ArticlesPreferential Voting
For Australia’s House of Representatives, each eligible Australian is required to (at least show up to) vote. They vote under a system called Preferential Voting. Preferential Voting is a moderately complicated voting system, when compared to First Past the Post but, arguably, it better reflects the voting public’s desires.
The voter must number, in order of preference, each candidate. There are around six to eleven candidates to choose between, with eight being a typical value. [Ref: Sampling of How-To-Vote cards from 2004 election]
In practice, however, there is only one or two (or occasionally three) candidates that have more than, say, a 1-in-10,000 chance of winning. For the remainder of this article, imagine an electorate with a (typical) eight candidates, and where only two candidates could conceivably be elected, given the electoral mood (also typical). The ordering of the other candidates in such an election has no practical effect – all that effectively matters is how you rank the two candidates against each other.
Information Theory
So, from an perspective of Claude Shannon‘s Information Theory perspective, the entire ballot paper conveys little more than one bit of information.
Given that the voting card allows for (log2(8!)) = 15.3 bits of information, that is a waste of over 14 bits!
Well, 14 bits doesn’t sound like much but 14 bits per voter sounds far bigger, especially when you look at the cost involved of collecting the ballots. However, you need to work the maths here carefully – 1000 voters won’t give you 14 kilobits of information, because there is no ordering between the voters. This article is already too mathematical for a blog, so I will leave that to the interested readers.
A Modest Proposal
So, how could we get more information out of the ballot, without actually impacting the election results?
Here’s one way.
First, come up with a list of 720 possible statements the public might like to send to the winning candidate, and against each one put a unique six-digit number – a permutation of the digits 3, 4, 5, 6, 7 and 8.
Get the public to read through the statements, and select the one that most closely represents their point of view.
Explain to the voters that they should look at how they were originally intending on voting, and just pull out the respective positions of the two most-likely candidates and place them one and two on the ballot. Then use the rest of the empty boxes to enter the permutation associated with the message they want to send.
If the AEC would then publish very detailed results of the voting, we could retrieve an extra 9 bits of information from each ballot paper. The public could use that channel to send a loud and clear message to all politicians about what they really thought was important.
Addressing the Concerns
Worried that such a system might prevent a third party from being elected? Fine, we can handle that. Determine the risk you are willing to take (1 in 10,000 would be my suggestion – that’s one wrongly-elected official coming to power every 30,000 – 40,000 years.) Any half-decent statistician with a moderately-sized sample could ensure that a particular election wouldn’t be affected. If another party has a chance, then let the voter rank the first three, and use the remaining 5 positions to send one of a smaller group of messages.
Worried that people voting regularly might be accidentally sending a message? If you are willing to sacrifice some bits as a marker or checksum, you could cater for this.
Worried that the minor parties will miss out on funding? That’s a good point. Under Australian law, there are some financial benefits to receiving at least 4% of the first-preference votes? The voter should select the favourite party first, and then the two most-likely-to-win candidates. This will cost a few bits of information, but we might be able to win some of those back if we customise the messages based on the first votes. If you vote for a relatively unpopular party first, we can start characterising your possible opinions more accurately in the published lists.
Think the same system would work better in the Senate where there was between 11 and 78 candidates in the last election (Ref: Group Voting Tickets) containing up to 382 bits of vote-carrying information? The Senate’s complicated method of assigning proportional voting makes the mechanisms required here beyond me – and beyond my ability to vote accurately enough to send the correct signal. We don’t want to create our own Florida debacle.
Applicability to the idea of Mandates
Am I really serious here? No, not really. I don’t propose we actually go ahead with this plan. What I am trying to illustrate is that the amount of information that the politicians receive through the electoral process is tiny.
Like other Australians, I am forced to choose between two people with complex policy positions, neither of which accurately reflects what my positions on any of a large number of issues.
Giving that the politicians are only receiving one-bit of information from me, it is meaningless to claim a mandate on any one issue, let alone claim a mandate on a whole platform of issues. Yes, the politician has been given a mandate to rule, but that can’t be converted into a “Get-Out-Of-Debate free card”.
Further Reading (For Me)!
I haven’t read Platypus and Parliament: The Australian Senate in Theory and Practice myself. I apologise for not checking the original sources. However, an article in The Age quotes the author, Stanley Bach, as reaching similar conclusions:
All claims of electoral mandates should be viewed with profound suspicion unless it can be verified that they accurately reflect the knowledge, preferences and intentions of the voters. Most often we can expect to find that mandates are mirages, the wishful thinking of those claiming to have received them.
