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Introduction

There is no perfect voting system.

Whatever system you use, there can be situations where the system delivers the wrong result, according to some fairly obvious criteria for a fair system – and this has been mathematically demonstrated.

But this does not mean that all voting systems are equally bad: some wrong results are much more likely than others, and the fact that no system is perfect should not stop us from using the best system available.

Some voting systems take more time and involve more work than others – and in many democracies, voters are remarkably fond of results which can be produced quickly and cheaply. It seems to me that it is worth investing a little thought, and a little time and money, if the result is that we are less likely to elect someone who is incompetent or corrupt, or who represents a small portion of the electorate.

Why This Matters

In the UK, the usual voting system – often called ‘First Past the Post’ (‘FPP’) – is deeply flawed. There are some obvious problems with it.

• A small preference among the electorate can lead to a large (or ‘landslide’) majority in parliament.
• It denies fair representation to supporters of minority parties.
• Consequently, it drives the electorate towards a two-party system, which limits voter choice and skews political debate.
• It can (and often does) give the winning party a significant majority of seats on the basis of a minority of voters actually voting for them. Even if there are only two parties, you can form a government under FPP with only 25% of the total votes; with three parties, 1/6 of the total is sufficient.
• It encourages candidates to demean the other parties and alienate their supporters – these people will not vote for you anyway, and this is likely to make your supporters more determined to get out and vote for you.
• It encourages tactical voting.

Tactical voting is a problem for several reasons.

• It requires voters to vote for someone they don’t want to win because they don’t want someone else even more.
• It requires voters to cast their vote based on their guess about how other people will vote, and not on the strength of the candidates.
• As a consequence, tactical voting makes it impossible to understand the actual wishes of the electorate from the votes cast.

Many (if not most) voters will have a preferred ranking of many of the candidates, and also a strength of preference for each place in the ranking – so maybe a small preference for candidate A over candidate B, but a strong preference for candidates A and B over candidate C; most voting systems cannot take this into account.

It should be obvious that any engaged voter will have a complex set of desires, fears and preferences, all of which are important to them; and it is impossible to express this complex reality solely through the choice of one candidate from a list. The more information which can be captured in the voting system, the better able the system will be to translate the wishes of the electorate into a fair result.

For more about why this matters, please see the article about Electoral Reform.

The Task

We want a system which enables a specified group of people (the ‘electorate’, which may be very large) to choose (‘elect’) one person from an arbitrary number of candidates. There are seven fairly obvious criteria which we want the system to meet.

1. Honest: voters must know who is standing, and be able to vote as they choose.
2. Reasonable: increasing the votes for a candidate should not make them lose; decreasing their votes should not make them win.
3. Universal: the result must be produced from the votes of all the electorate – nobody should have their choice ignored, and every person’s vote should be worth the same as every other person’s vote.
4. Consistent: if voters unanimously support candidate A over candidate B, then candidate A should beat candidate B.
5. Transparent: anyone with a complete knowledge of the votes and the system will understand how the outcome was arrived at. This implies that everyone who applies the system, and who has a complete knowledge of the votes, will arrive at the same outcome. Of course, a complete knowledge of the votes does not mean knowledge of who cast which votes, which must remain secret.
6. Specific: the relative ranking of any two candidates should only depend on the voters’ preferences between those two candidates. This is often called the ‘Independence of Irrelevant Alternatives’, or ‘IIA’; it means that, if a third candidate is introduced, and if the preferences of the voters for the first two candidates is unchanged, then whatever votes the third candidate receives, this will not affect the relative ranking of the first two candidates.
7. Relevant: voters should be able to vote solely on the basis of their assessment of each of the candidates. Voting choices should not depend on any other factors, such as how other people are expected to vote.

It may also be desired that a voting system always produces a clear winner, but no fair voting system can avoid the possibility of a tied result. In the UK, the returning officer is responsible for resolving this difficulty, but no explicit system is mandated: if there are two possible winners, the returning officer may decide the winner by tossing a coin; when there are more, they may decide by pulling a name out of a hat.

