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Western-Style Voting 'A Loser' 614

Posted by Zonk
from the math-and-politics-two-great-tastes dept.
sethawoolley writes "In light of the upcoming elections in the US, author William Poundstone was interviewed about voting systems by Mother Jones. In it he advocates the benefits of Range Voting as a solution to Arrow's Impossibility Theorem. Approval, Borda, Instant Runoff, and Condorcet Voting, which are often solutions advocated by the Greens and Libertarians (in the US), are discussed, as well, in light of Warren Smith's recent empirical research using Bayesian Regret. My local party (of which I'm the Parliamentarian) uses Single Transferable voting, but we're considering using Range Voting in the future. One thing is for certain: any system is better than the West's out-dated plurality voting system."
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Western-Style Voting 'A Loser'

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  • "Western"? (Score:5, Informative)

    by docotron (799894) on Sunday January 06, 2008 @07:41AM (#21931094)
    Excuse me, but a great number of what I'd call 'Western' countries use other systems than pluralist votes. For example, the German Federal Diet is elected by a hybrid of the first-past-the-post election system and party-list proportional representation. Proportional systems are also used in countries like Finland, Austria, Spain and many others. Remember: Just because the USA and the UK use it, it doesn't make it "Western" by default. (Just because -their- minds boggle when we here get along well with a four-party coalition government....)
  • Re:"Western"? (Score:5, Informative)

    by Anomolous Cowturd (190524) on Sunday January 06, 2008 @07:54AM (#21931142)
    Down under, I too am mystified by summary guy's "West" blooper. Australia uses preferential voting for most of it's elections. Geographically we might not be very west, but we're usually lumped in with them politically. This is going to be another "USA sucks" thread. Must .. not .. mock .. America .. *twitch* ..
  • Re:"Western"? (Score:4, Informative)

    by xaxa (988988) on Sunday January 06, 2008 @08:20AM (#21931254)
    The UK needs voting reform too, see http://www.electoral-reform.org.uk/article.php?id=103 [electoral-reform.org.uk] for instance (or articles on BBC News).

    Under the current system many people think that voting for e.g. the Green Party or an independent candidate is a waste of their vote.
  • by kvezach (1199717) on Sunday January 06, 2008 @08:30AM (#21931292)
    Systems like the Condorcet Method, Meek's Algorithm and Range Voting have some theoretical advantages, but they fail in one crucial respect: they are hard to count. Range Voting creates possibly hundreds of rounds of counting. The Condorcet Method creates exponential numbers of counts.

    That's completely wrong. Range Voting consists of adding up the numbers and then taking the average. As anyone knows, that's linear in the number of candidates and votes. Even if you do it by counting "pseudovotes" (this candidate got that many ones, twos, threes, etc up to nines), the granularity of the ballot is a constant, so it's still linear.

    As for Condorcet, counting a ballot takes quadratic (0.5*n^2) time with respect to the number of candidates. If A, B, and C are ranked on a ballot, then you just check if A is more highly ranked than B, A more highly ranked than C, and B more highly ranked than C.
    Finding out who the winner is is linear in the best case - that there's a candidate who's preferred to all the others one-on-one and that's the first candidate you checked, and quadratic in the worst case if there's still a candidate who's preferred to all the others. If there is a cycle, the methods vary, but in public elections, that would be exceedingly rare. Though for the case of completion, I'll note that most of the good Condorcet methods (like CSSD [wikipedia.org] which Debian uses [debian.org]) are n^3 in the very worst case. In either case, determining the winner once the votes have been totaled up into the matrix takes logarithmic time in terms of the number of ballots (since all you have to do is compare numbers in the matrix or the averages list).

    Another advantage with Range or Condorcet is that you can count the ballots where they're gathered and then only transmit a small amount of data (the pairwise counts for Condorcet, or the numerators and denominators for the average for Range), instead of having to count everything at the central place as in IRV.

    That it is compulsory in Australia helps to moderate our politics by ensuring that the almost the whole population turns out to vote, not just ultra-motivated special interest groups (churchies, to pick a purely random example).
    Too bad about the how-to-vote cards then, no? Though there's nothing about IRV that demands you have to rank absolutely all the candidates, the implementation you have is flawed.

