7 ms·

Arrow's Theorem (2014)

94 points by cscurmudgeon 9y ago

marcoperaza 9y ago
I think plurality/first-past-the-post gets an unjustified bad rap. If you focus only on the moment of election, it is not a very good system. But a broader view reveals something else. The process of settling on two options, that each represent a coalition of factions that have come together and compromised on a common platform, is doing most of the work that other systems try to do within the voting system itself. Proportional voting also solves the problem in a similar way, except that the politicians representing each faction, rather than the faction at-large, do the work of forming coalitions with other factions. Of course the distinction between the two is a little more blurry, since broad-coalition parties also exist in proportional systems, and politicians do play a large role in the at-large coalition-forming in plurality systems. But nonetheless, they clearly lead to different outcomes. As for ranked and approval-type voting systems, I’m not really a fan since I think they don’t have any hope of representing coherent thought about politics. People have a hard enough time making a principled choice of one party to vote for; asking people to rank them seems likely to produce even less principled choices.
- sampo 9y ago
  At recent times, American politics seems to suffer from getting stuck in a near 50-50 position with only two parties, and this probably is a direct consequence of the first-past-the-post voting system. The Continental European system with proportional voting and multiple political parties with changing support seems more agile. New parties can form, gain and lose support, not quite as quickly as in one 4-year election cycle, but in about 3 or 4 election cycles the political landscape of a country can change. But then again, the American democratic system has already had a pretty good run for over 200 years, so can we know if present-day problems are indicative of actual problems in the system, or something that will pass?
  - chewbacha 9y ago
    It’s hard to argue against the longest running democratic system in current existence.
    - gnulinux 9y ago
      USA is not the longest running democratic system. Even if it were, it wouldn't mean anything.
    - sampo 9y ago
      No, it's not. American politics, especially recently, draws heavy criticism every day in a multitude of newspapers.
      - chewbacha 9y ago
        There are many other nation-states around the world that have been drawing heavy criticism for their politics. Even ones with different voting systems (or none at all). Such as UK, France, Netherlands, etc. Perhaps it’s not the system but some other factor influencing the current political climate. To me, the fact that political turbulence is occurring worldwide indicates that the issue is not with how one country votes, but likely from some other factor.
      - deleted 9y ago
        [deleted]
- baddox 9y ago
  Why do you think that people have a hard time choosing which of two parties to vote for? My impression is that the opposite is true, at least in the United States. My impression is that most elections are largely decided by the relative turnout of existing populations of individuals, each of which are firmly committed to one party and simply haven’t decided whether to actually show up and vote.
  - marcoperaza 9y ago
    You make a good point, but a good percent of the population is swing voters and they do decide elections, in addition to turnout dynamics. All of the movement that you see in polls is people shifting their opinions, as well as moving from undecided to a particular preference. Some polls account for intention to vote, but others are of all registered voters, and others even all Americans. They see a lot of movement too.
    - winstonewert 9y ago
      Actually, apparently there is some reason to think that a lot of poll movement isn't really people shifting their opinion. Instead, people shift in how willing they are to talk to pollsters. On good news day for your candidate, you are much more likely to be willing to talk to a pollster about it.
    - dragonwriter 9y ago
      > You make a good point, but a good percent of the population is swing voters No, they aren't. Studies have repeatedly shown that US voters have very high party voting consistency, and that those that identify as independents are almost as consistent as those that identify with a party. Turnout and change in composition of the electorate decides elections, more than anything.
- mtgx 9y ago
