8 ms·

Voting is a Sham Mathematically Speaking

95 points by eibrahim 14y ago

mtgx 14y ago
Approval Voting mostly solves the "strategic voting" part that almost forces you to choose the "most likely to win" candidate, or if you hate that one, the one closest to him, while eliminating the spoiler effect, and giving 3rd party candidates a much higher chance of winning than with current traditional voting systems. http://www.electology.org/approval-voting http://www.electology.org/approval-voting http://en.wikipedia.org/wiki/Approval_voting http://en.wikipedia.org/wiki/Approval_voting
- DennisP 14y ago
  Plus it doesn't run into trouble with Arrow's theorem, since it's not a "rank-order voting system," unlike plurality, instant runoff, and various others. Range voting has the same advantage. In computer simulations measuring how well the election result matches voter preferences, either range or approval is as much an improvement over plurality as plurality is over picking someone at random (or, if you like, monarchy). http://rangevoting.org/BayRegsFig.html http://rangevoting.org/BayRegsFig.html
  - gus_massa 14y ago
    I'm not sure about the definitions, but if the Arrow theorem doesn't apply to the Approval Voting sistem them I think that it must not be applicable to the "majority rules" criterion. In this two system the idea is that you get very little information from the voters (best candidate / a set of candidates) and don't know all the information about the order of preference and the relative strength. So I don't understand why having less information is better (theoreticaly).
    - Empact 14y ago
      > I don't understand why having less information is better (theoreticaly). A ranked-choice ballot only encodes the orders the candidates against one another, whereas approval and score votes also encode the candidates' positions within the voter's range of subjective preferences. That is, if we have 3 candidates (A, B, C) and a few voters which each voters has a range from love to hate for each candidate, like so: Love Hate |-A--B-------------------C-| |-A-------------B-----C----| |-------------------A-B-C--| |-A-B---C------------------| Under ranked choice voting, every one of these voters' ballots would look the same: 1)A, 2)B, 3)C Ranked choice voting encodes the ordering of the preferences, but the intensity of those preferences is lost when the ballot is cast. Whereas under approval and score voting, every one of these voters represents their preferences differently, because they're reflecting their personal response to each candidate: Approval | Disapproval |-A--B-----|-------------C-| |-A--------|----B-----C----| |----------|--------A-B-C--| |-A-B---C--|---------------| Of course, some information is lost in the fact that we only have 2 values approval/disapproval to encode positional preferences. But I would argue this information is already more meaningful than a fully-expressed ranked ballot. And if necessary, score voting can capture more of that information by offering > 2 levels to divide the candidates into.
      - gus_massa 14y ago
        OK, this method recollect some information that the ranked choice voting ignores. But I still don't understand why the Arrow's theorem doesn't apply. If in a hypothetic population everyone loves/hates each candidate equally spaced, then in that population it is possible to apply the Arrow's theorem and prove that for that population this method doesn't work. But the method should be useful for every population, even the pathological ones.
  - jivatmanx 14y ago
    Don't know if anyone is going to read this, but I was reading about ordinal vs. cardinal utility, which are interesting because they seem to correspond to Ranked Choice vs. Approval voting, with the various voting systems simply being a different algorithm of calculating the winner from these. Anyway, apparently, with "Inter-temporal choice", or, different utility of the same thing measured in different time periods, Cardinal Utility needs to be used. I wonder if the same applies to grouping utility of different people together in order to get an aggregate. If so, it's an argument for the use of Approval/Score voting as opposed to Ranked choice. The quote is "Models of utility with several periods, in which people discount future values of utility, need to employ cardinalism in order to have well-behaved utility functions." an appears in the cardinal utility article.
- bhauer 14y ago
  Score voting is actually slightly superior to Approval Voting (which is Score Voting with a range of 0 to 1). To my understanding, the Center for Election Science ("electology.org") is the preeminent organization championing Approval and Score Voting. http://www.electology.org/score-voting http://www.electology.org/score-voting Eric Sanders of that same organization has written a few articles on the subject, including the following: http://bigthink.com/action-in-action/why-the-republicans-lost http://bigthink.com/action-in-action/why-the-republicans-los... I've personally been trying to campaign for the adoption of score voting: https://usa.brianstaskforce.com/task/362/score-voting-for-national-elections https://usa.brianstaskforce.com/task/362/score-voting-for-na...
