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 March 29th, 2011, 08:15 AM #1 Newbie   Joined: Sep 2009 Posts: 13 Thanks: 0 Analysis of Alternative Vote vs First Past the Post With the debate starting over the voting system in the UK and with Alternative Vote on the table against First Past The Post. I was wondering what a mathematical analysis could tell me about the 2 systems, such as characteristics at different levels of voting and representativeness of the proportion of the vote. However my maths is not much better than high school, so I was wondering if anyone could give me some ideas about where to get started in taking an approach to look at this? Also I wondered what your thoughts about this were? ([color=#FF0000]edit[/color]) Of course I can look into any suggestions of things more advanced than Hight School level.
 March 29th, 2011, 11:45 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Analysis of Alternative Vote vs First Past the Post FPTP (plurality voting) has lots of problems. Vote-splitting is the most famous; in the UK that's typically Labour's votes being taken away by the Liberal Democrats. The alternative vote (also known as IRV) is a better system all around, but not a good system compared to some other systems that have been designed (the various Condorcet methods for ordinal votes or range voting for cardinal votes with trustworthy voters).
 March 29th, 2011, 01:51 PM #3 Newbie   Joined: Sep 2009 Posts: 13 Thanks: 0 Re: Analysis of Alternative Vote vs First Past the Post Interesting response. Most commentary on this I've read indicated that the Lib Dems would benefit from AV as first past the post supposedly tends to favor the leading 2 parties (for example; http://pa.oxfordjournals.org/content/64/1/5.full). I was hoping to take a more mathematical look at the behavior of AV voting, but I'm much less confident now I see how complicated it actually is. I've spent a good few hours today just trying to write down a pseudo-code style function (as my background is programming) that tells you based on voting who won, and I've found that it's deceptively complex. Also the information I've been able to uncover is no where near clear enough to say how votes are actually handled in a number of circumstances.
March 29th, 2011, 03:41 PM   #4
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Re: Analysis of Alternative Vote vs First Past the Post

I moved the thread to Mathematical Economics, where game theory and social choice theory are typically discussed.

Quote:
 Originally Posted by mikey Interesting response. Most commentary on this I've read indicated that the Lib Dems would benefit from AV as first past the post supposedly tends to favor the leading 2 parties
Maybe... but more favorable to the LimDems would be a proportional representation scheme. Their extra MPs would come mostly at the expense of Labour.

Quote:
 Originally Posted by mikey I was hoping to take a more mathematical look at the behavior of AV voting, but I'm much less confident now I see how complicated it actually is. I've spent a good few hours today just trying to write down a pseudo-code style function (as my background is programming) that tells you based on voting who won, and I've found that it's deceptively complex. Also the information I've been able to uncover is no where near clear enough to say how votes are actually handled in a number of circumstances.
AV is harder than some, easier than others. Kemeny-Young in particular is a nightmare to implement efficiently.

 March 30th, 2011, 04:06 AM #5 Newbie   Joined: Sep 2009 Posts: 13 Thanks: 0 Re: Analysis of Alternative Vote vs First Past the Post Thanks for moving this to the appropriate forum (my original choice was a guess since my main question is to ask what parts of mathematics apply to looking at voting systems such as AV). So far I've found some information on fairness criteria which while interesting is not exactly the kind of analysis I was looking for. What I was hoping to look at was how the voting system affected the results in a particular constituency and the overall profile of candidates for each party elected to constituencies. One thing I had visualized as something interesting to look at was to look at a typical voting pattern under FPTP and see what proportion of MP's would be elected under FPTP as compared to the proportion of the overall vote given to each of the parties. And also carry out the same comparison for AV, or even PR. If anyone has any links to further reading material or even suggestions for topics of types of analysis I could use then I would be grateful.
March 30th, 2011, 04:59 AM   #6
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Re: Analysis of Alternative Vote vs First Past the Post

Quote:
 Originally Posted by mikey If anyone has any links to further reading material or even suggestions for topics of types of analysis I could use then I would be grateful.
How much do you want? You could read papers and books on this topic for the rest of your life without exhausting the literature.

