{"id":84,"date":"2005-09-15T15:33:23","date_gmt":"2005-09-15T05:33:23","guid":{"rendered":"http:\/\/www.somethinkodd.com\/oddthinking\/?p=84"},"modified":"2008-03-02T10:50:46","modified_gmt":"2008-03-02T00:50:46","slug":"shannonpolls","status":"publish","type":"post","link":"https:\/\/www.somethinkodd.com\/oddthinking\/2005\/09\/15\/shannonpolls\/","title":{"rendered":"Shannon Poll<\/em>: Information Theory and Electoral Mandates"},"content":{"rendered":"

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Preferential Voting<\/h3>\n

For Australia’s House of Representatives<\/a>, each eligible Australian is required to (at least show up to) vote. They vote under a system called Preferential Voting<\/a>. Preferential Voting is a moderately complicated voting system, when compared to First Past the Post<\/a> but, arguably, it better reflects the voting public’s desires. <\/p>\n

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<\/a>]<\/p>\n

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.<\/p>\n

Information Theory<\/h3>\n

So, from an perspective of Claude Shannon<\/a>‘s Information Theory<\/a> perspective, the entire ballot paper conveys little more than one bit of information.<\/p>\n

Given that the voting card allows<\/em> for (log2<\/sub>(8!)) = 15.3 bits of information, that is a waste of over 14 bits!<\/p>\n

Well, 14 bits doesn’t sound like much but 14 bits per voter<\/em> 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.<\/p>\n

A Modest Proposal<\/h3>\n

So, how could we get more information out of the ballot, without actually impacting the election results?<\/p>\n

Here’s one way. <\/p>\n

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. <\/p>\n

Get the public to read through the statements, and select the one that most closely represents their point of view. <\/p>\n

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.<\/p>\n

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.<\/p>\n

Addressing the Concerns<\/h3>\n

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.<\/p>\n

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.<\/p>\n

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<\/em> 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.<\/p>\n

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<\/a>) 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.<\/p>\n

Applicability to the idea of Mandates<\/h3>\n

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.<\/p>\n

Like other Australians, I am forced to choose between two people<\/strong> with complex policy positions, neither of which accurately reflects what my positions on any of a large number of issues.<\/p>\n

Giving that the politicians are only receiving one-bit of information from me, it is meaningless to claim a mandate on any one issue<\/strong>, let alone claim a mandate on a whole platform of issues<\/em>. Yes, the politician has been given a mandate to rule<\/a>, but that can’t be converted into a “Get-Out-Of-Debate<\/em> free card”.<\/p>\n

Further Reading (For Me)!<\/h3>\n

I haven’t read Platypus and Parliament: The Australian Senate in Theory and Practice<\/em><\/a> myself. I apologise for not checking the original sources. However, an article in The Age<\/em><\/a> quotes the author, Stanley Bach, as reaching similar conclusions:<\/p>\n

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.<\/p><\/blockquote>\n

Howard and Mandates<\/h3>\n

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.<\/p>\n

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: <\/p>\n