  FPTP leads to the long-term creation of a duopoly. That's bad for humans in any situation. You need for parties to refresh their platforms, as well as politicians, and the fastest way to do that is to have competition among parties. Also, primaries are made to make people think they have a multitude of options, but it's usually people within the same line of thinking with the party that win, and the rest are marginalized. Proportional voting also has higher turnout rates and especially the list-based system seems to have a higher number of women in politics. FPTP countries tend to have the highest inequality, too, likely because there is that lack of competition, which tends to allow powerful people to have a bigger influence on the two parties over time. Coalition of parties is better than the alternative of one party dominating the whole government, because then parties are forced to work with each other and compromise on their most extreme views. That's usually a good thing. Plus, you don't get totally opposite platforms every 4 years. Like say if Democrats were to dominate once, raise taxes for everyone to 40%. Then Republicans came. Lowered them to 10%. Then Dems came again, raised them to 30%, and so on. RCV is a little harder to understand. But so is the caucus system, and the electoral college system, and other quirks the current American political system has. RCV has some real advantages, like optimizing for positivism in elections rather than negativity (because you may need your opponent's voters). That's usually a good thing. I don't believe people have a hard time choosing parties. If anything, what happens in most countries, even PR countries, is that people say that they don't have a good option. Ultimately, FPTP is also undemocratic, because it allows parties to dominate the government when they have less than 50%, sometimes even less than 40% of the voters' support (at it has happened in Canada, and sometimes in mid-terms in the US). I don't know why anyone would support FPTP when that is the case. Why would a party dominate the government with less than 40% support in election day?
  - KerrickStaley 9y ago
    RCV has some weaknesses compared to Condorcet methods (which use the same voting mechanism of ranking candidates but different ways of determining the winner). RCV can punish people for voting according to their true preferences. For example, say a country is 49% Republicans and 51% Democrats. In addition, a Socialist candidate is running. 30% of the Democrats actually prefer the Socialist candidate, but under a plurality system they would vote for the Democrat candidate because the Democrat has broader appeal. If those 30% chose to rank the Socialist as their #1 choice, then the Republican will win the election, because the Democrat will be eliminated in the first round. So the Democrats are incentivized to not vote their actual preference. Look at the various Condorcet methods [1], and also check out Approval Voting [2] for a system that produces fairer outcomes without the complexity of RCV/Condorcet. [1] https://en.wikipedia.org/wiki/Condorcet_method https://en.wikipedia.org/wiki/Condorcet_method [2] https://en.wikipedia.org/wiki/Approval_voting https://en.wikipedia.org/wiki/Approval_voting
- KerrickStaley 9y ago
  I disagree. I think plurality tends to create a polarized system where there are two parties with opposite extreme views. The two parties don't have an incentive to represent the entire populace, they simply have to represent half the voter base as best as possible. A two-party system is a zero sum where shooting down the opposing party advances you just as much as making meaningful positive contributions. Also, a two-party system means that views that overlap both of the two extremes on different issues aren't represented. Approval voting could potentially fix these problems, without any additional complexity at the ballot box (it's really simple! the only difference is you're allowed to vote for more than one candidate), but sadly has seen almost zero traction. Adopting approval voting more broadly could go a long way towards fixing the somewhat broken political system we have in the United States, for example. I'm not a political scientist so take my opinion with a few grains of salt :) [1] Approval Voting on Wikipedia: https://en.wikipedia.org/wiki/Approval_voting https://en.wikipedia.org/wiki/Approval_voting
  - marcoperaza 9y ago
    My sense is that approval voting will just select a milquetoast agreeable candidate who lacks any real conviction or vision, other than avoiding upsetting anyone. It is the ultimate protector of the status quo and the enemy of bold leadership.
    - macawfish 9y ago
      I feel like score voting is much better in that regard. It lets people express their whole range of opinions.
    - KerrickStaley 9y ago
