Countries rarely change their election systems, and when they do the changes usually ‘stick’ for a very long time. So the UK’s promised referendum on adopting the Alternative Vote in May 2011 is an historically important occasion. Rafael Hortala-Vallve argues that voters and politicians both need to take a long-term view of their decisions to back or oppose reform. Each system has its own problems and limitations.
An ideal electoral system does not (cannot) exist. This key fact has been known in the social sciences for more than fifty years, where it goes by the name of Arrow’s “impossibility theorem”. Questions about the design of any electoral system always generate political confrontations amongst advocates of different rules. A problem for the neutral observer is that these advocates often highlight only the good properties of their preferred electoral system, but ignore its unavoidable limitation.
In the United Kingdom, the First Past the Post System (FPTP) has the key problem that it only elects a single member of parliament per constituency, which creates anomalies where parties that receive a large share of votes nationwide but don’t come first locally are under-represented in parliament.
Yet this problem is not centrally addressed by the referendum choice, which will have only one possibility for a change – that is, to introduce the Alternative Vote (AV). This is a system where citizens rank candidates in order of preference. LSE’s Simple Guide of Alternative Voting Systems describe how the system then operates as follows:
Voters fill in a ballot paper where they number the candidates in order of preference – that is, they put 1 for their first preference; 2 for their second choice; 3 for the party they like 3rd, and so on.
We count all the first (top) preferences that voters have given, as now. If any candidate gets majority support (i.e. 50% +1), they immediately win the seat. If not, the candidate who has the fewest 1st preference votes is knocked out of the contest, and we look at the second preferences of their voters, redistributing these votes to the remaining candidates in line with these voters’ number 2 choice. This process of knocking out the least popular candidate and redistributing their voters’ choices as voters intended continues until one candidate gets 50 per cent.
In the USA this system is called ‘instant run-off’ and this is a good summary of what AV does – it delivers a run-off election when no one gets an outright majority on first preference votes.
Because it retains the current single-member constituencies, AV will not answer the issue above of disproportionality. But in the ‘classic’ or Australian form of AV described above it does take account of the citizens’ full preference ordering over the candidates.
For most constituencies, the change in electoral rule will probably not have any effects. When a candidate has the support of a majority of the electorate both AV and FPTP select that candidate. In the UK now, two thirds of the winning candidates for Westminster under FPTP do not have the support of a majority of their local voters. Yet in these seats some voters may already be voting strategically to try and prevent one candidate they dislike from winning the seat, as with Labour voters choosing to back the Liberal Democrats to try and stop the Conservatives winning a seat. This effect may mean that again the same candidate is elected under both AV and FPRP electoral rules.
However, there will be some cases (maybe only in 20 or 30 seats countrywide in the UK) where AV elects a different candidate than FPTP. If you think about this situation, you should realise that in these areas a majority of voters prefer the candidate elected by AV to the one elected by FPTP. It follows then that in each and every constituency where AV makes a difference, voting reform favours a majority of voters, while in constituencies where it makes no difference voters should be neutral between FPTP and AV. Given this, we might assume that an automatic majority of voters would exist nationwide to ensure the passage of the AV reform.
However, this relies on the assumption that voters only care about electing their local MP. It is obvious that elections are not only about this and that British citizens are also (indirectly) electing a Prime Minister and government. Under such considerations it may no longer be the case that a majority supports electoral reform. Quite a lot may depend on how much the electorate values the representation of their constituency interests.
The current debates around electoral reform already highlight the different properties of FPTP and AV. There are however a few misconceptions, some of which are being pushed by the Deputy Prime Nick Clegg and his colleagues, that I would like to clarify. First, AV does not eradicate the possibility of strategic voting. It is a mathematical fact that all electoral rules with three or more candidates are susceptible to strategic voting. (This rule is known as the Gibbard–Satterthwaite theorem).
Second, it is simply inaccurate to claim that AV unequivocally elects the MP preferred by a majority of voters. It is perfectly possible for AV to select a candidate who is ranked below another candidate in the race by a majority of the population. The example below shows a hypothetical election where candidate B is elected under AV even though a majority of voters would prefer candidate A to B in a straight contest between the two.
A hundred citizens are electing one of three candidates. The citizens’ preferences can be described as follows:
– 36 voters rank candidate C top, then candidate A second and candidate B as worst choice.
