Voting Systems II – Referenda

This post is part of a series of posts on Voting Systems.

Leaders usually have a significant amount of power, so it is fairly easy to convince people that such elections are important, giving these elections a higher turnout than other elections (for example US Presidential Elections almost always have higher turnout than Midterm Elections). This means that we didn’t need to worry too much about low turnouts in the previous section.

This is no longer the case for referenda. Voting has a cost – at a bare minimum, it costs voters the time and effort needed to cast their ballot, and it can cost even more time and effort if a voter wants to become well informed about the issue being voted on. There are therefore several reasons why a large number of people might not vote in a particular referendum:

• They could be unfamiliar with a proposal or an issue, and deem it not worth investing the time in learning about it
• They could be opposed to a proposal but not sufficiently strongly opposed to overcome the cost of voting
• They could be strongly opposed to a proposal but not be expecting it to be popular, resulting in a “tragedy of the commons” like situation, in which people rely on the efforts of other people to vote down a proposal

This results in a risk that a very small number of passionate voters could pass legislation that a large number of people are against.

Thresholds

For this reason, some referenda are implemented with a turnout threshold, such that if fewer than a certain proportion of the electorate vote, the proposal automatically fails and the status quo is maintained.

This leads to its own issues however. If you set the turnout threshold to a level less than 50%, a minority view could be held by a number slightly below the minimum turnout, such that voting against a proposal can validate a result in favour of the proposal. For example, imagine a hypothetical country with a population of 1,000 and a turnout threshold of 40%, where 390 people are strongly in favour of the proposition, and the remaining 610 are against it:

• The 390 people in favour are going to vote for the proposition, so what should the remaining people do?
• They could all boycott the referendum, and it will fail to reach the threshold to be a valid result, meaning that the status quo would continue with the proposition not being implemented.
• If at least 391 of them vote against it, this would mean that the proposition was voted down, meaning that the proposition would similarly not be implemented.
• If however, enough people decided to boycott the vote that fewer than 390 people voted against it, this would be a problem – the turnout would be >40%, validating the referendum, and the proposition would win with more than 50% of votes cast.
• There could be a situation where most of the electorate boycott the vote, but 10 people “don’t get the memo” and vote against – these 10 votes cause the threshold of 40% to be reached, resulting in the proposal passing with a 97.5% majority, despite 60% of the electorate being opposed to the proposal, but abstaining from voting or boycotting the vote.

In fact, this issue can occur with an even higher minimum turnout threshold. A threshold of 60% would simply mean that this situation would occur if between 210 and 390 people voted against. The higher the threshold is, the narrower this band is, making this situation less likely, but the possibility of this situation does not completely vanish until the threshold is 100%.

If we decide that we can live with this band being sufficiently narrow, does a high minimum turnout threshold work in other scenarios? Unfortunately not. The problem with having a minimum turnout >50% is that even if something is largely supported, it can be very hard to get people sufficiently motivated to turn out. For example, in the Republic of Ireland, the referendum on the 38th amendment to the constitution was passed with 82% of voters in favour, but turnout was only 51%. If a high threshold such as 60% had been in force, this would not have passed.

Clearly there is an important balance to be struck between allowing minority views to hijack legislation and requiring an unrealistic level of voter engagement, and turnout thresholds are not it. The discontinuity in outcomes that exists around the turnout threshold results in pathological behaviour of the voting system.

Avoiding Discontinuity

Thankfully, this balance can be achieved without such behaviour by using a particular form of our new friend Range Voting. Rather than using a range of 0–4 or the Approval Voting “range” of 0–1 we can use -1–1. This has been given a few names including Combined Approval Voting and Evaluative Voting (EV). By allowing both positive and negative scores, this allows people to vote against propositions as well as voting for them, and gives a convenient way of representing the level of support.

If we use a system that calculates results as a percentage of the total eligible population, and treat a vote of zero the same as an abstention for the purposes of the results, we get the following outcomes:

Votes for (+1)	Votes against (-1)	Neutral votes (0) & Abstentions	Total Score
20%	0%	80%	20%
20%	1%	79%	19%
30%	10%	60%	20%
30%	11%	59%	19%
40%	20%	40%	20%
40%	21%	39%	19%
50%	30%	20%	20%
50%	31%	19%	19%
52%	48%	0%	4%
60%	40%	0%	20%

This means that we can introduce a score threshold without causing the issues described above. If a score threshold of 20% were in effect for the above results, the first row would be a success for the proposition (i.e. nobody cares, except for the 20% of people that want it), but a small number of people voting against it have their votes subtracted from the score, pushing the outcome below 20%, meaning that the proposition fails (in contrast to the turnout threshold above).