Quote:
 Originally Posted by mikey What I was hoping to look at was how the voting system affected the results in a particular constituency and the overall profile of candidates for each party elected to constituencies. One thing I had visualized as something interesting to look at was to look at a typical voting pattern under FPTP and see what proportion of MP's would be elected under FPTP as compared to the proportion of the overall vote given to each of the parties. And also carry out the same comparison for AV, or even PR.
A strategic analysis? The dominant strategy in FPTP is to find the two most likely candidates and cast your vote for the one you prefer. The strategy of AV is extremely complex, but in the absence of information on the preferences of other voters the strategy is to rank the candidates in your true preference order. If you know enough about the other voters to determine which two candidates are most popular, you vote as in FPTP. If you know that that candidate will survive at least k rounds, your strategy is to rank your favorite k candidates first, then that candidate if not already ranked, then the others in preference order. For example, if you prefer A > B > C > D and know that C and D are the most popular, but also know that more than a quarter of voters will rank C first (but you're not sure if more than a third will rank A first or A second and the least-popular* candidate first), then you vote A > C > B > D. This is useful if your information is imperfect: maybe you think that C and D are most popular, but actually many voters secretly support A.

Unfortunately the AV is subject to a number of pathologies. In particular it is not monotonic: ranking a candidate more favorably can actually hurt the candidate in some cases. Pathologies are unavoidable (Arrow's theorem etc.), but that's a particularly nasty one.

* In terms of number of votes.

 March 30th, 2011, 06:44 AM #7 Newbie   Joined: Sep 2009 Posts: 13 Thanks: 0 Re: Analysis of Alternative Vote vs First Past the Post Sorry, I am aware that I am being hopelessly vague about what I'm looking for, in part because I'm slightly vague about it myself. Thanks for the reply again. The vote in the UK is on whether to adopt AV as a voting system, so I'm not really looking at how to vote tactically. The debate on AV is a typical polarized political debate that fails to really get to grips with the voting system itself. Even the government's own information on AV is too simplistic for me for example to carry out an AV vote of my own for say who in my flat does the washing up. I had on my original posting somewhat naively that I could consider the AV system as a function for selecting candidates based on the voting patterns of the constituents, and try to consider how that function effects the outcome of the voting. I might be better of considering FPTP to get going as it is a far simpler system to describe (if not to actually vote in).
 March 30th, 2011, 09:10 AM #8 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Analysis of Alternative Vote vs First Past the Post An advantage (in general, but esp. for the UK since it has only 3 real parties) of the AV is that it stops the least popular candidate from winning, unlike FPTP. Suppose that in a district 40% of the population prefer Torries, while 35% prefer Labour and the balance LibDems. Suppose further that the LibDems prefer Labour to the Conservatives, and similarly Labour voters prefer LibDems if they can't have Labour. (I guess they don't like the Cameron-Clegg coalition?) Under FPTP, the Conservatives win. But 60% of the population wants them out -- they'd be defeated by either of the other candidates head-on! I'm not a fan of the AV, as I've suggested, but it's an improvement over the plurality vote, especially in the UK. It's not clear if that means it should be passed, however -- a more proportional system would be better, I think, though I haven't yet found a proportional system that suits me.
 April 6th, 2011, 01:58 AM #9 Newbie   Joined: Apr 2011 Posts: 5 Thanks: 0 Re: Analysis of Alternative Vote vs First Past the Post Thanks for this thread. When I finally read what the AV voting system is, I think I felt similar. It's simple enough to see how it works, but could be very complicated to understand what it actually entails - such as the true representativeness of the outcome. Presumably it is less representative than PR? I wanted to understand this but I think reading these posts it would be too difficult and the decision will have to be made by a different route. Working out the full implications like this was only to be a starting point anyway.
 April 6th, 2011, 02:05 AM #10 Newbie   Joined: Apr 2011 Posts: 5 Thanks: 0 Re: Analysis of Alternative Vote vs First Past the Post Actually what would be good is if mathematics could confirm or refute the charge made in this post here http://www.newstatesman.com/blogs/da...party-liberals. AV looks good, but if it achieves what's good about it in a basically ad hoc and illogical manner then I think that would put me off. First Past the Post at least has a consistent logic, even if it's more suited to voting for candidates at a local level than parties at a national level.

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