  • Re:"Western"? (Score:5, Informative)

    by Malekin (1079147) on Sunday January 06, 2008 @08:56AM (#21931418)
    Voting is not compulsory in Australia. Attendance on polling day is. What you do once you're in the booth is entirely your business. You may vote, or you may fold your ballot into a jaunty hat and draw a picture of a happy flower.
  • Re:"Western"? (Score:3, Informative)

    by jez9999 (618189) on Sunday January 06, 2008 @09:01AM (#21931438) Homepage Journal
    In the last general election the Liberals won more votes than the Conservatives but won less seats.

    Excuse me? There are massive problems with first-past-the-post electing, but this statement is bollocks, as my page [game-point.net] shows.

    A better criticism is something like, "the Conservatives got more votes in England than Labour, but won 92 fewer seats".
  • Re:"Western"? (Score:4, Informative)

    by sqrt(2) (786011) on Sunday January 06, 2008 @09:03AM (#21931446) Journal

    This was due to Maggie Thatcher redrawing various electoral boundaries
    This is called Gerrymandering [wikipedia.org]. It's quite common here in the States as well.
  • Other Countries (Score:4, Informative)

    by Anonymous Coward on Sunday January 06, 2008 @09:07AM (#21931472)
    I never understood why the US keeps mucking about with these increasingly bizarre voting systems. Pretty much every other democracy - Western democracy - I know off either has a 1) parliamentary system, or 2) uses multiple votes.

    Parliamentary systems: Here, the populace elects parliaments, usually with proportional representations. The parliaments then elect the 'single seat', such as the head of government.

    Multiple votes: Here, the populace elects the 'single seat' directly. If in the first n [n>0] votes no candidate achieves an absolute majority, then a final plurality vote is conducted.

    As said, pretty much every "Western" democracy other than the US seems to use some variant of those two. I personally like the first better as it keeps the center of power in the parliament, which is sort of a good thing for a democracy. But either solves the problem in a clean, easily understood and verifiable manner. So... what's the deal with the US and their funky voting systems craze?

    Also, I'm rather thankful for the various people pointing out the blatant mis-use of the term "West".
  • by Cally (10873) on Sunday January 06, 2008 @09:31AM (#21931586) Homepage
    Single Transferable Vote (STV) is in use in Scottish and Ulster electoral systems (to the respective devolved assemblies. (The geographical British Isles is now moving towards a much looser confederation of mini-states with varying degrees of independence from London; thanks to the Peace Process, Northern Ireland now has full devolved control of it's own governance, as do Scotland and Wales (there are differences between each of these, don't get me started); the Republic of Ireland has had full independence since 1922 of course.) Some form of PR, a party-list based system IIRC, is also used in the UK for elections to the European Parliament.
  • Re:This is stupid. (Score:3, Informative)

    by s7uar7 (746699) on Sunday January 06, 2008 @09:32AM (#21931588) Homepage
    That's not quite the same. In the US you vote jointly for a President and Vice President, so you know who's going to take over. In the UK you vote for the party, and anyone in the party could take over as leader.
  • Re:"Western"? (Score:2, Informative)

    by cbunix23 (1119459) on Sunday January 06, 2008 @09:38AM (#21931628)
    As the difficulty of voting increases the participation of voters drops off but not uniformly. It tends to be Democrats that drop off more than Republicans. Everyone knows this but doesn't say it in public, except on slashdot where people say anything. The US State of Ohio -- has a Democrat for governor now and executive branch -- is kicking around the idea of making elections last over a few days and making it easier to vote, but that's going to be a hard sell to the Republicans in the legislative branch.
  • Re:Two party system? (Score:5, Informative)

    by WaZiX (766733) on Sunday January 06, 2008 @09:59AM (#21931734)

    I'm from Belgium, and here there are a lot of parties. The orange (catholics), the blue (they seem to be for the people not working for the state, people who like to keep as much money they earn), the red (the socialists, but do not think this is some kind of communism, the world is not black & white you know ;) ), the greens, and so on...

    When the elections are over, the winning party needs to form a government, and they do this by making a coalition with one or two other parties so they represent more than 50% of the voting people in the country. This way all major opinions should be represented in a government. A new party might not be a part of a new government, but they are able to use there representation power in the parlement, for example when new laws are discussed and voted for.

