Exactly what will change if the UK adopts the Alternative Vote (AV) system in next May’s referendum? Reformers argue that AV removes any need for large numbers of voters to choose to vote tactically, rather than supporting their top preference party. But social science theory insists that tactical voting can occur under all voting systems, although showing up in different ways. Rafael Hortala-Vallve makes clear that AV will probably cut the incidence of tactical voting, but cannot get rid of it altogether.
Tactical voting denotes any situation where voters can improve their welfare (get a better outcome, given their preferences) by supporting a party that is not their top preference, that is by voting ‘insincerely’ for a party that is lower down their preference ranking but has more chance of winning, or defeating a strongly disliked opposing party. Under first past the post elections at present, of course, many voters are forced to vote tactically so as to avoid their votes being ‘wasted’.
This blog has seen a lively debate on whether tactical voting would continue if Britain votes to adopt the Australian system of Alternative Vote in the May 2011 referendum – see comments on earlier posts by Roger Mortimore, Andy White, and myself. Luckily, there is no disagreement amongst us that tactical voting remains a theoretical possibility under AV. Instead the disagreement focuses on whether tactical voting is at all likely in future UK elections held under AV. With the following example I’ll show that tactical voting may indeed be less likely under AV than under FPTP, but it is still a very likely event.
Before doing so I want to make sure we all agree on what is tactical voting (also called strategic voting, rather confusingly). A player (in the game-theory sense) acts strategically when he acts to maximize his own utility, while taking into account all other players’ actions. In a voting situation being strategic implies (1) taking into account the expected votes of other citizens, and (2) voting for the party that maximises expected utility (i.e. utility times the probability that the individual’s vote is pivotal). Note that often (indeed usually) a strategic vote may also coincide with supporting the party that is most preferred by the player. However, a sincere voter will stick with voting their top preference even if this produces a poorer result for them. In this post I will say that a voter is tactical when s/he is strategic and s/he is not voting her/his top preference.
First Past the Post
A typical constituency that displays tactical voting under FPTP is one where there is a progressive majority but the Conservatives have plurality support. (Alternatively, we could think of a constituency with a conservative majority but with plurality support towards a progressive party).
As an example think of the following preferences in the population:
35% Labour, 25% Liberal Democrats and 40% Tories.
In some circumstances we may observe the supporters of one of the progressive parties voting tactically in order to avoid a Tory candidate. In the previous example, some Liberal Democrat supporters may vote for the Labour candidate to ensure that the Tories do not win. In a way, the tactical vote does what the voting rule cannot do: it allows a majority of citizens to select a candidate that is preferred by them.
Let’s now analyse what would happen under AV. Some at least of the Tory supporters know that, once second preferences are taken into account, it is impossible for them to win (because there is a progressive majority in the constituency). However, they can try to influence which progressive candidate is elected. They especially want to do so when the progressive candidate that has most support among progressive citizens is the one they most dislike.
Suppose then that the second and third preferences in the previous example are set up in the following highly simplified way:
35% of voters prefer Labour to LibDem, and then LibDem to Tory
25% prefer LibDem to Labour, and then Labour to Tory
40% prefer Tory to LibDem, and then LibDem to Labour
In the above example, under the Alternative Vote sincere voting by everyone will elect a Labour candidate. However, some of the Tory voters could act strategically by marking the Liberal Democrat candidate as their first preference, and the Conservatives second. If 11 per cent of voters follow this course of action, the Tory candidate is eliminated under AV, the Liberal Democrat candidate is elected in a run-off against Labour. Notice here that the tactical vote of relatively few citizens (11 per cent) makes a majority (65 per cent) of all citizens better off than if everyone votes sincerely!
On strategic voting
So tactical voting is indeed a possibility under both electoral rules. However, the citizens that act tactically are not the same. In my example, under FPTP the Liberal Democrat supporters vote tactically, but under AV some of the Tory voters vote tactically. When there is a progressive majority but a conservative party has plurality support, then there is always scope for tactical voting under FPTP. The same thing applies in reverse if there is a locally conservative majority of Tory and Liberal Democrat supporters (as there may be under the current coalition government) but Labour has the largest single vote, hence the intense discussion of electoral pacts at the recent Tory conference fringe. Under AV, however, there will only be tactical voting when supporters of the party with plurality support prefers a centrist candidate that would not be elected unless the run-off stage is altered to include them.
It follows that tactical voting is less likely to occur under AV. In addition, social science research has also shown that voters are less likely to act strategically with voting rules that are more complex. Now AV is slightly more complicated than FPTP, and so recent work shows that we should expect less tactical voting here. However, there is also evidence of a different kind that the amount of tactical voting in proportional representation (PR) systems and FPTP systems is surprisingly similar. This effect occurs because the number of parties is mostly higher in PR systems (i.e. it is endogenous to the vote counting process being used). With more small parties in PR systems, the opportunities for voters to behave tactically increase (see Abramson et al, 2010). The number of parties in Britain is likely to rise somewhat under AV, so this will offset the effects above.