  - jivatmanx 14y ago
    I think that, over time, people would drift towards using only 0 and 10 and none of the middle scores, similar to how, over time a plurality voting system drifts towards only having two political parties (Duverger's Law). 0 And 10 are the "strategic votes" of score voting as 2-major-parties are the "strategic votes" of plurality voting. A possible counter-argument to this is that score voting doesn't have a reinforcing feedback loop (each election, the minor parties get weaker until they remain at around 1%)
    - bhauer 14y ago
      An interesting point. Since you're speaking about strategy and honesty, I would defer to those who have done research, where I can only speak for myself. http://ScoreVoting.net/Honesty.html http://ScoreVoting.net/Honesty.html I know I would not hesitate to vote my actual opinion and I suspect others would not either. I would be happy to give a score to each candidate, and it would not necessarily be binary. Just as I am happy today to vote for a third-party candidate though that is not a strategic move. Again speaking just for myself, if nothing else, having the ability to score candidates would reduce my feeling of regret or disappointment with the outcome because it's less polarizing.
- bradbeattie 14y ago
  Let's say there are two head-line candidates: A and B. I hate A, am neutral towards B, and love the less popular of the three candidate C. So do I vote 0/0/1 or 0/1/1? Well, that depends on how popular the three are and is very much an example of strategic voting. When proposing an alternative, one should probably be up-front with its flaws.
  - jivatmanx 14y ago
    That's not strategic voting according to the definition. In both cases you're still voting for C, the candidate you like the most. "In voting systems, tactical voting (or strategic voting or sophisticated voting or insincere voting) occurs, in elections with more than two candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.[1]" If you mean it in the larger sense of using strategy when voting, Gibbard–Satterthwaite theorem shows that no voting system is strategy free unless it's either dictatorial or nondeterministic.
    - bradbeattie 14y ago
      My decision to vote either 0/0/1 or 0/1/1 is explicitly to prevent my desire for B over A from causing B to win when C might have a chance. Whenever you have to consider the ballots of other voters, you're dealing with tactical voting.
      - lmkg 14y ago
        Approval voting is immune to a particular definition of tactical voting, which is somewhat weaker than the traditional one. Which isn't perfect, but it's better than most other methods can offer. Most traditional voting methods are preference systems: You take your N candidates and rank them from 1 to N. Every voter is assumed to have a "ground truth" preference of ranking. Tactical voting means that a rational voter may sometimes be encouraged to vote with a ranking other than their true preference. The weaker criteria that approval voting satisfies is this: A rational voter can always make a rational vote by writing down their true preference ranking in order, drawing a line, and approving everyone above that line. In other words, there is no situation where a rational voter would want to vote A > B when their true preference is B > A. This is a significant bound on the effects of tactical voting. As you correctly point out, the rationally optimal place to draw that line can be tactical. Nonetheless, there is a strong argument that this is "less tactical" than many other systems allow.
- Steko 14y ago
  Approval voting suffers the largest number of "Especially Intolerable Failures" in the comparison here: http://en.wikipedia.org/wiki/Comparison_of_instant_runoff_voting_to_other_voting_systems#Voting_system_criteria http://en.wikipedia.org/wiki/Comparison_of_instant_runoff_vo...
  - Empact 14y ago
    If you examine these supposed failures of Approval voting, you'll find that the bulk of them can be attributed to the divide between a "Majoritarian" or a "Consensus-driven" perspective. That is, many of the criteria suppose that the most-preferred candidate of the majority should win, but should that be the case? Imagine there are 3 candidates, one who is adored by the super-majority, a second who is very well-liked by that super-majority and a third who is hated. Meanwhile the minority hates the first and third candidates, but well-likes the second. We can visualize this like so: # Approval | Disapproval 80 |-1--2----|--------------3-| 20 |-2-------|-----------3--1-| So while the first candidate is the favorite candidate of the super-majority, the second candidate has the unanimous approval of population. Which is preferable? I would say the second candidate. So you see, the criteria themselves incorporate an ideological perspective - a majoritarian bias - rather than articulating some absolute objective truth. Also I have to take issue with the basis for the "Especially Intolerable Failures" explanation - does it make sense to reject a system for being theoretically capable of producing a result, "regardless of the probability that these paradoxes may occur"? Given 2 systems, one which exhibits several flaws often, and another which rarely exhibits flaws but is theoretically capable of exhibiting a certain offensive flaw, does it make sense to reject the better-behaving system because of a theoretical result? I think not.