      In my opinion, that's actually better. In the United States the Republicans are actively trying to dismantle all the legislation that was passed by the previous Democratic congress, and there seems to be little rhyme or reason to their platform other than that if the Democrats support it, they're against it. This is especially noticeable with healthcare, and the volatility around the government's stance on healthcare has lead to real uncertainty for insurance companies that has led to higher premiums and spottier coverage. Approval voting actually allows candidates that break the mould of existing parties, because voters can support a candidate with unorthodox views without compromising the campaign of their party's primary candidate.
- roenxi 9y ago
  I have a favorite article on voting [1]. It has good visual descriptions of how different systems favour different styles of candidates. Plurality voting is a lot better than not having a democracy; imho at least the worst candidate will be excluded. My understanding is also that democracies of any form (including republics) tend to get much better military results than dictatorships, but I don't have any actual evidence to cite :(. [1] http://zesty.ca/voting/sim/ http://zesty.ca/voting/sim/
  - anigbrowl 9y ago
    The Dictator's Handbook by Bruce Bueno de Mesquita and Alistair Smith is about just this issue, and if you want a more theoretical take (along with a detailed model) try The Logic of Political Survival by the same writers.
  - sampo 9y ago
    While good and illustrative, that page is based on the very restrictive view, that of choosing only one candidate. This applies to presidential elections, sure. There can be only one president. But most countries don't have one-member sized voting districts in their parliament elections, rather they choose 10 to 30 members per voting district.
- dragonwriter 9y ago
  > I think plurality/first-past-the-post gets an unjustified bad rap. If you focus only on the moment of election, it is not a very good system. But a broader view reveals something else. Yes, it reveals that empirically, it produces a narrower political dialogue, poor participation, and low satisfaction with government compared to systems that produce better proportionality. See Lijphart's Patterns of Democracy.
  - Bromskloss 9y ago
    For us who haven't seen Lijphart's _Patterns of Democracy_, how does one establish such a conclusion, measure the width of political dialogue, for that matter? It would seem that a proper, randomised trial could be difficult to make, or has it been done on a small scale and extrapolated to country size?
    - sampo 9y ago
      One measure could be the typical voter turnout in elections. Lower turnout could mean less trust in the political system. United States (2016): 56% India (2014): 65% Germany (2017): 76% Denmark (2015): 86%
      - yorwba 9y ago
        Voter turnout essentially reflects whether their vote is worth it. If they think everything is going to get worse no matter how they vote, they won't bother. But the same happens when they think everything will be alright no matter how they vote! So you can't really distinguish between those cases based on voter turnout alone.
    - dragonwriter 9y ago
      The short version is you compare actual existing democracies on multiple axes. The long version is, well, Lijphart's Patterns of Democracy.
  - marcoperaza 9y ago
    >it reveals that empirically, it produces a narrower political dialogue, poor participation, and low satisfaction with government compared to systems that produce better proportionality. I am very skeptical of studies purporting to run statistical analysis on such small data sets as the recent history of countries, let alone the recent history of democracies. It seems that in the quest to produce quantitative political science research, people forgot all the statistical lessons about sample size, confounding factors, and so forth.
dnautics 9y ago
I find this is one of the best videos on the subject: https://www.youtube.com/watch?v=tJag3vuG834 https://www.youtube.com/watch?v=tJag3vuG834
- carl_corder 9y ago
  This video really helped me to digest the concept. Thanks for sharing!
- spookyuser 9y ago
  Great video, sounds like CGP Grey's twin brother.
- throwaway613834 9y ago
  Great video except that it's misleading at the end. Arrow's theorem is only about rank-order voting. But if e.g. you can express your preferences as numbers (e.g. if you can state your preferences as 10% strawberry, 30% vanilla, and 60% chocolate) then it no longer applies.
  - Bromskloss 9y ago
    Indeed. It seems that those voting systems too can be proven [0] to have these problems, though. [0] https://politics.stackexchange.com/questions/14015/does-gibbard-satterthwaite-theorem-apply-to-all-voting-systems/14245 https://politics.stackexchange.com/questions/14015/does-gibb...
    - throwaway613834 9y ago