Notice also that tactical voting under AV may not only be observed by manipulating preference transfers or second preferences, which requires a high level of precision in knowing citizens’ preferences (as recent posts on this blog by Roger Mortimore or Andy White) have argued. It may instead be observed by directly manipulating the person that gets first preferences. Tactical voting of this second kind only requires the sort of information that is needed under FPTP.
Finally, I’d like to emphasise that tactical voting may not be that bad a thing. In my example above, tactical voting has allowed the selection of a candidate that is preferred by a majority of citizens. It would be difficult to disagree with the wish of finding electoral rules that are not manipulable -such manipulations do usually benefit those who are better at computing the best strategy or those who have better information. In most circumstances it allows voters to achieve overcome the limitations of the voting rule and achieve an outcome that is better for them.
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(Continuing my previous comment…)
“With the following example I’ll show that tactical voting may indeed be less likely under AV than under FPTP, but it is still a very likely event.”
Where in your post do you show that AV tactical voting will be a “very likely event”, and what do you mean by that? Do you mean it will be widespread, or do you mean that it is very likely that it will happen somewhere? Will it affect election outcomes?
Prof Nicolaus Tideman shows in his book ‘Collective Decisions and Voting’ that AV, based on real elections, is about 97% resistant to strategic manipulation. The equivalent figure he gives for FPTP is, off the top of my head, about 63%.
Your post assumes likelihood on the basis of theoretical possibilities and hypothetical examples. It glosses over the importance of opinion polling, yet given that opinion polling is the *only* source of information available to influence voters’ tactical decisions, it is crucial to the debate.
Indeed, as I focused on opinion polling and error margins in my own article, I think I’m well placed to ask you to forget your preconceived ideas for a minute and read my article again before replying.
It’s just not good enough to say, “I don’t know enough about polling data but i’m sure we can find many constituencies where this is the case.” How can you be sure if you don’t know enough?
I did read what you wrote, and perhaps I should explain why I didn’t agree with it:
The example of tactical voting you outline does not “only [require] the sort of information that is needed under FPTP”. Why? Because your example assumes that voters have predicted transfer patterns (in this case from Lib Dem voters) as well as first preference votes. That is a big leap from FPTP tactical voting, which only requires first preference assumptions. On top of that, the evidence seems to be that lower preferences are more volatile.
Your example also suggests that voters of a party with 40% of first preferences would sacrifice the chance of winning in order to elect a least-hated candidate.
I suggest you look at the AV model built by the British Election Study – http://www.oxfordjournals.org/our_journals/parlij/gsq042.pdf – which shows why such a strategy is unrealistic. Transfer patterns are not as tidy as your examples (by necessity) assume, meaning that first preference leaders are still the most likely to win after transfers. Empirical evidence of this is available in Australia at state and federal level.
In the election you describe, the sensible strategy for Conservative voters – based on the information available at election time – would be to vote sincerely.
I’m gonna tell you I tell young PhD students: Forget your preconceived ideas for a minute and READ trying to understand what the post says! You can later relate it to what you think is true!
In the post I show a situation in which tactical voting is a viable strategy with very little information. And the tactical move happens in first preferences! Let me explain you the example step by step:
– 35% of voters prefer Labour to LibDem, and then LibDem to Tory
– 25% of voters prefer LibDem to Labour, and then Labour to Tory
– 40% of voters prefer Tory to LibDem, and then LibDem to Labour
Sincere voting under AV yields the following results:
– 35%: 1st: Lab; 2nd; LD; 3rd: T
– 25%: 1st: LD; 2nd; Lab; 3rd: T
– 40%: 1st: T; 2nd; LD; 3rd: Lab
After first preferences are aggregated, the LD is dropped and the second preferences of citizens that ranked the LD candidate first are considered. This implies that the Labour candidate wins the seat.
However, the Tories have incentives to change their vote. What do they need to know to be sure that strategic voting is profitable? They simply need to realise that there is a majority of voters that favour LD or Lab above Tories (just the same information you need for strategic voting in first past the post). In such scenario, the Tories know the winner will be a Labour or a LibDem candidate (the Tory candidate is a Condorcet Loser thus can never win with AV) and they want to influence which of these two is elected. In other words, all Tories have incentives to vote in the following way: 1st: LD; 2nd; T; 3rd: Lab. Indeed a tactical vote because they are mis-representing their first preference!
I hope this point is now clear!
However, following your concerns, it is indeed true that tactical voting is less present with AV than with FPTP.
You say that AV tactical voting “may instead be observed by directly manipulating the person that gets first preferences.”
I think you need to illustrate how this would work.
“I don’t know enough about polling data but i’m sure we can find many constituencies where this is the case.”
I think the nature and limitations of polling data are actually crucial to this debate. In any election, different pollsters will use different methodologies, sometimes producing quite different results. At the national level, they’re usually pretty close, but constituencies are often incorrectly called – by pollsters, bookmakers, and ‘experts’. The truth is that the margins required to vote tactically are inherently too tight to ensure confidence in projected vote shares.