    Well, I'm from Belgium as well, and our electoral system is one of the worst ones around! For these reasons:

    - As a resident of Flanders, I can only vote for Flemish parties, this means that, at best, I'm only allowed to vote for a bit more then half the decisions made in this country... This means that I, being Flemish, can only vote for Flemish interests, how absurd is that?

    - Up until a month ago, the 3 major tendencies (Liberals, Conservatives/Catholics/Humanists and socialists) were all in the government (either regional or national), and guess what, we will now have the same 3 tendencies (except for the Flemish socialists) in our future government! How is it exactly that the people chose if everyone is still in the government anyways?

    - Whatever party you chose, you _know_ that they won't be able to fulfill what they promised us, since they will have to make a coalition and find middle solution for everything anyways...

    The Belgian system in all its glory has become a particracy, where the heads of the different political parties have much more to say about who rules what then the people. Our system is probably one of the most anti-democratic systems there is around, and this had grave consequences... In Flanders up until the last elections, the biggest party was an extreme rights party (well duh, they're the only opposition), in Walloon, the French socialists have had their hands on on local and regional matters for the best part of the last and the beginning of this century, leading to corruption scandal after corruption scandal, and since they have only been thought to think for themselves, their education system is so lame language wise that most of them never even get a chance at working in the Flemish part. Our country became just two cultures stuck together round a common economic interest (Brussels), without any prospect of ever forming a true nation.

    Bravo, please copy our electoral system, it's great!
  • Re:This is stupid. (Score:3, Informative)

    by vidarh (309115) <vidar@hokstad.com> on Sunday January 06, 2008 @10:31AM (#21931962) Homepage Journal
    That's only halfway true. In the UK you vote for members of parliament. The queen asks someone to form government, but the cabinet needs the approval of parliament (vote on their "Speech from the throne"), and hence the prime minister is usually the candidate favored by the largest party.

    But as in most countries with a prime minister, there's no guarantee that the largest party will be the one to form a cabinet - it all depends on who is willing AND can avoid being voted down by parliament. In the UK that usually mean the party leaders would be offered the opportunity starting with the largest party, going downwards.

    Also worth noting is that once a UK prime minister has been appointed, he/she stays prime minister until he/she resigns, irrespective of election results. Parliament can force the cabinet, including the prime minister to resign, but there's not an automatic change. Edward Heath, for example, waited to resign until after he'd attempted to get support of the Liberals when the Conservatives lost their majority in the 1974 election.

    When he finally resigned a few days after the election results were in and he couldn't get support, Harold Wilson formed a minority government under Labour.

  • STV sucks (Score:5, Informative)

    by xZgf6xHx2uhoAj9D (1160707) on Sunday January 06, 2008 @10:52AM (#21932108)

    One thing is for certain: any system is better than the West's out-dated plurality voting system.

    Not so. Single Transferrable Voting fails the monotonocity criterion [wikipedia.org]. Basically, ranking someone higher can cause them to lose, and ranking someone lower can cause them to win. There's debate on how often this might come up in practice. It might be missing the larger point, though, which is that in STV, it's very hard to predict what impact your vote will actually have.

    STV is the only mainstream electoral method which fails the monotonocity criterion. Even the much maligned plurality method, which everyone is familiar with, passes. Voting for someone will never cause them to lose, and not voting for someone will never cause them to win.

    Arrow's Theorem says we can't have everything, but I consider the monotonocity criterion as something which is an absolute must. At the very least, if you are contemplating switching away from the plurality system to something else, be sure that it is strictly better than plurality, which STV is not.

  • Re:I would be wary (Score:3, Informative)

    by A beautiful mind (821714) on Sunday January 06, 2008 @12:48PM (#21932906)

    The problem with proportional voting and accommodating small parties with narrow agendas is that you're going to be politicizing legitimizing the message and empowering people on the fringe with extremist views.

    As opposed to empowering major parties with extremist views? I'll take that deal any day. The fact that the USA is governed effectively by two parties means that no matter how bad those parties get, they will still be in power. There is no way to get your opinion represented if, for example your views on foreign policy differ from the famously similar views of the two parties.

    Don't disrupt a 200+ year old system because you don't like George Bush.