      Holy hell, that is mindblowing. Thank you for sharing this.
inputcoffee 9y ago
One of the cognitive science labs was hiring experts in graph theory, and it turns out they wanted to express Arrow's Theorem -- and the related theories -- in the form of a graph so they could reason about decision making in the brain. If I recall correctly, the paradox of voting gets represented as a top cycle which leads to irrational decisions. They wanted to come up with mechanisms where they break top cycles. (In these graphs a higher ranked decision was higher on the Y axis.)
- baddox 9y ago
  The paradox of voting usually refers to a different claim: that the cost of an individual voting tends to be greater than the expected benefit to the individual. Confusingly, the term (and the extremely similar “voting paradox”) sometimes refers to the Condorcet paradox, which notes that collective preferences between three or more options can be intransitive. I expect that is the concept you are referring to. https://en.wikipedia.org/wiki/Condorcet_paradox https://en.wikipedia.org/wiki/Condorcet_paradox
  - inputcoffee 9y ago
    Yes, the latter.
straightarrow 9y ago
Like a car swerving side to side as 2 drivers wrestle for control of the wheel, the 2 party system is an erratic vehicle. But I have good news: we can steer a more stable course with score voting. Score voting doesn't violate Arrow's Theorem (because it's not a ranked-choice system). Here's how it works: * Each voter gives candidates a score from 0 to 1. * The highest average score wins. (The average can be weighted to account for abstentions.) The upshot: * No political parties are needed. * It resists gerrymandering because it's non-partisan. * If there's a bias in the system, it's towards the center. * Simulations indicate score voting is socially optimal. * Arrow, himself, expressed preference for approval voting (a variant of score voting) Further reading: electology.org en.wikipedia.org/wiki/Range_voting
- deleted 9y ago
  [deleted]
- platz 9y ago
  So in the U.S. then Dems will vote 0-10 and Republican 10-0. I'm not sure I see the difference as long as there is only one winner What the U.S. really needs is proportional representation, similar to parlimentary systems of other countries
  - gboudrias 9y ago
    > So in the U.S. then Dems will vote 0-10 and Republican 10-0. Then someone who identifies as neither could get a 6 on average and get elected. (Assuming both other candidates are close to tied.) That said as a Canadian I'm down with almost any change in the voting system.
    - platz 9y ago
      You replace the claim about voting method with a claim about who can get on the ballot. That is as big of a change as changing the voting method.
      - 9y ago
Iv 9y ago
So, if some of you have felt despair at the idea that this may indicate that true democracy is impossible, fear not: it hinges on the fact that some preferences can be cyclic: A wins over B who wins over C, who wins over A. These situations are possible but rare and in such a case, it is arguable that all potential winners are legitimate.
- Judgmentality 9y ago
  Yep, this is when you have non transitive properties. A really cool embodiment of this same concept is non transitive dice. https://en.wikipedia.org/wiki/Nontransitive_dice https://en.wikipedia.org/wiki/Nontransitive_dice
- baddox 9y ago
  Indeed, a non-transitive election like that means that there is no Condorcet winner. Some voting methods (including first past the post) are guaranteed to select a Condorcet winner if one exists, but when one doesn’t exist (if A>B>C>A), various voting methods will result in various winners. I love reading about the theory behind voting methods, but one common criticism is that these edge cases are rare and thus a pure theoretical approach isn’t sufficient for getting a “desirable” (however you define that) outcome. https://en.wikipedia.org/wiki/Condorcet_method https://en.wikipedia.org/wiki/Condorcet_method
- fny 9y ago
  Arrows theorem is misleading because it only applies to rank order systems. Range voting (i.e. 0-5 rating system) satisfies all the criteria. [0] So yes, democracy is theoretically possible. [0]: https://youtu.be/e3GFG0sXIig https://youtu.be/e3GFG0sXIig
  - macawfish 9y ago
    Good video, thanks for sharing that!
Iv 9y ago
Am I the only one who finds that the Stanford encyclopedia of philosophy is generally less clear than the matching Wikipedia article?
- baddox 9y ago
  I almost always scroll down for the Wikipedia article when Google puts sources like the Stanford Encyclopedia of Philosophy or Investopedia or WebMD or IMDb first. For me, it’s less about which source I trust more, and more about my familiarity with and enjoyment of the writing/organizational style of Wikipedia articles.