– 34 citizens rank candidate B top, then candidate A second and candidate C as worst choice; and
– 30 citizens rank candidate A top, then candidate B second and again candidate C as worst choice.
If we write > to mean ‘is preferred to’, then we can summarize the preferences of our electorate as follows:
for 36 citizens: C > A > B
for 34 citizens: B > A > C
for 30 citizens: A > B > C
Assuming that all citizens vote sincerely (i.e. follow their own top preference), then FPTP elects candidate C and AV elects candidate B.
The risks of FPTP are highlighted in this example: candidate C is the candidate ranked last by almost two thirds of citizens here, and this majority would prefer either candidate A or candidate B over the actual FPTP winner.
However, we can also see in this case how candidate B selected under AV does not have unequivocal majority support. In a ‘pairwise’ straight head-to-head choice between A and B – that is, if it was a run-off contest between these two candidates – then A gets 66 votes and B only 34. Thus a clear majority of voters prefer A to B.
(Incidentally if we also checked to see if A is preferred to C, this run-off would give candidate A 64 votes and candidate C only 36. In a rule suggested in the eighteenth century by the Marquis of Condorcet, A would clearly beat both her rivals in straight comparison votes).
The possibility of strategic voting (often called tactical voting in Britain) is present under both electoral systems:
– Under FPTP, voters supporting candidates A and B have incentives to coordinate and try to outvote candidate C.
– Under AV, if seven voters backing C pretend that they favour candidate A, then they will elect their second most preferred option as winner (candidate A instead of B).
It is worth noting here, however, that under FPTP, this example above also shows that the winning candidate would be C, who is actually the least popular candidate and the person considered worse than any other candidate by a majority of the voters. One thing you can say for sure about AV is that the system would never elect such an unpopular candidate, dubbed by political scientists ‘majority losers’!
The comparison between electoral rules is never straightforward: AV may be preferable to FPTP in certain aspects and hence solve some problems. But it also introduces some risks that are not present under FPTP. Because it is difficult (perhaps impossible) to foresee the full consequences of electoral reform, politicians should be careful in what changes they claim AV will bring about. Likewise, we should be wary of believing political fiction writers and their predicted consequences for electoral reform. Reform will in all likelihood considerably modify the actions of voters. It will also influence the strategies of candidates, parties, donors, interest groups, journalists, etc. There is however something of which we can be certain: AV would make UK politics more inclusive by making candidates compete for high rankings from the majority of citizens, instead of solely targeting their own core supporters.
The example shown at the begining assumes that each voter uses all thier choices, giving a ranking to each candidate. What happens to the results if votes choose not to use all their available votes – i.e. voting for 2 out of 5?
In that case, as long as at least one of the two preferred candidates remains in the count, those votes will continue to be counted.
However, should both the preferred candidates be excluded, then those votes will be discarded and take no further part. Such votes are said to have exhausted (as in, this vote exhausts after its second preference).
The winning candidate is the one who achieves more than fifty percent of valid non-exhausted votes.
Needless to say, the more votes exhaust, the closer the outcome is to FPTP. In the recent election in New South Wales – which uses AV of the kind proposed for the United Kingdom – about half of all votes exhausted and just one seat out of 93 went to a candidate who did not lead on first preferences. In the last federal election in Australia – where it’s compulsory to put a preference next to every candidate – candidates who trailed on first preferences won eleven of 150 seats (including one very rare case of a candidate winning from third).
In Australia, which uses preferential voting (similar to AV, but it’s compulsory to put a number in every box), tactical voting is extremely rare but it does happen.
For example, if a major party feels that they have no hope in a particular seat but that an independent might stand a chance, they will \run dead\ (that is, not campaign at all) in the hope of not coming second so that their preferences can determine the winner.
There have even been a few cases of the Labor Party running two candidates for a single seat to split their own vote so that they wouldn’t come second. This tactic never worked – their bitter enemy that they were trying to shoot down inevitably won with more that 50% of first preferences – so it was stopped in the early 1980s.
In May 2005 Labour won 355 seats- a majority of 72- with 35.2 per cent of the vote, or 21.6 per cent of all those eligible to vote. We protest against Mugabe keeping power with near 40 per cent of the vote and invaded Iraq, where it would have more than likely that Saddam would have done better than this in a free election. Should we invade ourselves to ensure fair election results?