“At the same time, i am sure we can find a few constituencies where the vote intentions prior to the elections are so close (or alternatively, these predictions are so noisy) where tactical voting may have pervasive effects and elects a candidate a majority of the population despises.”
No, as I said in my article, there is no incentive to vote tactically in this situation – precisely because the outcome is too close to read.
Dave claims that tactical voting under FPTP “can’t go wrong”. But I think is most definitely can. Consider, for example, a constituency where the popularities are Lib Dem 31%, Labour 32%, Conservative 32%; and let’s continue the (rather debatable) assumption from the article that Lib Dems would rather have a Labour candidate elected than a Conservative one. In that case, some Lib Dems could be tempted to vote tactically for Labour rather than Lib Dem. However, if the preferences of the Conservative and Labour voters are each in favour of the Lib Dems in second place, under FPTP a few of them might also vote tactically for the Lib Dems. In that case, tactical voting on the part of people with a Lib Dem preference would manage to keep out their number 1 preference.
STV is also susceptible to tactical voting. In fact, there’s a mathematical theorem called Arrow’s Impossibility Theorem that basically proves that no voting system is fair. Look it up on Wikipedia: it’s an interesting read when discussing this kind of topic.
Thanks for you rcomments. You are entirely right that AV is nothing like PR (i already said so in a previous post). It was an error to bring in the reference on the comparison between FPTP and PR because, as you well say, it may lead to misunderstanding.
Now in terms of the level of information you need to be tactical with AV. I entirely agree with you that there are no time machines that allow us to look at the exact voting intentions of the population. Polls, however, can give us a good guidance… However, in the example above, the only information needed by a tory voter is realising that his candidate always looses against a labour or a libdem candidate. Under such circumstances there is no risk for any tory voter to vote tactically (as there is no risk for a third runner to vote tactically in a FPTP system). I don’t know enough about polling data but i’m sure we can find many constituencies where this is the case. At the same time, i am sure we can find a few constituencies where the vote intentions prior to the elections are so close (or alternatively, these predictions are so noisy) where tactical voting may have pervasive effects and elects a candidate a majority of the population despises.
I hope i’ve clarified some of your concerns.
Dave, the link has now been fixed – thanks for pointing that out.
Interesting – but I think it is wrong in some respects. If you think I am wrong though please do post back so I can get a better understanding
What you have shown is theoretically possible – but what is also practically possible is that it can backfire. A party could have won but by using tactical voting move into second place and lose (I think this is what mortimer showed in his blog). I’m not sure why you didn’t show this but this fact alone means parties will not use it because the result of tactical voting becomes random. Under FPTP it can only ever be beneficial because it means a third place party voting for a second place party – it can’t go wrong and that is why millions of people do this every election which deprives them of voting for who they really want in order to keep out someone they don’t want at all. AV will give people the choice o voting for who they want and then who they don’t mind which allows a true reflection of voter option as well as ensuring that the winner gets over 50% of the vote – far far better.
As you have shown it is totally possible to construct numbers on paper to support an argument for tactical voting – but by doing so you are manufacturing the result. You are in the position of knowing how everyone is going to vote and you have power to compel the supporters of one party to do something all together in unison. The only way it could work is if people have a time machine to see what everyone is going to do in the future and then go back a get everyone of their supporters to do what they are told. But in reality…
1) people don’t know what the result will be until after it as happened.
2) people don’t know who all their supporters
3) supporters will act randomly, some will follow instruction, some wont. The party won’t know what percentage they need to follow instruction and how many need to vote the other way – it becomes unworkable complicated. Its ok having models and its easy to fit a model to real data but it is far more difficult to fit real data to a model. i.e. its easy to model something once you know what it is going to do, it is far more difficult to predict an outcome from a model
4) The party thinking of using tactical voting would not be able to because the know it could lose them the seat that they could have otherwise won
You mention that people can manipulate second preferences but this would be difficult From what I can see exactly the same problems will occur with first preferences (as described above and I think in the Mortimer blog as well). If you have any analysis to the contrary please present this because I want to make sure I know the facts. The problem with all theories of voting is that the only hold after the election but tactical voting needs to be applied before everything is known
AV does really get rid of the chance of tactical voting.
Also I am puzzled at your statement about PR – AV isn’t PR of course, this needs to be stated I suppose just in case people read this without a complete understanding..
STV doesn’t seem lend itself at all to tactical voting so your statement here appears incorrect. I suppose if someone wants their friend to be an MP but realises they will only get a hundred votes they may vote for something else but mainstream tactical voting is irradiated because people can get who they really want. If you have any more information on this could you please post it again. As you say in a multi party political system like the UK people are going to want to (and can) get their desired representative so why vote for someone else ?
If you disagree with any of this please do get back to me.
To conclude – I think the only way tactical advantage can be assured is to vote for who you really want first.
PS I can’t get into the PR link unfortunately.