Anyone who has attended more than the occasional election count will undoubtedly have heard someone say that their party has lost a seat because of another party splitting ‘their’ vote; it might be a Conservative accusing UKIP, or a LibDem pointing a finger at Labour, or vice versa, but whether on the left or the right, partisans tend to assume that the vote on their side of the political spectrum belongs to their party, and to no one else.

It’s particularly apposite to think about this at the moment, given Michael Fabricant’s discussion paper on the hypothetical benefits from a Con-UKIP pact, and the revived myth (as definitively rubbished by Anthony Wells, http://ukpollingreport.co.uk/blog/archives/4444 ) that at the 2010 General Election, UKIP cost the Tories 20-40 seats.

I had already been thinking of looking at this, as I’d been assembling a large data set of local election results, for council elections in the South East England region, for the most recent election cycle (2009-2012). Whereas the General Election had a maximum of 650 data points – constituencies – to examine for evidence of potential vote-splitting, not all of which will have multiple parties from the same political wing, local elections offer several times the number of data points to analyse.

Does the data bear out the belief that vote-splitting hurts, and that it is parties who should be our best friends – or at least as friendly as that bloke from work we sometimes play five-a-side with and have a drink afterwards – who are splitting our votes?

**Parameters of the Analysis**

For the purpose of this analysis, I’m counting the following parties as right wing and left wing respectively (in descending order of electoral success):

Right: Conservatives, UKIP, BNP, English Democrats (ED)

Left: Labour, Liberal Democrats, Greens

The elections used are council elections from all county, district, borough and unitary authorities in the South East region of England, from 2009 to 2012. Only main council elections (taking place in May of each year) are used; by elections may be subject to many other factors and influences, and have been excluded.

Council wards may be represented by one, two or three members, who may elected one at a time, or simultaneously. If multiple members are elected in one election, and hence there are multiple candidates from a single party, it becomes much more difficult to determine how an election might have been different if a particular party had not stood; therefore, the analysis is based only on single-seat elections.

**The Data**

Limiting the dataset to single-seat elections gives us 1,895 elections to work with. Of this number, 3 have no candidate from either left **or** right (all candidates are either Residents, Independents, or other, small parties); 6 wards have no right candidate, and 74 have no left candidate. Further, 38 wards were won by Residents’ Association candidates, and 30 by Independents. This leaves 1,744 seats won by a candidate of the right or left. These can be divided into four groups:

a) 1 right and 1 left candidate: 240 seats

b) multiple (2, 3 or 4) right candidates, 1 left candidate: 151 seats

c) 1 right candidate, multiple (2 or 3) left candidates: 740 seats

d) multiple right and multiple left candidates: 613 seats

**a) The Baseline: Head-to-Head Contests**

The straightforward contests in group (a) break down into 183 right wins, all Conservative (81 over Labour, 95 over LibDems, 7 over the Greens) and 57 left wins (30 Lab over Con, 2 Lab over UKIP, 25 LD over Con). So in straight 1 right/1 left contests, right wins 76.25%, left wins 23.75%. This is a baseline we can use to compare the other results against.

Right Wins | Left Wins | |||

Baseline Case: Head to Head Contests | 76.25% | 23.75% |

**b) Splitting the Right Vote?**

The Conservatives contested all 151 of these seats; 137 were against UKIP, 7 against BNP, 5 against the English Democrats, and 2 against UKIP *and* BNP

The left was represented (only one party from the left in each seat in this category, remember) by Labour in 45 seats, the LibDems in 104, and the Greens in 2.

The results were 118 Conservative wins, 1 UKIP win (i.e. 119 right wins), 14 Labour wins and 18 LibDem wins (i.e. 32 left wins)

Right Wins | Left Wins | |||

Head to Head Contests | 76.25% | 23.75% | ||

Multiple Right, Single Left | 78.81% | 21.19% |

As can be seen, there is no significant difference in results with multiple parties on the right contesting a seat.

To go further, in 7 of 14 Labour victories, and 9 of 18 LibDem victories, the winning party’s vote was greater than the total of all right parties, meaning that even if there had been a single party on the right contesting the seat, *and* every right voter in the real election had voted for that party, the right would still have lost. We can therefore add these to the seats actually won by Conservatives and UKIP as seats where splitting the right vote **definitely** made no difference: a total of 135 seats. So this leaves us 16 seats, or 10.60%, in which a theoretical transfer of 100% of votes to the leading right party would gain them 16 seats, or 10.60%.

A YouGov survey from 2010 (http://cdn.yougov.com/today_uk_import/YG-Archives-Pol-YouGov-BNP-UKIP-Formattedv2-291110.pdf) shows that not every voter would transfer uniformly to a party on the same side of the political spectrum (in this case, UKIP or BNP to Conservative); the net transfer (the difference between transfers to the Conservatives and a Labour or LibDem opponent) would be around 18 or 19%. If we examine some hypothetical thresholds, assuming that a net of 50%, 25% or 10% of votes would transfer, the Conservatives would gain 6, 3 or 2 seats.

