Parliamentary Voting System and Constituencies Bill - Alternative Vote System

This page first posted 23 December 2010

The coalition government has introduced a Bill to change the way that constituency boundaries are drawn up and to hold a referendum on changing the voting system from first-past-the-post to the Alternative Vote scheme. This bill is called the Parliamentary Voting System and Constituencies Bill. This article analyses the potential impact of the Alternative Vote (AV) System. Our boundary change analysis is already available.

1. The Alternative Vote system

The Alternative Vote system is an another way of running elections for parliament. The current system, usually called the "first past the post" (or FPTP) system is quite simple:

The Altervative Vote (AV) system is a little more complicated. The basic idea is that voters rank candidates in order of their preference. If a voter's most favoured candidate is not popular, then the vote is transferred to the voter's second favourite candidate, and so on. The rules of the system are these:

The AV system can be good for voters who have a preference for more than one candidate (eg a Lib Dem supporter who also likes Labour, or a UKIP supporter who also likes the Conservatives). If the voter's first preference candidate does not succeed, then the voter's second (or further) preference will be used. The AV system is not so good for voters who only like one of the candidates.

From the candidates' point of view, AV is good if the candidate appeals at least partly to many voters, even if only a few are strongly attracted. Conversely, AV is bad for a strong candidate who has several (divided) opponents.

2. Alternative Vote example

It might help to see an example of the AV system working in an actual seat. Let's look at Bristol North West, which was won by the Conservatives in May 2010.

Bristol North West
County/Area: Bristol area (West)
MP: Charlotte Leslie  (CON)
Electorate: 73,469
Turnout: 68.51%

2010 Votes2010 Share
OTH2,321 4.61%
CON Majority3,274 6.50%

Suppose the AV system had been in use at this election. What would the result have been now?

Round 1 - Eliminate the "Other" party

The "Other" party has come last, so it is eliminated and its votes are transferred. It received 2,321 first preference votes, whose second preference votes are divided as follows:

Total Votes
No further

In fact, the "Other" party is actually the total of three parties (UKIP, English Democrats, and the Greens) rather than one single party, but the net effect is the same.

The transfer amounts come from the table in the section below. For example, the Conservatives receive 2,321 x 21.8% = 505 votes from the Others.

Round 2 - Transfer Labour votes

Now the Labour party candidate is in last place, so he is eliminated and his votes are transferred according to their second preferences (or the third preferences of the 316 votes which were transferred to Labour from Other at Round 1).

Total Votes
No further

Round 3 - Final winner

There are only two candidates left, and the Liberal Democrat candidate has more votes than the Conservative candidate, so the Lib Dem is elected with a majority of 4,564 (9.07%).

So under AV, the Liberal Democrats win this seat rather than the Conservatives. This is because Labour was in a strong third place, and Labour votes greatly prefer the Lib Dems as their second preference rather than the Conservatives.

3. Modelling the AV system

We can model the results of an AV system in a straightforward two-step process:

To do this, we need to know what voter's second preferences are. Peter Kellner at YouGov has kindly provided Electoral Calculus with polling results on this question. The poll was conducted just before the May 2010 general election, so it should be a relatively good guide to voters' intentions.

May 2010Second choice
Source: The Sun/YouGov, survey conducted 4 May 2010 - 5 May 2010, sample size 1901 voters. "DK" = Don't Know.

Each row of the table corresponds to the first-preference supporters of each party. For example, the first row corresponds to voters whose first preference is the Conservative party. The percentage numbers in that row indicate the second preferences of those Conservative supporters. For instance, 4.9% of first-choice Conservatives will switch to Labour for their second choice, and 46.0% of them will switch to the Liberal Democrats as their second choice.

This shows us that Conservative voters tend to give their second preference support to the Liberal Democrats rather than to Labour. Similarly, Labour voters also give their second preference votes to the Lib Dems (65.2%) rather than to the Conservatives (6.2%). Liberal Democrat voters are more evenly split, but generally favour Labour (42.8%) over the Conservatives (28.4%).