Politicians are self-serving rather then being interested in the will of the people. Parliament should represent all sections of society and the Prime Minister directly elected. There is no perfect system but al least chose one that best serve the people rather than the politician.
Put simply the Alternative Vote (or Instant Run-Off voting which is actually a more descriptive name for it) appears to be a better voting system to ensure a higher degree of majority for the winning candidate when there is just one position to fill from a field of multiple candidates, which is why it’s used for selecting the winner of the Best Picture Oscar, selecting the speaker of the House of Commons & also most recently for the selection of a new Peer to join his/her fellow *unelected* Peers in the House Of Lords. Voting in our general elections is just the same- all we vote for is for 1 person to become our local MP- nothing else directly, just that 1 job (from a list of multiple candidates).
In my local constituency nearly 6 out 10 voters didn’t vote for the guy that won, as he squeaked home under our current threadbare system with a touch over 40% of the votes cast. This is a poor state of affairs regardless of if you vote for the guy who wins or not. AV would help sort this situation out, which is why out of a straight choice between FPTP & AV I’m certainly in favour of AV. Coalitions happen under FPTP as well as AV & aren’t just the ‘fault’ of the voting system….and dare I say it- aren’t necessarily such catastrophic things either. Compromise is something nearly all of us do in various aspects of our lives- why is it such a dreadful thing when it comes to those who govern in our names?
Sorry! The political transformation to beat them all is our hostage status as a milch cow within an EU of 500 million “fellow citizens”….all executed with utter contempt for the principles of democracy and the views of the British people.
Perhaps you “polsters” and psephologists (and your fellow travellers at Westminster and in the City of London) need reaquainting with the real world….as run by folk like Hitler/Mussolini/Franco and Osama Bin Laden?
And when are we getting an English parliament/assembly?
In fact the most successful political transformations have been backed by indifference and contempt for the law and the electoral process…and here I speak of the Irish nationalists in Northern Ireland under Messrs Adams and McGuiness.
But they had the Americans and America`s handmaidens at the BBC quietly supporting them……whereas British nationalists like Nick Griffin and the EDL most certainly don`t!
You chaps in the London political/media bubble would never allow Nick Griffin to form a coalition government in the way Adams and McGuiness were installed by Queen Hilary the Misrememberer!
This is a complete red herring ….now that whatever way you vote you get much the same government policies and priorities ….and have done since around 1980!It`s just like re-arranging the deckchairs on HMS Astute!
We would be better off petitioning Washington to become part of the USA and voting in US elections…or bowing to the realities of our true status in the global capitalist world by sacking the entire political class,selling off Westminster as a museum and calling in Warren Buffet or George Soros as our interim dictator ….while we adjust to our minor role as a post-industrial,post-democratic Second World member of the USA`s european empire.
Hi there –
Thanks for the plucky attempt. But I’m afraid that as a reasonably literate but unmathematical voter, I still don’t understand the A.V. system, its advantages and pitfalls.
I can’t see how the entire U.K. electorate is going to be able to take a meaningful decision in a referendum on this complex issue. I hardly think that politicians are going to give us a disinterested answer, and so I fear the whole exercise is going to be an expensive mistake.
What your article does not appear to address is how common is the use of A.V. ; and is it considered to work by the electorate in those ares which have adopted it ? I would have thought that consideration would be worth a thousand theories. But then I’m not an academic, either !
The Gibbard–Satterthwaite theorem, named after Allan Gibbard and Mark Satterthwaite, is a result about the deterministic voting systems that are designed to choose a single winner from the preferences of a set of voters, where each voter ranks all candidates in order of preference. The Gibbard-Satterthwaite theorem states that, for three or more candidates, one of the following three things must hold for every voting rule:
1. The rule is dictatorial (i.e., there is a single individual who can choose the winner), or
2. There is some candidate who can never win, under the rule, or
3. The rule is susceptible to tactical voting, in the sense that there are conditions under which a voter with full knowledge of how the other voters are to vote and of the rule being used would have an incentive to vote in a manner that does not reflect his preferences.