94 points by cscurmudgeon 9y ago

I think plurality/first-past-the-post gets an unjustified bad rap. If you focus only on the moment of election, it is not a very good system. But a broader view reveals something else. The process of settling on two options, that each represent a coalition of factions that have come together and compromised on a common platform, is doing most of the work that other systems try to do within the voting system itself. Proportional voting also solves the problem in a similar way, except that the politicians representing each faction, rather than the faction at-large, do the work of forming coalitions with other factions. Of course the distinction between the two is a little more blurry, since broad-coalition parties also exist in proportional systems, and politicians do play a large role in the at-large coalition-forming in plurality systems. But nonetheless, they clearly lead to different outcomes. As for ranked and approval-type voting systems, I’m not really a fan since I think they don’t have any hope of representing coherent thought about politics. People have a hard enough time making a principled choice of one party to vote for; asking people to rank them seems likely to produce even less principled choices.

sampo 9y ago
At recent times, American politics seems to suffer from getting stuck in a near 50-50 position with only two parties, and this probably is a direct consequence of the first-past-the-post voting system. The Continental European system with proportional voting and multiple political parties with changing support seems more agile. New parties can form, gain and lose support, not quite as quickly as in one 4-year election cycle, but in about 3 or 4 election cycles the political landscape of a country can change. But then again, the American democratic system has already had a pretty good run for over 200 years, so can we know if present-day problems are indicative of actual problems in the system, or something that will pass?
- chewbacha 9y ago
  It’s hard to argue against the longest running democratic system in current existence.
  - gnulinux 9y ago
    USA is not the longest running democratic system. Even if it were, it wouldn't mean anything.
  - sampo 9y ago
    No, it's not. American politics, especially recently, draws heavy criticism every day in a multitude of newspapers.
    - chewbacha 9y ago
      There are many other nation-states around the world that have been drawing heavy criticism for their politics. Even ones with different voting systems (or none at all). Such as UK, France, Netherlands, etc. Perhaps it’s not the system but some other factor influencing the current political climate. To me, the fact that political turbulence is occurring worldwide indicates that the issue is not with how one country votes, but likely from some other factor.
    - deleted 9y ago
      [deleted]
baddox 9y ago
Why do you think that people have a hard time choosing which of two parties to vote for? My impression is that the opposite is true, at least in the United States. My impression is that most elections are largely decided by the relative turnout of existing populations of individuals, each of which are firmly committed to one party and simply haven’t decided whether to actually show up and vote.
- marcoperaza 9y ago
  You make a good point, but a good percent of the population is swing voters and they do decide elections, in addition to turnout dynamics. All of the movement that you see in polls is people shifting their opinions, as well as moving from undecided to a particular preference. Some polls account for intention to vote, but others are of all registered voters, and others even all Americans. They see a lot of movement too.
  - winstonewert 9y ago
    Actually, apparently there is some reason to think that a lot of poll movement isn't really people shifting their opinion. Instead, people shift in how willing they are to talk to pollsters. On good news day for your candidate, you are much more likely to be willing to talk to a pollster about it.
  - dragonwriter 9y ago
    > You make a good point, but a good percent of the population is swing voters No, they aren't. Studies have repeatedly shown that US voters have very high party voting consistency, and that those that identify as independents are almost as consistent as those that identify with a party. Turnout and change in composition of the electorate decides elections, more than anything.
mtgx 9y ago
FPTP leads to the long-term creation of a duopoly. That's bad for humans in any situation. You need for parties to refresh their platforms, as well as politicians, and the fastest way to do that is to have competition among parties. Also, primaries are made to make people think they have a multitude of options, but it's usually people within the same line of thinking with the party that win, and the rest are marginalized. Proportional voting also has higher turnout rates and especially the list-based system seems to have a higher number of women in politics. FPTP countries tend to have the highest inequality, too, likely because there is that lack of competition, which tends to allow powerful people to have a bigger influence on the two parties over time. Coalition of parties is better than the alternative of one party dominating the whole government, because then parties are forced to work with each other and compromise on their most extreme views. That's usually a good thing. Plus, you don't get totally opposite platforms every 4 years. Like say if Democrats were to dominate once, raise taxes for everyone to 40%. Then Republicans came. Lowered them to 10%. Then Dems came again, raised them to 30%, and so on. RCV is a little harder to understand. But so is the caucus system, and the electoral college system, and other quirks the current American political system has. RCV has some real advantages, like optimizing for positivism in elections rather than negativity (because you may need your opponent's voters). That's usually a good thing. I don't believe people have a hard time choosing parties. If anything, what happens in most countries, even PR countries, is that people say that they don't have a good option. Ultimately, FPTP is also undemocratic, because it allows parties to dominate the government when they have less than 50%, sometimes even less than 40% of the voters' support (at it has happened in Canada, and sometimes in mid-terms in the US). I don't know why anyone would support FPTP when that is the case. Why would a party dominate the government with less than 40% support in election day?