    This 200+ year old system was brilliant when it was created, but mainly because it gave some power to the people as opposed to systems elsewhere in the world. The problem is, it has a built-in tendency to create two parties with a more or less 50 percent split barring small fluctuations. This is due to the nature of the winner gets everything scheme. This presents a very large barrier of entry for new parties. You make the mistake of equating small parties with fringe and large parties with mainstream. This is due to your snapshot way of thinking of the parliamentary system while you should be factoring in time aswell. For a democracy to function it is absolutely necessary to have some recourse against an offending party. It is not enough that you don't want to vote for a certain party, you need to have an _alternative_ aswell. Small parties can grow by time into mainstream parties, but only if the parliamentary system allows for it. It is true that some of the small parties would be extremist ones, but of course because of that they would never grow into a large party either. These parties would also help in cleaning out the extremists from the government/mainstream/bigger parties. But of course, not _all_ small parties represent fringe groups. Some were just never given a chance to grow into a large party. They couldn't enter the parliamentary system because the barrier of entry is in double digits. If the barrier of entry would be in single digits (that is, let's say 5% for the sake of example), they would gain media coverage and some power. They would have a say in Congress etc., they would have some seats in commissions and IF their conduct is judged to be good based on this small responsibility, they would grow into a larger party with more responsibility and this is how you would get recourse and accountability. This would mean that if the democrat or republican party does not perform well enough, they could cease to exist as parties and this would be a good thing, because you would have more alternatives to select from and more importantly, more capable people in government than the republicans OR the democrats. Think of the small parties as a breeding ground for your future government. It is a way to bring in change. Without this, the situation just slowly deteriorates and the two ruling parties learn how to cooperate in the shadows. Choice is severely reduced.

    In the US, this means that anti-abortion parties, libertarians, socialists will begin to wield real political power.

    Indeed, but if they represent some percentage of the population who voted for them then that is the right thing to do. Do not think though, that small parties would wield an excessive amount of power, they would need to gain much more support in that case and then they wouldn't be a small party anymore.

    And although they won't win alot of seats, their power will be magnified because they will become swing votes.

    This is the beauty of the whole thing. Under a reformed election system swing votes wouldn't have that much importance anymore. Sure, it still matters who gains the majority, and unlike your scenario of two major parties and one small, the case realistically would be some major parties and a lot of small ones. The extortio

  • by logicchop (1213778) on Sunday January 06, 2008 @01:33PM (#21933300)

    This guy is dead wrong. He thinks his voting system escapes Arrow's result because it allows "scoring" rather than "ranking." This is utter nonsense. Ranking can be viewed as a particular kind of scoring, i.e., it's possible for everyone to "score" the candidates in such a way that the information on each ballot is equivalent to a "ranked" vote. Since, as this bonehead acknowledges, Arrow's theorem applies to ranking methods, it applies to scoring methods as well, since ranking is a particular kind of scoring. In other words, if your voting system allows "scoring" then it's possible for everyone to simply score the candidates in a way that is equivalent to ranking them. So unless the voting method bars people from scoring the candidates in a "ranked" way (which would be completely absurd), moving to a scoring system cannot avoid Arrow's theorem. This point is common knowledge in social choice theory.

    Let me say it again, in a different way: if there is no solution to a particular set of cases, then there is no solution to a broader set of cases that includes that smaller set. This should be obvious.

    Here's what the fool wrote/said, in case anyone is curious: "For decades, there was almost a kind of despair among voting theorists of getting any better system than we had. What's interesting, though, is that the impossibility theorem doesn't apply to systems where you score the candidates rather than rank them. With scoring, you're essentially filling out a report card--if you think there are two candidates who deserve four stars you can give them both four stars--whereas with ranking you have to artificially give one a number one and one a number two. That turns out to be crucial."

    Also, some here have criticized some of the conditions of Arrow's theorem, in particular, IIA. Unfortunately, criticisms of IIA are largely misunderstood. Even the philosopher Michael Dummett, who wrote a rather large book on voting theory, gets it wrong. IIA is best understood as the condition that the only information we are going to take into account is that which is present on the ballot; we will not, e.g., ask people whether they hate their "last choice," whether they love their "first choice," where they'd place Stalin or Hitler in the ranking, and so on.

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