The pie-chart (see right) gives a graphical view of these preferences. The outer ring consists of voters' first preferences - 37% support the Conservatives, 30% support Labour and 24% support the Lib Dems. The inner ring shows the second preference of the voters. We see that Conservative supporters mostly give their second preference to the Lib Dems (pale yellow slice, labelled ConLib) or Other (biege slice, labelled ConOth), which includes "Don't Knows" or no further preference. There is only a thin slice of Conservative supporters who will transfer to Labour (pink slice, labelled ConLab). Labour voters mostly switch to the Lib Dems or Other, but Lib Dem voters can go to the Conservatives, Labour or Other.

4. History revisited with AV

We can use our table of second preferences to "re-run" previous general elections and see whether the result would have been different under AV. Note that this exercise is very indicative and approximate, rather than definitive. It is subject to three main approximations: (1) the YouGov table is just one medium-sized sample and is subject to sample error; (2) second preferences at previous elections might be very different from May 2010; (3) voters' responses to a pollster may be different from their considered view if AV were the official system.

Given those caveats we can calculate the result of each election since 1983 under both FPTP and AV:

Jun 1983FPTP39720923417Con majority of 144
AV34722459317Con majority of 44
Jun 1987FPTP37622922617Con majority of 102
AV33323759417Con majority of 16
Apr 1992FPTP33627120717Con majority of 21
AV29828842419Con short 28 seats of majority
May 1997FPTP165419461019Lab majority of 179
AV11242693919Lab majority of 193
Jun 2001FPTP16641352919Lab majority of 167
AV13841681519Lab majority of 173
May 2005FPTP19835662921Lab majority of 66
AV16435898521Lab majority of 70
May 2010FPTP30725857919Con short 19 seats of majority
AV26825897621Con short 58 seats of majority

We can see that generally AV is fairly bad for the Conservatives, very good for the Liberals / Liberal Democrats, and mildly good for the Labour party. However, most election results are not actually changed by using AV. But there are two main exceptions:

1992: Prime Minister Kinnock?

In April 1992, John Major's Conservative party won a narrow victory over Neil Kinnock and the Labour party. The Conservatives had a majority of 21 seats, though they soon lost much popularity in September 1992 when Sterling left the ERM.

However, with AV the Conservatives would not have had an overall majority. They would have been the largest party with 298 seats out of 651, and Labour would have been close behind with 288 seats. The newly-formed Liberal Democrats, led by Paddy Ashdown, would hold the balance of power. A Conservative/LibDem coalition would have a majority of 29 seats, but a Labour/LibDem coalition would also have a majority of 9 seats.

It cannot be certain what Mr Ashdown would have decided to do. But his later efforts to form an alliance with Tony Blair suggest that he could have been very open to a coalition with Neil Kinnock in 1992. History would have been very different if John Major had lost to a Labour/LibDem coalition, which would then have faced the coming financial crisis.

2010: Prime Minister Miliband?

At the general election May 2010, there was a hung parliament. David Cameron's Conservatives were 19 seats short of a majority and they formed a coalition government with Nick Clegg's Liberal Democrats, who won 57 seats. The Liberal Democrats had held discussions with both major parties, but chose the Conservatives over Labour because Ultimately the parliamentary arithmetic was one of the most important factors. Together, Labour and the Lib Dems only had 315 seats, which is eleven seats short of a majority.

However, under the AV system the parliamentary calculus would have been quite different. The Conservatives would have only won 268 seats (58 seats short of a majority), with Labour just 10 seats behind that. A Con/Lib coalition would have a majority of 80 seats, but a Lab/Lib coalition would also have had a comfortable majority of 60 seats.