- KerrickStaley 9y ago
  RCV has some weaknesses compared to Condorcet methods (which use the same voting mechanism of ranking candidates but different ways of determining the winner). RCV can punish people for voting according to their true preferences. For example, say a country is 49% Republicans and 51% Democrats. In addition, a Socialist candidate is running. 30% of the Democrats actually prefer the Socialist candidate, but under a plurality system they would vote for the Democrat candidate because the Democrat has broader appeal. If those 30% chose to rank the Socialist as their #1 choice, then the Republican will win the election, because the Democrat will be eliminated in the first round. So the Democrats are incentivized to not vote their actual preference. Look at the various Condorcet methods [1], and also check out Approval Voting [2] for a system that produces fairer outcomes without the complexity of RCV/Condorcet. [1] https://en.wikipedia.org/wiki/Condorcet_method https://en.wikipedia.org/wiki/Condorcet_method [2] https://en.wikipedia.org/wiki/Approval_voting https://en.wikipedia.org/wiki/Approval_voting
KerrickStaley 9y ago
I disagree. I think plurality tends to create a polarized system where there are two parties with opposite extreme views. The two parties don't have an incentive to represent the entire populace, they simply have to represent half the voter base as best as possible. A two-party system is a zero sum where shooting down the opposing party advances you just as much as making meaningful positive contributions. Also, a two-party system means that views that overlap both of the two extremes on different issues aren't represented. Approval voting could potentially fix these problems, without any additional complexity at the ballot box (it's really simple! the only difference is you're allowed to vote for more than one candidate), but sadly has seen almost zero traction. Adopting approval voting more broadly could go a long way towards fixing the somewhat broken political system we have in the United States, for example. I'm not a political scientist so take my opinion with a few grains of salt :) [1] Approval Voting on Wikipedia: https://en.wikipedia.org/wiki/Approval_voting https://en.wikipedia.org/wiki/Approval_voting
- marcoperaza 9y ago
  My sense is that approval voting will just select a milquetoast agreeable candidate who lacks any real conviction or vision, other than avoiding upsetting anyone. It is the ultimate protector of the status quo and the enemy of bold leadership.
  - macawfish 9y ago
    I feel like score voting is much better in that regard. It lets people express their whole range of opinions.
  - KerrickStaley 9y ago
    In my opinion, that's actually better. In the United States the Republicans are actively trying to dismantle all the legislation that was passed by the previous Democratic congress, and there seems to be little rhyme or reason to their platform other than that if the Democrats support it, they're against it. This is especially noticeable with healthcare, and the volatility around the government's stance on healthcare has lead to real uncertainty for insurance companies that has led to higher premiums and spottier coverage. Approval voting actually allows candidates that break the mould of existing parties, because voters can support a candidate with unorthodox views without compromising the campaign of their party's primary candidate.
roenxi 9y ago
I have a favorite article on voting [1]. It has good visual descriptions of how different systems favour different styles of candidates. Plurality voting is a lot better than not having a democracy; imho at least the worst candidate will be excluded. My understanding is also that democracies of any form (including republics) tend to get much better military results than dictatorships, but I don't have any actual evidence to cite :(. [1] http://zesty.ca/voting/sim/ http://zesty.ca/voting/sim/
- anigbrowl 9y ago
  The Dictator's Handbook by Bruce Bueno de Mesquita and Alistair Smith is about just this issue, and if you want a more theoretical take (along with a detailed model) try The Logic of Political Survival by the same writers.
- sampo 9y ago
  While good and illustrative, that page is based on the very restrictive view, that of choosing only one candidate. This applies to presidential elections, sure. There can be only one president. But most countries don't have one-member sized voting districts in their parliament elections, rather they choose 10 to 30 members per voting district.
dragonwriter 9y ago
> I think plurality/first-past-the-post gets an unjustified bad rap. If you focus only on the moment of election, it is not a very good system. But a broader view reveals something else. Yes, it reveals that empirically, it produces a narrower political dialogue, poor participation, and low satisfaction with government compared to systems that produce better proportionality. See Lijphart's Patterns of Democracy.
- Bromskloss 9y ago
  For us who haven't seen Lijphart's _Patterns of Democracy_, how does one establish such a conclusion, measure the width of political dialogue, for that matter? It would seem that a proper, randomised trial could be difficult to make, or has it been done on a small scale and extrapolated to country size?
  - sampo 9y ago
    One measure could be the typical voter turnout in elections. Lower turnout could mean less trust in the political system. United States (2016): 56% India (2014): 65% Germany (2017): 76% Denmark (2015): 86%
    - yorwba 9y ago
      Voter turnout essentially reflects whether their vote is worth it. If they think everything is going to get worse no matter how they vote, they won't bother. But the same happens when they think everything will be alright no matter how they vote! So you can't really distinguish between those cases based on voter turnout alone.
  - dragonwriter 9y ago
    The short version is you compare actual existing democracies on multiple axes. The long version is, well, Lijphart's Patterns of Democracy.
- marcoperaza 9y ago
  >it reveals that empirically, it produces a narrower political dialogue, poor participation, and low satisfaction with government compared to systems that produce better proportionality. I am very skeptical of studies purporting to run statistical analysis on such small data sets as the recent history of countries, let alone the recent history of democracies. It seems that in the quest to produce quantitative political science research, people forgot all the statistical lessons about sample size, confounding factors, and so forth.