    - chimeracoder 14y ago
      > Given 2 systems, one which exhibits several flaws often, and another which rarely exhibits flaws but is theoretically capable of exhibiting a certain offensive flaw, does it make sense to reject the better-behaving system because of a theoretical result? I think not No, but if we want to go on the basis of how likely it is to produce those outcomes, Instant-runoff voting beats approval voting by a long shot. Amartya Sen has shown that, not only is IRV is highly unlikely to produce an outcome which violates transitivity and independence, but if ideologies are assumed to be relatively linear[1], then it never violates those conditions. [1] Ie, very few people would rank Nader > Bush > Gore
streptomycin 14y ago
Also, there's this: http://papers.nber.org/papers/w15220 http://papers.nber.org/papers/w15220
saraid216 14y ago
> Voting is a method that a group of people use to pick the “best choice” out of a set of candidates. It’s pretty obvious, right? And like many other pieces of "common sense", this isn't correct. Wikipedia says, "Voting is a method for a group such as a meeting or an electorate to make a decision or express an opinion—often following discussions, debates, or election campaigns. Democracies elect holders of high office by voting." This is very different from "picking the best choice". I realize that the American public has been indoctrinated for the past few decades that voting is the only way you make yourself heard, but this isn't true and never has been. I recently learned about Wellstone Action ( http://en.wikipedia.org/wiki/Wellstone_Action http://en.wikipedia.org/wiki/Wellstone_Action ); I encourage everyone to look into enrolling. (I haven't done so myself yet. I probably will at some point, though.) > On one hand, this seems to be an endorsement of the two-party political system we have in the United States. Actually, what it's an endorsement of is all of our other voting systems where the choice is between APPROVE and REJECT. You have to endorse the existence of political parties in the first place before you can endorse a two-party system, and Arrow's theorem goes nowhere near that.
- derleth 14y ago
  > I realize that the American public has been indoctrinated for the past few decades that voting is the only way you make yourself heard This has never been true. Americans have always protested, signed petitions, and even joined special interest groups like the ACLU and the NRA. Americans have a very long tradition of things like that.
  - saraid216 14y ago
    Tell that to the next person who complains that their vote doesn't count.
    - derleth 14y ago
      It's entirely possible to be active in the ACLU, for example, and still be annoyed that since you live in Montana your vote for a Democratic presidential candidate is basically pointless.
basseq 14y ago
> A voting system can only, at times, choose the most preferred of the options given. But it doesn't necessarily present us with the best candidates to choose from in the first place. Reminds me of HHGTTG: "Anyone who is capable of getting themselves made President should on no account be allowed to do the job."
aprescott 14y ago
In this case, Hanselman is the clear winner with three votes, whereas the other two candidates each have two votes. This is how our elections are held today. This is dependent on the exact election taking place. With the US presidential elections, my understanding is that a plurality of electoral college votes is not enough to win, you need an actual majority. In the event of a simple plurality win with no majority, the result is decided by the House of Representatives (which may itself be tied).
- rjzzleep 14y ago
  is it? the actual candidates already get preselected. even if youre right, which is likely, it doesn't matter, because any majority was previously generated by pluarility.
wam 14y ago
Learning about Arrow's theorem definitely changed the way I think about elections in the US. It also changed the way I think about election news coverage. I used to be an ardent "horse race news" hater. I still am, in terms of how utterly it dominates election news, but now I see some utility in it as well. Arrow and these others have focused how I look at the game-theoretic underpinnings of elections and the importance of being up to speed on exactly how candidates and interested parties are crafting strategies around the complexities built into the game. When people conflate the "message" of the candidate with the strategy (which is always) I still get irritated. I have a tendency toward partisanship and that kind of thing clouds my judgment. But the day-in day-out workings of the campaigns and PACs are more interesting to me now, because they shed light on what's fundamentally "broken" (from my point of view) in the underlying system, as opposed to what I simply find distasteful or disappointing. Math!
- saraid216 14y ago
  Social choice theory is One Of Those Things which everyone (myself included) needs to spend more time learning about.
hcarvalhoalves 14y ago
If you look at Brazil, which has multiple parties and plurality voting, the problems are pretty clear. In this year's elections, the candidate with 28% of the votes was elected mayor in my city.
Noughmad 14y ago
I find it interesting that in all those discussions about voting systems, which are mostly focused on USA president elections, nobody mentions two-round voting, also known as run-off voting. This is what we have in Slovenia for electing our president. In the first round, there are many candidates, and each voter can vote for one. If any candidate gets at least 50% of votes, he automatically wins. If, on the other hand, there is no majority winner, the two best candidates compete head-to-head in the second round. Such a system allows you to always vote for your favourite candidate in the first round, and if your candidate doesn't make it into the second round, you can vote for the fallback one. Details: https://en.wikipedia.org/wiki/Two-round_system https://en.wikipedia.org/wiki/Two-round_system
- kscaldef 14y ago
  I don't believe this satisfies the Condercet criterion either. Consider these rankings of preferences: 20% A ... 20% B ... 15% C ... 15% D C ... 15% E C ... 15% F C ... In a two-round run-off, one of A or B will be elected, despite the fact that 60% of voters prefer C over either A or B.