The Challenges

No voting system can deliver all of the seven desired criteria described above in all plausible situations, so we have to accept that any system we choose will be imperfect – but this does not mean that the different systems are equally imperfect. We can compare the weaknesses of the different options, according to the type of weakness permitted, and the likelihood of this weakness changing the result.

The last two criteria (‘specific’ and ‘relevant’) are the two we struggle to meet. There are two major theorems which demonstrate the inherent failings of voting systems.

Relevant. The Gibbard–Satterthwaite theorem from 1973 shows that it is impossible to completely eliminate tactical voting: it is impossible to design a straightforward voting system, where it is always obvious to a strategic voter which ballot they should cast.

However, tactical voting always depends on guesses about how the rest of the electorate will vote – and this, of course, must include guessing about the amount and nature of tactical voting. Given that people also tactically lie about their voting intentions, this is never a simple activity, even with FPP; it is far more difficult – and therefore less likely to be attempted – with more accurate voting systems.

Specific. Arrow’s Impossibility Theorem (first published in 1950) showed that no ranked voting system can completely eliminate the ‘spoiler effect’ – that is, it no such system can satisfy the ‘Specific’ criterion described above: an ‘irrelevant alternative’ will sometimes affect the ranking of other candidates.

However, this is essentially an academic objection. If you know the preferences of the electorate for all the potential candidates, and those preferences are spread in a fairly specific pattern, then it is reasonably easy to devise two lists of candidates: one where C stands and A wins, another where C does not stand and B wins. But, in practice, we do not know the preferences of the electorate (that is why we are holding an election!), and nobody knows who is standing until the nominations are closed, so nobody can choose whether or not to stand, depending on the precise details of who else is standing.

Also, please note that this is only a weak and potential problem for ranked voting systems: with FPP, it is trivially easy to enter a spoiler candidate. If you don’t want a candidate to win, simply enter a very similar candidate, and you have a good chance of splitting the vote. Your candidate must appear to be genuine, but these days, if you are prepared to spend money on marketing, this is not difficult.

And, in any case, while it is a weak and potential problem for all ranked voting systems, some of them are less vulnerable than others. But this is not the place for such details of the systems, their costs and benefits; in my judgement, the potential dangers are not particularly dangerous, so the most important considerations are the cost and ease of implementation, but other views are also available.

The key point, is that any ranked system will translate the wishes of the electorate into an election result far more effectively than FPP.

The Main Options

First Past the Post. Everybody votes for one candidate, and the candidate with the most votes wins; we have already described the major weaknesses of this system. Globally, this is the second most common system in use: the majority of countries use some form of ranked system, which for our purposes, can be taken as another term for proportional representation. Among the ranked systems are the following.

Single Transferable Vote. Everybody ranks the candidates in order, according to their preference, the person you most want to win is number 1, and so on. If a candidate has the majority of first place votes, they are elected. Otherwise, the candidate with the fewest first place votes is eliminated, their votes are then distributed among the remaining candidates and a second count is made. If no candidate now has the majority, the person with the fewest votes is again eliminated and the process continues until one candidate has a majority.

This system encourages candidates to appeal to more than their core supporters, so it works to discourage extremism and generally produces a candidate with reasonably wide support. However, the candidate with the most support may not be elected: if everyone places them second, they will be eliminated in the first count.

Ranked Vote. Everybody ranks the candidates in order, according to their preference, the person you most want to win is number 1, and so on. Anyone not chosen, is jointly in the last place, so if a voter selects candidates 1, 2 and 3 out of nine then, for their vote, candidates 4 to 9 are all ranked 9. Add the ranks of each candidate together, and the candidate with the lowest number wins.

The main drawback of this system is that it encourages dishonest tactical voting against a candidate’s rivals: If there are numerous candidates and two main contenders, their supporters may choose to rank the other main contender last, even if in reality they prefer that person to some (or all) of the alternatives. But, even so, the candidate with the greatest support is still overwhelmingly likely to win.