Why do referendums use a binary choice rather than a numerical score?

Question

In some democracies, citizens may be asked if they accept a law or the modification of a law in a "yes or no" referendum.

Most of the time, legal texts are complicated and specialized, so why does the government ask citizens to be absolutely sure in their vote of yes/no?

What difference would there be in a voting system where citizens were asked to give a proposal a numerical score between 0 and 100, where 0 would mean "no" and 100 would mean "yes"?

Has this kind of 'quantum voting' been used before, and if so, was it useful?

Answer 1

Because the system highly incentivises strategic voting. The voting system you describe is more commonly known as score voting, although it has plenty of other names. It's been used before in the USA - the example given by Wikipedia is the election of officers in the Utah Green Party rather than on a referendum or legislative proposal - this used a ballot as shown below.

_{Image: Independent Political Report}

However, in his paper entitled Strategic Evaluation in Majority Judgement, Professor Jack Nagel explains how the voting system is highly susceptible to strategic voting.

For example, using the ballot above, a voter might believe that Guymon is worth a score of 8, Twitchell a score of 6, and Styles a score of 3. To increase the chance of Guymon winning, the voter might instead score Guymon a 9, and to decrease the chance of Styles winning, score him a 0. This is an example of "pairwise polarisation" - the least-favoured candidate being scored 0, and the most-favoured candidate being given the maximum score. In "complete polarisation", all candidates are given either the maximum score or the minimum score - which, Nagel argues, degenerates the voting system to simple binary approval.

It's not hard to see how this logic would apply to a referendum-style vote - even if a voter would sincerely give a proposal 80/100, this implies that they would rather the proposal pass than not, and they are incentivised to score the proposal 100/100 in order to maximise its chances. The end result is that the ballot degenerates to a simple "yes/no" vote.

Answer 2

In the specific case of a one-law referendum, which is what the question was asking about, what would be the purpose?

Let's pick a subject that will be polarizing and motivate people strongly, abortion for example. Now we have a referendum to allow it (Ireland did that recently, IIRC). Could be a referendum to forbid it, doesn't matter.

What does it mean to be 67% for abortion rights? Your brain is saying "well, I am 33% against too"? If you were voting on two different laws or two different political offices, then yes, you might "spend" 67% of your voting power to have your way on your most important subject, and 33% on your second important choice.

This logic might even work for 1 office and 5 candidates. 67% to your favorite candidate, 33% on your second-best choice. That makes sense.

But, again, for voting on one law and one law only, with a binary yes-no, what is the purpose of this quantified vote system? (please don't use quantum, it means quantified in discrete steps, not just quantified and poor word is overused ;-). You either want something or you do not. If you don't care - don't vote at all.

p.s. One valid reason for a quantified vote would be places that have laws forcing you to vote, even if you didn't care: voting 50/50 would essentially spoil your ballot, assuming there was no other way (such as voting blank or checking off both Yes and No). But that's a special case at best.

Answer 3

This answer is in the same vein as the one by CDJB, but explained a little differently. Consider the following voting system: There is a referendum, and everyone who votes gets to choose two things.

1. Whether they vote "for" or "against."
2. How much their vote is worth, or how much "weight" it has, on a scale of 1 to 100.

Then, the side that gets the most points wins. In other words, if there are only two voters, and one votes "against" with a weight of 20, while the other votes "for" with a weight of 70, the "for" side wins.

My voting system here actually turns out to be equivalent to your voting system, in the following sense: For every vote in your voting system, there's an equivalent vote in my voting system, such that the end result when totaling the votes as described by my voting system is identical to what it would have been if totaled in your voting system. For example, someone who votes 75-25 in favor of "for" in your voting system would vote "for" with weight 50 in my voting system.

With this equivalence in place, it becomes easier to see why the incentives for voting are a little bit weird; although it seems like it, the number assigned to your vote in your voting system is not actually an expression of how much the voter agrees with the proposal. Rather, its an expression of the voter's confidence in their own vote. Obviously, a strategic voter who is looking to maximize the chance that their preferred outcome is chosen would always assign their vote a weight of 100.