dnautics 9y ago

I find this is one of the best videos on the subject: https://www.youtube.com/watch?v=tJag3vuG834 https://www.youtube.com/watch?v=tJag3vuG834

carl_corder 9y ago
This video really helped me to digest the concept. Thanks for sharing!
spookyuser 9y ago
Great video, sounds like CGP Grey's twin brother.
throwaway613834 9y ago
Great video except that it's misleading at the end. Arrow's theorem is only about rank-order voting. But if e.g. you can express your preferences as numbers (e.g. if you can state your preferences as 10% strawberry, 30% vanilla, and 60% chocolate) then it no longer applies.
- Bromskloss 9y ago
  Indeed. It seems that those voting systems too can be proven [0] to have these problems, though. [0] https://politics.stackexchange.com/questions/14015/does-gibbard-satterthwaite-theorem-apply-to-all-voting-systems/14245 https://politics.stackexchange.com/questions/14015/does-gibb...
  - throwaway613834 9y ago
    Holy hell, that is mindblowing. Thank you for sharing this.

inputcoffee 9y ago

One of the cognitive science labs was hiring experts in graph theory, and it turns out they wanted to express Arrow's Theorem -- and the related theories -- in the form of a graph so they could reason about decision making in the brain. If I recall correctly, the paradox of voting gets represented as a top cycle which leads to irrational decisions. They wanted to come up with mechanisms where they break top cycles. (In these graphs a higher ranked decision was higher on the Y axis.)