Howard and Mandates
I am writing this in a non-election year. I am not really trying to attack any particular politician or any particular party. I am attacking the very idea of a mandate for a policy being provided via the Australian electoral system. I am attacking any politician who claims such a mandate, and any member of the press who lets them get away with it. I think that Information Theory proves it wrong, even if nothing else does.
Lest you think I am purely attacking the current Prime Minister, John Howard, at a time when he is pushing the sale of Telstra, let me re-assure you with two pieces of counter-evidence:
- A Stanford Uni researcher compared the 2004 Howard and George W. Bush elections and claimed that, after the 2005 Election, compared to Bush:
Howard seems reluctant to claim a mandate for conservative policies
- The same Age article, mentioned above, quotes Howard, back in 1987 when he was in Opposition, as saying:
The mandate theory of politics from the point of view of proper analysis has always been absolutely phoney.
Of course, if the reader can find examples of quotes from Howard that contradict these two points, then that would put Howard in the set of politicians being attacked here.
Comment by Alastair on September 16, 2005
You almost lost me there with the information theory discussion, but after slogging through it I think I agree with your conclusion on mandates.
In fact I raised a similar concern a while back (just after the last Federal election in fact), and proposed a (rather brute force) solution.
Comment by Casey on September 16, 2005
I think you are, perhaps deliberately, confusing a couple of different concepts here. Your comment about the information content of a ballot is a nice insight; given the type of data that I”m sure the Electoral Commission or various statistics bureaus have, it would actually be possible to compute the entropy of not only the ballot as a whole, but of each individual candidate also (taking into account the complete flow of preferences, etc). I’m not sure that your figures are quite right, I would guess that the entropy is probably a bit closer to 1.5 than 1, but your point is well taken.
If I follow your reasoning, your next steps are as follows. You assume that, by holding an election and giving space to a certain number of votes, they are making a statement about the amount of information they are willing to recieve from the voters. Since this information is currently wasted on noise, your proposal is to co-opt it for passing more data in the form of direct policy-related questions.
First, the assumption that the government is actually interesting in collecting information from us. The cynic in me wants to say that the government (whoever is in at the time) does not view an election as information collection at all. Referenda are a different matter, since it is a direct question-based vote, but again, the information actually of interest to the government is actually on the order of about one bit per question, per state. (adjust figures to match whatever arcane rules are actually in place).
Second, while I know that you’re not serious about your proposal, there’s nothing wrong with the idea of more direct representation in government – which is what you are advocating by passing more information through the ballot, and thus giving evidence of a “mandate” on a certain issue. A ballot, however, is probably not the right place to do it. Other proposals for open and participatory government are too much of a sidetrack here, but again, aren’t necessarily dumb ideas!
Information theory is a good way to look at community politics like this. While a letter to a politician contains a lot of words, and hence potentially a lot of information, quite often it is merely filed as a plus or minus on some policy. The extreme example of this comes from cases like GetUp, which automates the process of sending boilerplate emails to multiple senators. The information rate for such a campaign is continually dropping.
An interesting question to consider is a variation upon your own proposal. Let’s assume that the government has an infinite desire, and infinite capacity, to deal with information from its constituency (a wonderful pretense indeed). Now place a limit on the amount of information (read: mental effort) that each constituent is willing to give (read: time spend thinking about). Further, there is a certain amount of demographic information that is known for each person. The challenge: if you could make every ballot as different or similar as possible, how can you maximise the information you get out the process? The answer is difficult: you need to ask each person the questions for which knowing their answer should mean the most. What exactly that means, I’ll leave open to interpretation! Most interesting is if you could show that (within some bound) such a process approximated asking everyone all the questions. Then, you have a system which is no longer strictly “one man one vote”, since not everyone votes on each issue, but which is still equally “democratic”! Would you be happy if your neighbour got to vote on a tax cut, and you didn’t? People often grumble about their vote “not making a difference”, this is taking it to one logical extreme.
Gosh, this was a bit long, sorry.
Comment by Julian on September 17, 2005
So the formal and informal feedback on this article was that it wasn’t very clear at all. Sorry about that. I’ll be reviewing my practice of segueing from one topic to another in the same blog entry.
To clarify, I have always been confused (and distrustful) of politicians claiming a mandate ever since I first heard the word. I never really got how the concept could apply. Last week, I got an insight about how Information Theory could apply to prove that politicians were (wrongly) extracting more information from the election results than was there.
