Wednesday, 20 April 2011

UK Alternative Vote

Hi all, yesterday it occurred to me that I didn't really understand how votes are reallocated after each round in the proposed Alternative Vote system here in the UK. The Yes2AV group didn't help the case by explaining it almost as badly as the No2AV group, but after much discussion with friends I did refine it to a process that I did understand.

The basic idea is that you mark your preferences in order. This is simple enough to grasp. What isn't is when all the first preferences are added up and there is no majority (more than 50%), what happens next. The Eelctoral Reform Society has it as this:
If no candidate gains a majority on first preferences, then the second-preference votes of the candidate who finished last on the first count are redistributed. This process is repeated until someone gets over 50 per cent.
To me that is just not clear about what is going on. I spent over an hour on the phone and still did not understand. So we began our own based around Ice Cream to help demonstrate what is going on. Full details can be found on Kitty's blog. It also includes the raw data and my Python implementation amongst others. I recommend you check it out, but I'll come back to it later.

The way I found best to understand this was this:
  1. Imagine your ballot paper is a queue, you choose who is first, second, third and so on in that queue.
  2. When the votes are counted, you count ONLY the first person of each queue.
  3. If one candidate has more that 50%, that candidate wins. If not, the lowest candidate is eliminated, and removed from ALL queues, meaning anyone behind them moves forward into their place. Any that were 2nd choices have now been effectively added to the first choices. 
  4. Go to 2.
That may sound just as cryptic, but lets look at some visual examples. Say we have 3 candidates and 5 voters, and they vote the following. The votes are displayed horizontally, the preferences vertically, the green area being the first preference area.

So, blue has the least 1st preference votes, so is eliminated from the running, leaving this:


Now all the remaining votes move forward, like so:

And we now recount the votes in the green section. If there is still no majority, you continue eliminating the last place and moving votes forward until you do. In this case red wins even though all parties had the same number of votes, because it had the higher preference votes.

If a vote runs out of preferences, it is just discarded (and the quota is decreased accordingly) and the rules for tie-breaking depend upon the rules of the particular ballot you are participating in.

Hopefully you've understood that analogy. Now I'll talk some more about our test ballot. We took 70 votes for 5 candidate flavors of ice cream. Now using First Past The Post, Mint won, with 22 votes for and 44 votes against (the other 4 ballots were spoiled and invalidated). So more people would prefer not to have Mint than to have it.

This is where Alternative Vote comes in. The lowest vote was Strawberry, so we removed it from the votes, and moved the 2nd preferences forward. This was followed by the elimination of Fudge and Chocolate. What this left us with was Vanilla as the winner. It may not have had the most first preference votes, but because more people would accept it than mint (33 instead of 22), it's the least objectionable option, something the majority can enjoy.

So what does AV get us? More than one vote? No. Our first choice? Not necessarily. Someone we'd prefer over another candidate? Most definitely.

I'm not going to try sway anyone's vote for May 5th, everyone is entitled to their own opinion. Whatever your view, I hope this has helped you to understand the counting process under AV. 

2 comments:

  1. Under AV votes are WASTED. Read about it here: http://inaugural-uk.blogspot.com/2011/04/condorcet-paradox-vs-alternative-vote.html

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  2. Hi polibox, thank you for commenting on my blog post.
    However it is immediately evident that you have not read or correctly understood my post. My post is unbiased and is purely for informational purposes. It does not try to say one system is better than the other, it merely explains the mechanics of AV to try to help people make a more informed decision. As you will notice from the overall content of this blog, I have tried where possible to remain unbiased and keep my content purely informational. Whilst there have been cases that I appear to have endorsed a product, service or candidate, it has been mainly because using them I can provide the best examples of use.
    I did however take the time to read the linked post. The arguments in the post are biased and logically flawed. Whilst I agree with the point that AV is indeed more complicated that FPTP, it is not overly complicated once you have reach an analogy that works for you. This is the process I undertook as I initially had difficulty getting to grips with it myself.
    In the example vote we did the candidate that was in second place after round one won overall. The explanations for this are clear in the post, as were more people that disliked the first place candidate than the second place. What we proved is you get the least unpopular candidate, rather than the most popular. We also proved that AV does respect One Person, One Vote.
    Now, I'll move on to why your example is flawed. The votes you gave would (as you stated) result in a three way tie. In an election with only three voters there are only two possible outcomes, and it is mathematically provable that the second preference vote will not be used. The two outcomes are either a clear majority, or a three way tie. In the event of a tie, one of many tiebreaking rules can be used. This can be random selection, drawing straws, or forming a coalition.
    Let’s compare that to FPTP. If we took three voters, there are two possible outcomes. These two outcomes are either a clear majority, or a three way tie. In the event of a tie, one of many tie breaking rules can be used. This can be random selection, drawing straws, or forming a coalition.
    Therefore in the example you gave, both FPTP and AV would have had exactly the same outcome.
    The final flaw in you example is that you inferred that voters are able to change their preference after the vote has been cast. This is not true, once the ballot has closed all votes are sealed, and therefore Voter 3 has no agenda-setting power whatsoever.
    The only way this is possible is if all the voters collaborated before casting their vote. This is completely impractical in reality where the number of voters is much larger; it is less likely that the final voter will know what everyone before him has voted.

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