5. Measures of Fairness

Some people prefer the AV system because it is fairer than FPTP. There is more than one way to measure fairness, but a simple thing to look at is the number of votes cast for each party divided by the number of seats that it wins (the "Votes per seat" ratio). In fact we will look at this ratio for the Conservatives and Liberal Democrats relative to Labour's ratio. We use Labour as a baseline as they often have the smallest Votes/seat ratio.

If a party has a relative ratio of more than 100%, this means that it needs more votes to win each seat than Labour does. If its relative ratio is less than 100%, then it needs fewer votes. If the relative ratios are around 100%, then the voting system is approximately proportional. The graph shows the relative ratios for the Conservatives and Lib Dems under both FPTP and AV for the elections between 1983 and 2010.

The following points appear from these data:

So AV is more fair to the Liberal Democrats, but less fair to the Conservatives.

Breakeven gap fairness

Another possible measure of fairness is to look at the gap between the Conservatives and Labour. In a fair system, the two major parties should get a similar number of seats if they get equal amounts of votes. In practice this does not happen for a number of reasons (see Gap Analysis Article for details). We can summarise the amount of unfairness in the gap, by calculating how much percentage lead the Conservatives need over Labour to get the same number of seats.

After the May 2010 election, this breakeven gap is 4.1%. That is, the Conservatives need 4.1% more votes than Labour to get the same number of seats. (This happens when the Conservatives get 35.4% and Labour get 31.3%.) But under the AV system, this gap increases to 6.5%. (The Conservatives need 36.6% compared with Labour's 30.1%.)

The graph on the right shows the breakeven gap for each election from 1983 to 2010, under both FPTP and AV systems. A gap of 0% is "fair", with a negative gap being favourable to the Conservatives (as in 1983 and 1987 under FPTP) and a positive gap being favourable to Labour (as in 1992 to 2010).

We see that, according to this measure, the AV system actually increases unfairness. In six of the seven elections, the size of the gap increases, which indicates the electoral landscape is less "fair". Only in 1987 does the gap size decrease, and then only slightly (from -3.9% to +3.5%).

This unfairness of AV between Labour and the Conservatives reflects the relative Vote/share unfairness that we saw above. Perhaps this should be balanced with the increased fairness which the AV system gives to the Liberal Democrats.

6. Changes in opinion since May 2010

Since the general election, there have been changes to voters' first preferences. The general trend was for Labour to gain at the expense of the Liberal Democrats. But there have also been changes to voters' second preferences. These are shown in the pie chart (left) and the table (below)

July 2010Second choice
Sources: Average of two polls
(1) The Spectator / YouGov poll, 5 Jul 2010 - 6 Jul 2010, 2224 voters;
(2) Lord Ashcroft / Populus, 9 Jul 2010 - 13 Jul 2010, 6003 voters.

These new data show that the remaining Liberal Democrat supporters are now more likely to favour the Conservatives (36%) over Labour (32%) with their second preferences. But Labour voters are confused and are now less likely to make the Lib Dems their second choice. Conservative voters are relatively unchanged, though slightly more supportive of Lib Dems.

Since the forming of the coalition government, it seems that Labour-leaning Liberal Democrats have abandoned the party and switched their support to Labour directly. The remaining Lib Dem supporters are more Conservative-inclined, and might be assumed to be natural coalition supporters. Many Labour voters are confused by the formation of the Conservative/Liberal coalition, because they used to see the Liberal Democrats as left-leaning. The percentage of Labour voters whose second choice is the Lib Dems has plummeted from 65% to 37%. Most Labour votes now prefer minor parties or "Don't Know" (52%).

At the current time (December 2010), headline Labour support has increased to 40% and the Liberal Democrats have decreased to 10%. We are not aware of any second preference polling since July 2010, but it might be expected to mirror the headline trends.

The new AV prediction feature (user prediction, choose Voting System = "Alternative Vote (AV)") uses the July 2010 matrix of second preferences shown above.

7. Summary

The summary of our analysis is:

Useful links

Some relevant web links:
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