMOV 2 1.7 - 1.4 - 43.7
1999 OMOV 5 3.1 2.0 2.6 1.8 13.1
2006 OMOV 3 2.8 2.0 2.4 1.7 15.8
2007 OMOV 2 2.0 - 2.0 - 1.2
2015 OMOV 2 2.0 - 1.8 - 13.0
               

Notes: Figures for Conservative parliamentary ballots exclude abstentions and spoilt ballots
* Not all candidates participated in first ballot

 

 

UK Minor Party Leadership Elections 1999-2016

 

Contest System Candidates Laakso-Taagepera Golosov % win
      ENC (1) ENC (F) ENC (1) ENC (F)  
Green              
2008 OMOV 2 1.8 - 1.5 - 34.4
2010 OMOV 1 n/a - n/a - n/a
2012 OMOV 4 3.5 2.0 3.2 2.0 1.3
2016 OMOV            
               
UKIP              
2002 OMOV 1 n/a - n/a - n/a
2006 OMOV 4 3.2 - 2.5 - 20.9
2009 OMOV 5 3.1 - 2.4 - 21.8
2010 OMOV 4 2.3 - 1.8 - 40.2
2016 OMOV            
               
BNP              
1999 OMOV 2 1.7 - 1.4 - 44.9
2011 OMOV 2 2.0 - 2.0 - 0.4
2015 OMOV 2 1.5 - 1.3 - 56.6
               
               

 

Scottish Party Leadership Elections 1998-2015

 

Contest System Candidates Laakso-Taagepera Golosov % win
      ENC (1) ENC (F) ENC (1) ENC (F)  
Labour              
1998 EC (BV) 1 n/a - n/a - n/a
2000 Ad hoc 2 2.0 - 1.8 - 10.0
2001 Ad hoc 1 n/a - n/a - n/a
2007 EC (OMOV) 1 n/a - n/a - n/a
2008 EC (OMOV) 3 2.7 2.3 2.0 1.7 15.6
2011 EC (OMOV) 3 2.3 - 2.0 - 11.5
2014 EC (OMOV) 3 2.3 - 1.9 - 20.8
2015 OMOV+ 2 1.7 - 1.4 - 44.2
               
Conservative              
1998 Ad hoc 2 2.0 - 1.9 - 4.6
2005 Ad hoc 1 n/a - n/a - n/a
2011 OMOV 4 3.1 2.0 2.8 1.8 10.5
               
Liberal Democrat              
2005 OMOV 2 1.6 - 1.3 - 53.4
2008 OMOV 3 2.3 - 1.8 - 35.9
2011 OMOV 1 n/a - n/a - n/a
               
SNP              
1990 ACB 2 1.7 - 1.4 - 44.6
2000 ACB 2 1.8 - 1.5 - 34.2
2003 ACB 2 1.4 - 1.2 - 67.8
2004 OMOV 3 1.7 - 1.4 - 61.2
2014 OMOV 1 n/a - n/a - n/a

 

 

Welsh Party Leadership Elections 1998-2016

 

Contest System Candidates Laakso-Taagepera Golosov % win
      ENC (1) ENC (F) ENC (1) ENC (F)  
Labour              
1998 EC (BV) 2 1.8 - 1.5 - 36.4
1999 EC (BV) 2 2.0 - 1.9 - 5.4
2000 EC (BV) 1 n/a - n/a - n/a
2009 EC (OMOV) 3 2.8 - 2.1 - 22.8
               
Conservative              
1998 OMOV 2 1.9 - 1.7 - 16.1
1999 Ad hoc 1 n/a - n/a - n/a
2011 OMOV 2 2.0 - 1.9 - 6.4
               
Liberal Democrat              
1998 OMOV 2 2.0 - 1.9 - 8.0
2007 OMOV 1 n/a - n/a - n/a
2008 OMOV 2 1.9 - 1.7 - 19.6
               
Plaid Cymru              
2003 OMOV 3 2.8 2.0 2.6 2.0 1.4
2012 OMOV 3 2.7 2.0 2.2 1.7 14.2
2016 OMOV 1 n/a - n/a - n/a

 

 

Northern Irish Party Leadership Elections 1995-2016

 

Contest System Candidates Laakso-Taagepera Golosov % win
      ENC (1) ENC (F) ENC (1) ENC (F)  
Alliance              
1998 Ad hoc 1 n/a - n/a - n/a
2001 Ad hoc 2 1.8 - 1.5 - 31.2
               
DUP              
2008 Ad hoc 1 n/a - n/a - n/a
2016 Ad hoc 1 n/a - n/a - n/a
               
SDLP              
2001 ACB 1 n/a - n/a - n/a
2010 ACB 2 2.0 - 1.8 - 8.6
2011 ACB 4 3.5 2.0 3.1 1.8 10.6
               
UUP              
1995 Mar ACB 2 1.3 - 1.2 - 71.2
1995 Sep ACB 5 4.0 1.9 3.4 1.7 16.6
2005 ACB 3 2.3 2.0 2.2 1.9 5.6
2010 OMOV 2 1.8 - 1.5 - 37.2
2012 OMOV 2 1.5 - 1.2 - 61.2

 

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