Since rules which forbid certain candidates from winning or which are dictatorial are not suitable for real-life voting systems, all voting systems which yield a single winner either are manipulable or do not meet the preconditions of the theorem. Taylor shows that the result holds even if ties are allowed in the ballots: the winner is then chosen from the candidates tied at the top of the dictator’s ballot.
This is my understanding – please correct me if I have misread the theorem
This of course is a mathematical theorem which will hold true if a majority o the population know how the other people are going to vote for sure. The maths break down when people are involved because we are beautifully unpredictable and do strange things. Since people cannot understand who other people are going to vote for there is no way that the tactical voting can work effectively. The best way is to get what you want is to be honest.
Also under every system 1 and 2 can hold true anyway – i.e. there may be a very close run competition where the final vote cast decides the winner. (of course this last vote could be swapped with any other vote). I’m presuming this means that one party didn’t gain enough votes to ever win. Say the run of was between the greens, UKIP and the BNP and the BNP got 100 votes in total on all preferences whereas the others got thousands then this I’m guessing would fit into number three.
Because outcomes 1 and 2 are not known until after the results are in there is no way if knowing if outcome 3 would ever come off anyway – even if everyone knew what everyone else was going to do.
As I said if anyone understands this theorem in practice please correct me so I know what I am on about in future if I don’t now 🙂
From the studies I’ve seen AV is on average more proportional than FPTP which your (good) article misses – see Electoral Reform Society – AV a better alternative? for a full description. Since AV is more proportional and as the added bonuses you have listed it does become a better option than FPTP. admittedly STV or other PRs are better but the powers that be doesn’t want us to have that much power yet so we are stuck with getting AV.
Also about tactical voting – as other comments have said it is not possible really to tactically vote with AV. there can be a gentle ‘nudge nudge effect’ where some people can back a minority cause with their first preference and then knowing that wont win , back their first preference with their second vote – this has the advantage of sending a message to the establishment of the voters wishes while them still not losing their vote. However, proper tactical voting – like we see everyday in FPTP doesn’t work. Theoretically it might but all the reports I’ve seen of real life simulations show that tactical voting can have extreme adverse effects and actually do the favoured party damage rather than benefit them so it would not be used.
Again it is theoretically possible to get weird results come out but I would think the chances of this are statistically insignificant and the odd occasion that does crop up would not detract from the vast majority of cases where the voting is accurate. At the moment under FPTP the majority of voting could be said to be inaccurate because most people don’t ever want the elected mp to represent them (well more precisely they haven’t said they want them). You have shown that a problem could occur (as I said this is possible but statistically rare) but you have contrived the results to show this – for example but limiting the possible permutations and then but setting the cohort size and vote split specifically for this purpose. This wont usually happen in practice and as i said the odd dodgy result doesn’t detract from the majority of good results – the opposite effect of FPTP
When it comes down to it FPTP just is not fit for purpose and in no way reflects what the people want. At least AV can demonstrate a popular support for each MP which goes towards legitimising politics again.
Thanks for blogging the article – it has been a good talking point around some of the complexities that can be drawn out of AV. I believe though even when the complexities are drawn out AV is shown to be even more superior to FPTP.
It’s nothing to do with rationality — the key is available knowledge. It is simply not practical to vote tactically under AV. You would need detailed knowledge of the kind only available AFTER the count.
Let’s look at the kind of constituency profile needed to vote tactically under AV. The rules are quite basic:
1. The 1st place party (Party A) can lose to the 2nd place party (Party B) on preference transfers — i.e. Party A has less than 50% first preference support.
2. The Party A can shed enough ‘tactical’ first preferences to the 3rd place party (Party C) to switch the order of elimination without losing its own place in the ranking — i.e. the difference in first preferences between Party A and Party B is greater than that between Party B and Party C.
Already we’re envisaging something pretty difficult to predict, even with accurate polling. If you could predict constituency results to this level of accuracy then you would make an absolute fortune in the betting markets.
Given that Party A, in this context, would stand a reasonable chance of winning (based on pre-election expectations), it would be insane for that party to ask its voters to switch to Party C in order to prevent Party B from winning.
This is very different from FPTP tactical voting, where it is supporters of Party C (the third-placed party) who are encouraged to vote tactically — to choose between Parties A and B.
What I’m saying is that, in the real world (where elections happen), the secrecy and unpredictability of elections means that tactical voting is not an optimal strategy under AV. I was not passing any judgment on the rationality of British voters.