The Modest Proposal was a silly thought experiment to highlight that, while in theory there was a lot of information being passed in the ordering of the 8 candidates in a ballot, in practice there isn’t really – the public would never encode their vote so carefully. Without such a complex system – or the replacement of ballots with detailed surveys – the mandate claim is meaningless.
Comment by Julian on September 17, 2005
Alastair,
Yes, you do have a similar concern. I plan to post a comment on your blog entry to follow up with that idea there.
Comment by Julian on September 17, 2005
Casey,
I can see we are talking at cross-purposes; we are talking about different things – I apologise for the confusion, but also thank you, because your diferent approach is also interesting in its own right.
Effectively, what you are discussing is this idea: If the AEC were to come up with a loss-less compression system that could regenerate the exact same stream of ballot papers, in the order they were counted, what’s the fewest number of bits (on average) per ballot, that they would need. Because voters tend to be like-minded and vote the same way, they wouldn’t need many bits at all. Certainly it is above 1 bit; I am not particularly expert at estimating this, but even 1.5 bits sounds a bit low to me. This compression has nothing to do with the type of voting system – it is purely based on the similarity (low entropy) of ballot papers. This is an interesting view of the ballot, and not one I had given any thought.
What I am describing is slightly different. Each vote is going to be churned through the preferential system. That system throws away bits as certain parties are eliminated from the race; and it throws away bits in a predictable way if you know roughly which candidates have a chance of winning. So, if the AEC were permitted to come up with a lossy compression system that had a less than 1-in-10,000 chance of perverting the results of the election, they could bring it down to about 1-bit per ballot (or even less, where a large majority is expected for one candidate)
Again, this is to regenerate the stream of ballot papers in the order they were counted. Of course, ordering is not important in an election, so really, the AEC just needs to present the dozen or so bits for the whole electorate, which describes the ultimate outcome – and what we see on the televised coverage. As you point out, for a referendum, this compresses even further – as low as
It is these dozen bits that the unethical or confused politician claims is telling them that they should go ahead with the entire platform, without requiring further debate – and my real objection is that there is no way these dozen bits can carry that much information.
Comment by Julian on September 17, 2005
Casey, again:
I agree that this is another, perfectly valid, non-dumb way of doing democracy. I agree that the ballot paper is not the way get this information. I don’t agree that there is nothing wrong with the idea – there are the increased risks of Self-Inconsistency (Decisions to raise spending and decisions to lower taxes are popular.) and Tyranny of the Majority, just as examples. I agree that this is probably too much of a side-track to do this issue justice here.
Comment by Julian on September 17, 2005
Casey, one more time:
Certainly it is an challenging concept – especially the underlying result that people will only be asked to vote on topics that they are informed (or at least thoughtful) about. That would change the face of politics immensely! It has a certain amount in common with the idea of a politician meeting with selected focus groups, seeking their views – and all of the attendant problems of getting a representative sample.
Comment by Sunny Kalsi on September 19, 2005
I went on what I’d guess were a few man-dates with some friends of mine. Only one of them was available, and in today’s hurried lifestyle, it’s so hard to get everyone around for a BBQ.
In any case, you seem to be talking about minimising the number of bits per person. I don’t see how this is important, unless you want to save paper, or want to give people fewer decisions. In reality, it is often the case that we expand information to give to people. Text compression is an example: You would ask no one either to be able to read or write compressed text. Same with Ye Olde DVDs.
Maximising entropy might be good for giving the AEC smaller databases, but the usefulness of the data is not necessarily increased. In addition, it’s actually plausible that we can actually extract useful information from the extra bits. ie: If someone votes for one of the two major parties, you have the standard 1 bit. However, if someone votes for a third party (expecting their vote to work through preferences, as I often do) I’m actually telling you a lot more about what I want governing.
Also, you’re seeing people who only put a ‘1’ in one box and nothing else as also supplying 15 bits of information. I would argue they are only providing 1.
I conclude by saying: man-dating is necessarily gay, but often an important part of our increasingly metrosexual lifestyles.
Comment by Richard on September 20, 2005
Bah! You and your one-seat-per-electorate voting system. Give me Hare-Clarke with Robson rotation any day. Now that’s a system which might let you say “I’ve got a mandate! Hoorah!” It’s also a system where your candidates, above all else, need to be recognisable [Robson rotation tries to eliminate the effects of any donkey votes by making the order of candidates on a ballot different each time].
It still doesn’t eliminate the tyranny of the majority, but then nothing short of a government run on political correctness will prevent that. But that would just leave everyone feeling alienated by their government [but it could cause another minority to spring into being, which could then be the focus of the government, perpetuating the vicious cycle].