baddox 9y ago
The paradox of voting usually refers to a different claim: that the cost of an individual voting tends to be greater than the expected benefit to the individual. Confusingly, the term (and the extremely similar “voting paradox”) sometimes refers to the Condorcet paradox, which notes that collective preferences between three or more options can be intransitive. I expect that is the concept you are referring to. https://en.wikipedia.org/wiki/Condorcet_paradox https://en.wikipedia.org/wiki/Condorcet_paradox
- inputcoffee 9y ago
  Yes, the latter.

straightarrow 9y ago

Like a car swerving side to side as 2 drivers wrestle for control of the wheel, the 2 party system is an erratic vehicle. But I have good news: we can steer a more stable course with score voting. Score voting doesn't violate Arrow's Theorem (because it's not a ranked-choice system). Here's how it works: * Each voter gives candidates a score from 0 to 1. * The highest average score wins. (The average can be weighted to account for abstentions.) The upshot: * No political parties are needed. * It resists gerrymandering because it's non-partisan. * If there's a bias in the system, it's towards the center. * Simulations indicate score voting is socially optimal. * Arrow, himself, expressed preference for approval voting (a variant of score voting) Further reading: electology.org en.wikipedia.org/wiki/Range_voting

deleted 9y ago
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platz 9y ago
So in the U.S. then Dems will vote 0-10 and Republican 10-0. I'm not sure I see the difference as long as there is only one winner What the U.S. really needs is proportional representation, similar to parlimentary systems of other countries
- gboudrias 9y ago
  > So in the U.S. then Dems will vote 0-10 and Republican 10-0. Then someone who identifies as neither could get a 6 on average and get elected. (Assuming both other candidates are close to tied.) That said as a Canadian I'm down with almost any change in the voting system.
  - platz 9y ago
    You replace the claim about voting method with a claim about who can get on the ballot. That is as big of a change as changing the voting method.
    - 9y ago

Iv 9y ago

So, if some of you have felt despair at the idea that this may indicate that true democracy is impossible, fear not: it hinges on the fact that some preferences can be cyclic: A wins over B who wins over C, who wins over A. These situations are possible but rare and in such a case, it is arguable that all potential winners are legitimate.

Judgmentality 9y ago
Yep, this is when you have non transitive properties. A really cool embodiment of this same concept is non transitive dice. https://en.wikipedia.org/wiki/Nontransitive_dice https://en.wikipedia.org/wiki/Nontransitive_dice
baddox 9y ago
Indeed, a non-transitive election like that means that there is no Condorcet winner. Some voting methods (including first past the post) are guaranteed to select a Condorcet winner if one exists, but when one doesn’t exist (if A>B>C>A), various voting methods will result in various winners. I love reading about the theory behind voting methods, but one common criticism is that these edge cases are rare and thus a pure theoretical approach isn’t sufficient for getting a “desirable” (however you define that) outcome. https://en.wikipedia.org/wiki/Condorcet_method https://en.wikipedia.org/wiki/Condorcet_method
fny 9y ago
Arrows theorem is misleading because it only applies to rank order systems. Range voting (i.e. 0-5 rating system) satisfies all the criteria. [0] So yes, democracy is theoretically possible. [0]: https://youtu.be/e3GFG0sXIig https://youtu.be/e3GFG0sXIig
- macawfish 9y ago
  Good video, thanks for sharing that!

Iv 9y ago

Am I the only one who finds that the Stanford encyclopedia of philosophy is generally less clear than the matching Wikipedia article?

baddox 9y ago
I almost always scroll down for the Wikipedia article when Google puts sources like the Stanford Encyclopedia of Philosophy or Investopedia or WebMD or IMDb first. For me, it’s less about which source I trust more, and more about my familiarity with and enjoyment of the writing/organizational style of Wikipedia articles.