Split Effect

100% Transfer | 50% Transfer | 25% Transfer | 10% Transfer | |||||

Head to Head Contests | 0.00% | – | – | – | ||||

Multiple Right, Single Left | 10.60% (16) | 3.97% (6) | 1.99% (3) | 1.33% (2) |

**c) Splitting the Left Vote?**

449 seats were contested by Labour and the LibDems; 20 by Labour and the Greens; 18 by the LibDems and the Greens; 253 by all of Labour, the LibDems and the Greens.

The right was represented by the Conservatives in 738 seats, UKIP in 2, and BNP or ED in 0.

The results were 446 Conservative wins (446 right wins), 135 Labour wins, 150 LibDem wins and 9 Green wins (i.e. 294 left wins)

Right Wins | Left Wins | |||

Head to Head Contests | 76.25% | 23.75% | ||

Multiple Right, Single Left | 78.81% | 21.19% | ||

Single Right, Multiple Left | 60.27% | 39.73% |

This is significantly different to the baseline case, but the left has won more, rather then fewer, seats when the left vote is split. This is a counter-intuitive result; it is possible that this is because seats that are demographically more favourable to the left attract more left candidates, but it would be impossible to verify this without considerably more research.

In 338 of the Conservative victories, the Conservative vote was greater than the total of all left parties. Adding these to the seats actually won by left parties as seats where splitting the left vote **definitely** made no difference gives a total of 635 seats. The 100% theoretical transfer to the leading left party would gain them 108 seats, or 14.59%. This is comparable to the 10.60% where a split right vote would make a difference on a 100% transfer. The table shows the effects at 50%, 25% and 10% transfer.

Split Effect

100% Transfer | 50% Transfer | 25% Transfer | 10% Transfer | |||||

Head to Head Contests | 0.00% | – | – | – | ||||

Multiple Right, Single Left | 10.60% (16) | 3.97% (6) | 1.99% (3) | 1.33% (2) | ||||

Single Right, Multiple Left | 14.59% (108) | 8.24% (61) | 4.87% (36) | 1.76% (13) |

These figures are noticeably higher than the reverse scenario. This may reinforce the speculation that multiple left parties stand in demographically more favourable territory: not only do the left win more when multiple left candidates stand, but in such areas they could benefit more from theoretical transfers. This would lead logically to a hypothesis that where there are multiple left candidates, the *appearance* that vote splitting is costing the left potential victories is caused by the seat containing more left votes, rather than actually being caused by split voting. It would be useful to obtain some polling data on potential transfer inclinations of left voters, to see how important this is.

**d) Splitting Both Votes?**

These 613 seats break down as follows:

Right Candidates | Left Candidates | |||

407 seats | 2 | 2 | ||

175 seats | 2 | 3 | ||

20 seats | 3 | 2 | ||

10 seats | 3 | 3 | ||

1 seat | 4 | 2 |

The results were 388 Conservative wins, 1 UKIP win (389 right wins), 45 Labour wins, 178 LibDem wins and 1 Green win (i.e. 224 left wins). As the table below shows, this is similar to the previous analysis of seats where the right vote isn’t split, but the left vote is.

Right Wins | Left Wins | |||

Head to Head Contests | 76.25% | 23.75% | ||

Multiple Right, Single Left | 78.81% | 21.19% | ||

Multiple Right, Multiple Left | 63.46% | 36.54% |

Further analysis of multiple versus multiple elections is more complicated than above, as theoretical transfers are possible on both sides, but we can begin by determining the number of seats in which the winning party got more votes than the total for parties on the opposing side of the spectrum: this is 290 of the 389 right wins, and 162 of the 224 left wins. In the remaining 161 seats, we apply the same transfer thresholds – 50%, 25% and 10% – to both the winning party and the leading party on the opposite side of the spectrum. The results are shown in the table; the figures are marginally higher than, but very comparable to, the case with multiple right parties and a single left party.

Split Effect

100% Transfer | 50% Transfer | 25% Transfer | 10% Transfer | |||||

Head to Head Contests | 0.00% | – | – | – | ||||

Multiple Right, Single Left | 10.60% (16) | 3.97% (6) | 1.99% (3) | 1.33% (2) | ||||

Single Right, Multiple Left | 14.59% (108) | 8.24% (61) | 4.87% (36) | 1.76% (13) | ||||

Multiple Right, Multiple Left | 26.26% (161) | 4.89% (30) | 2.61% (16) | 1.47% (9) |

**Conclusions**

In areas where multiple right parties stand, there is no significant evidence of vote splitting harming the right. On the left, there is some evidence of harm, but at a very low level, 1 in 20 to 1 in 40 seats. Even this may be an artefact of seat demographics, rather than actual electoral damage. Further research, and opinion poll data, might resolve this.

In short, it would seem that not only does having more parties on the ballot paper mean more choice for the electors, it does not mean more problems for the politicians. Variety may indeed be the spice of (election) life.

I would welcome comments on or criticisms of the above analysis, or suggestions of different ways to look at the figures as presented or further analysis of the base data.