Electoral Reform Society
you seem to have a very low opinion of british voters rationality, but as the post explained the proposed rules will “influence the strategies of candidates, parties, donors, interest groups”. All of them have the incentives to acquire and, they might have quite a better chance of obtaining, the needed information for strategic voting (i.e voters preferences). With that info at hand they, probably will have the propensity to estrategicaly distribute the information to generate in voters the behaviour of strategic voting if they need that to avoid the victory of the less preferred candidate. So if it is theoretically possible to generate strategic voting to avoid their less favourable candidate to win, it is likely that candidates, parties, donors and interest groups will try for that outcome. It is true that the number of seats available will make such an strategy expensive, but in certain large constituencies it will prove to be worthwhile to try. And if something is true in social science is that one should never say never.
Tactical voting is NOT possible under AV in real-world situations. You can only give examples where the voters have some prior (fairly accurate) knowledge of vote counts, which is simply never the case in a UK parliamentary election. Moreover, if too many people voted tactically in a particular constituency, it would backfire. So not only would you need perfect knowledge of support for each candidate, but also perfect knowledge of how many other people will be voting tactically in your constituency!
For these reasons, I think it’s fair to say that AV does not allow tactical voting — even if mathematically there are ways of producing favourable results by voting dishonestly.
That is very different from FPTP, where tactical voting is quite effective and only requires a rough idea of which candidates can win a seat.
Electoral Reform Society
Your analysis assumes that elections take place in a vacuum, and relate to single issues. That is not so: there is polling and canvassing. Both of these are informal voting that can influence the outcome of the actual election. Moreover, there will be a learning process through which voters will discover when various forms of tactical behaviour are beneficial to their true preferences. This is especially true since voters are being asked to approve a bundle of policies from each candidate, not decide a single issue at an election.
I think AV will result in many more people voting for smaller parties as first preference, then playing safe with a big party in the second vote.
One of the problems of AV is it can tend to give preference to the second of votes of those with the smallest first vote.
Either I think its fairer and worth doing.
An interesting article which raises some important considerations. The Alternative Vote system is surely a poor compromise, when a more radical change is surely required.
Without knowing too much about Arrow’s impossibility theorem and Gibbard–Satterthwaite it seems that very rigid criteria are being placed on a voting system for it to be preferred, or even ideal.
We can say that some systems are better than others.
There is a great deal to be said in favour of the system endorsed by the Electoral Reform Society, STV. This is a preference voting method, but with multiple winner seats which provides proportionality. It also retains the practice of voting for individual candidates and not political parties.
The overwhelming problem with existing protocols is that we have single winner seats. Introducing the Alternative Vote would clearly not remedy this and if reform is as ‘sticky’ as the author suggests, this will be a mistake which is better avoided.
My own view is that we are much better off with multiple winner seats as this greatly reduces the advantage to be gained with tactical voting; a couple of systems which are not widely discussed are the Limited Vote which allocates to each voter a number of votes, and Approval Voting which effectively allows people to vote against candidates and not in favour of them, more analysis is provided here: http://bit.ly/cHXSBT
This is an important topic because the politics of a country is often driven by the method by which the votes are counted.
Thank you for an interesting article.
Have you examined approval voting (where each voter can vote for as many candidates as they wish) or score voting (where each voter can give each candidate a score from within a certain range (say, 0-9))?
I mention them because they pass the Gibbard–Satterthwaite theorem, for three candidates (but not for four or more), suggesting that they may be a quantum leap in improvement of electoral outcomes.
They can do this because G-S (like Arrow before it) was written under the assumption that all voting methods operate on voter’s ranked-order preferences; but approval and score voting do not use rank-order, but cardinality.
Sadly, the option appears to be AV or nothing 🙁
I had to read your article three times but I think I might have got it now, thanks for your very thorough explanation that lays out the mechanisms of what is a too rare occasion (for me at least) to really dig into.
It’s really pretty sad that you discuss Condorcet without mentioning that Condorcet can sink into a series of unresolvable cycles.
Thanks for reading the post.
Condorcet cycles are not present in the example I’m proposing. Besides, the idea that preferences may be cyclic is already captured when mentioning Arrow’s Impossibility Theorem.