But even if we accept for now that some voters would assign their vote a weight less than 100 because their vote "should" be worth less than that of others (maybe they believe they are less informed than the average voter), it's still not clear that this would actually produce better results. In particular, people who are likely to be confident and self-assured about their opinion would have a disproportionate impact on the political decision.

Answer 4

Referendums typically use binary choice because statistics, psychology and logic.

• How strongly do I even agree with some referendum?

  Trying to put that on a scale of 0 to 100 is just going to be very prone to inaccuracy.

• What does some percentage agreement even mean?

  One might say degrees of agreement give more information, but I'm not so sure about that.

  Let's say the question is whether dogs should be allowed inside. Someone might 95% agree that dogs should be allowed inside at night or during bad weather, but 40% during the average day, and maybe 5% that they should be allowed to sleep in our beds and 20% that they can be on furniture. If they were to try to average that all out, they might say that's about 70% agreement. But all those numbers could also be very different and they could still reach the same 70%. Not to mention that each of the above percentages can be broken down further.

  One percentage just doesn't give that much information.

• Different people may give different scores for the same level of agreement.

  If you ask people to rate things on a 1-5 star scale, some will give 3 stars for something perfectly acceptable (to keep 4 stars open for above average and 5 for excellent), while that would be 5 stars for others.

  The same might apply to voting in a referendum, so this could introduce a lot of noise.

• How do you combine all those percentages?

  Maybe you say 2 75%'s, 1 100% or 50 51%'s are all equivalent, but some might argue that very strong agreement should be given an even higher weight, while others might argue that all agreement should be weighted evenly.

  With yes/no there's no problem, but with percentages you're opening the floodgates for disagreement about how to actually add up the results.

  Not to mention needing to present this to the public. "60% of people agree" is a nice and easy summary, while it would be much less elegant and potentially more objectionable to say "60% of people agree, but most of them don't agree so strongly, while those who disagree disagree more strongly, so ultimately we decided to go with those who disagree".

• Only 0% or 100% make sense / people may "game" the system.

  If I want the "yes" decision to go through, voting 100% is most likely to achieve that, so that's the optimal vote, even if my agreement is only at 60%. There's little logical reason from a game theory perspective to vote anything other than 0% or 100%.

  Well, 50% might make sense to express indifference about the result, but most who would go for that option presumably wouldn't care to go and vote at all. There may be some exceptions, but that still wouldn't justify a percentage score, but rather a "maybe" or "I don't care" option (although for the most part that probably wouldn't be useful).

• It should all average out either way.

  Given enough data, the end result should generally be the same regardless of whether they give binary choices or scores.

  On both sides you're going to have some people who feel strongly and some people who don't care that much. And most of the people who don't care that much aren't going to vote one way or the other.

Answer 5

Because the outcome is binary

The proposition either passes or it doesn't. As others have said, the only rational numbers to use would be 0% and 100%, and that's because you can only prefer one outcome over the other (or you don't care either way and then abstain or void your ballot).

Even if an elector can have a nuanced opinion on the subject, the options are only to either keep the status quo or to have this predefined package of changes to it. If you want to be fancy, you can have a complex "value function", but it is only evaluated at two points.

More complex voting systems do exist, but they are only useful where there are more possible outcomes, such as an election among more than two candidates or the composition of a board.

Answer 6

The Australian Constitution can only be changed through a referendum, and it is a requirement that the change be first passed by the parliament and then approved by the people through a referendum.

One benefit of this mechanism is to prevent the government proposing a vague change to get approval, and then sneaking in something different once the approval has been given.

As a specific example, in 1999 there was a referendum to change Australia to a republic from a constitutional monarchy. This was rejected, in part because a significant number of voters did not agree with the proposed President appointed by parliament and wanted a directly elected president.

A vaguer 'Do you want to be a republic?' question, without a defined mechanism covering the powers and method of appointment of the president, may be considered and passed in a plebiscite but a referendum would still be required under to constitution to implement a change. This prevents a government using the vague question to justify appointing an all-powerful unelected president for life.