In the subsequent rows, it can be seen what proportions of voters for and against a proposition result in its success or failure at a particular turnout. Importantly though, it is never the case that turning up to vote against a proposition would result in a proposition succeeding that would otherwise have failed.

This approach also reduces the divisiveness of very closely fought votes: as can be seen from the second to last line, 52% voting +1 and 48% voting -1 would give a result of “4% in favour” which would not pass a score threshold of 20%, meaning that the status quo would continue until more people could be convinced to switch sides.

The score threshold therefore performs two functions simultaneously:

1. Preventing passage of laws that only a small proportion care strongly about
2. Privileging the status quo in a closely fought, divisive decision

Where to Draw the Line

Exactly what percentage this score threshold should be set at is a very good question, but I am inclined to suggest somewhere between 10% and 50%. For the first function, needing much less than 10% of a population to vote in favour of an issue could lead to situations where it is in a politician’s interest to keep publicity of a referendum to a minimum, so that most people don’t vote because they’re not aware that it is occurring. On the other hand, requiring more than 50% means that the only things that can be passed are things that a majority of the population are already motivated about. Things that certain groups are passionate about, but that the majority are indifferent about would never pass.

Looking at the second function, requiring a score of more than 50% would mean that things would be impossible to pass despite only being opposed by a quarter of the population. Although this might look like it would help avoid a “tyrrany of the majority” scenario, this would likely just result in legislative deadlock that would delegitimise the system and result in its eventual collapse. At the other end of the spectrum, requiring a score of less than 10% would mean that laws could be passed if the votes were 45-55 or closer. In a hotly contested vote, this is likely to cause great divisions within the country’s populace. The UK’s 4 year long (and counting…) constitutional crisis that resulted from the Brexit referendum is a good example of this, where out of the 46.5 million registered voters, 37.4% voted to leave the EU, 34.7% voted to remain in the EU and 27.8% abstained from voting. This would have given this referendum a score of only 2.7% in favour of leaving, but without any thresholds in place, this was deemed a mandate to deliver an enormous constitutional change. Such a divisive policy being implemented with such a slim majority has resulted in years of political deadlock and acrimony, as well as generating deep divides between different sections of the UK’s populace.

This might sound very similar to offering an ordinary vote between a new policy and the status quo, and simply subtracting the votes of one from the other. There is a subtle difference however – by allowing each choice to be scored positively or negatively, two additional features are able to be realised:

• It allows multiple proposals to be compared simultaneously (again with low risk of the spoiler effect). This means that rather than a single option that could be divisive or a poor compromise, many options can be put forward, and the one with the broadest appeal will win (as long as it scores above the threshold).
• It allows a government to determine a proposition’s popularity relative to the status quo without having to implement the proposition. If none of the options score above the threshold, the status quo will continue, but if the status quo is itself on the ballot, it may well have actually scored lower than many options. This would be very informative to a government, letting them know that there is a large appetite for a solution. At this point, rather than passing a divisive and half-baked law, a government could attempt to mediate between different interest groups to find a mutually agreeable solution that would have broad enough appeal to pass the threshold.

Of course, there is still no substitute for referenda being well worded and clear. One of the great features of the referenda that are used to amend the constitution of the Republic of Ireland is that they are votes on whether or not specific wording should be added to (or removed from) a document. The law being changed is clear, and the way in which it is changing is clear, so there is no room for ambiguity in the interpretation of the people’s wishes.

Using Evaluative Voting, multiple proposals to address the same issue could be put forward and voted on in a single referendum, but each proposal really should be well formed, to avoid confusion. Any referendum that is not asking about specific wording for a specific law is asking for trouble. This can be seen by the endless discussions and recriminations about whether the “will of the British people” was to [join the EFTA]/[continue within the ECJ]/[enter into a customs union] after leaving the EU (delete as appropriate). A referendum is not an opinion poll, and should be invoked with the same care and attention that any other election is due.