  - im3w1l 14y ago
    And in the real world, people would second guess this, and enough people would tactic vote for C that it would't be a problem. "But then they can't vote for their prefered candidate which was the whole point" Well, some people can. D, E, F could still get a few percentage points. More importantly, I don't think we would see convergence to a 2-party system. Unless I am missing something, it looks like at least 3 parties could be sustained.
gradstudent 14y ago
Preferential voting solves all these problems. You vote by ranking the candidates on order of preference. If your top candidate does not win the vote goes to next guy down the line until eventually it ends up for one of two candidates.
- Pinckney 14y ago
  Preferential voting does not satisfy the Condorcet criterion. http://en.wikipedia.org/wiki/Instant-runoff_voting#Voting_system_criteria http://en.wikipedia.org/wiki/Instant-runoff_voting#Voting_sy...
  - bradbeattie 14y ago
    To demonstrate this, consider the following. 80 people: A, C, B 50 people: B, C, A 35 people: C, B, A IRV eliminates C (as it has the fewest first-place votes) and elects B. But voters on the whole prefer C over B (115 to 50). This is the failure that Pinckney refers to.
    - deleted 14y ago
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  - finnw 14y ago
    You mean IRV does not satisfy the Condorcet criterion. IRV is not the only preferential voting system. There are others, e.g. ranked pairs[1] which do. Under ranked pairs, each pair of candidates is considered individually, largest majorities first. In bradbeattie's example we have: C > B: 115 votes C > A: 85 votes B > A: 85 votes So the group preference is C > B > A and C wins. Ranked pairs fails the participation criterion[2], but it is still possible to vote tactically in a way that guarantees you will not harm your first-choice candidate by participating (since if your first choice is A you can rank A first and all the others joint second. Similarly if your goal is to prevent C from winning, you can rank C second and all others joint first.) [1]:http://en.wikipedia.org/wiki/Ranked_pairs http://en.wikipedia.org/wiki/Ranked_pairs [2]:http://en.wikipedia.org/wiki/Participation_criterion http://en.wikipedia.org/wiki/Participation_criterion
bo1024 14y ago
This is a very nice summary of/intro to the classic/standard mathematical approach to voting and Arrow's Theorem.
frozenport 14y ago
This is why we have a 2 party system :-)
maratd 14y ago
This is off. Voting is not a system for selecting the best candidate. Voting, in whatever forms it exists, is a system to avoid violence and conflict. Each side feels it had a fair shot, regardless of outcome. The purpose of voting is to leave you with that feeling, to avoid unpleasant behavior from the losing party. The best person for the job almost never gets it. That's why we don't vote people in when hiring somebody at a company.
- diego 14y ago
  Yes, and in addition it's also a system to ensure that elected officials and their parties have accountability. If you win an election and then "betray" your voters, you won't be reelected. If you can't be reelected, you could damage the chances of your party. In essence, democracy in its current form is not so much about choosing the right/best candidate. It's more about making sure the winner cannot become a despot.
  - bad_user 14y ago
    In addition, people do not even try voting for the best candidate. People usually vote for the candidate whose interests best align with their own interests and if we're talking about that, then we can't avoid talking about compromises. Which is why it's easy to see why preferences between candidates may be non-transitive, as the space we're talking about is no longer one-dimensional so candidates don't have a natural order.
  - ontheotherhand 14y ago
    "If you win an election and then "betray" your voters, you won't be reelected." That ain't accountability, that's a joke. If you pay me 5000$ to do a job, and I don't lift a finger, and your "punishment" is that we won't do that a second time, then I have free money and you're a fool. It doesn't hurt the party one bit either; that's the whole point of corporatism, you can swap out individuals while the "brand" rolls on, saying "whoops, bad apple" every 5 seconds, with people forgetting after 2. "It's more about making sure the winner cannot become a despot." Correction: it replaces a single despotic individual with a tag team of people who basically can do whatever they want - within boundaries, sure, they at least have to be somewhat slick about it, and know how to make a puppy face, too; but certainly not within boundaries defined by the actual will of the people who handed their power as souvereigns over to their representatives. Having despotic entities control you is not one iota better than despotic humans, not in the long run. Despotism is marked by the control going only down, accountability going only up -- period. Not by angry men on podiums necessarily, and not by bloodshed. (Not that there isn't plenty bloodshed, but that's besides the point) If you seriously see a huge difference or improvement there, you've fallen for it I'm afraid.
mmphosis 14y ago
Mixed Member Proportional (MMP) Representation solves some of the problems. http://www.youtube.com/watch?v=QT0I-sdoSXU&feature=relmfu http://www.youtube.com/watch?v=QT0I-sdoSXU&feature=relmf... The problem with MMP is when the parties choose the ranking of their list of representatives. I think it would be even better if rather than use a party generated list, instead the representatives are determined by people's votes.
nikatwork 14y ago
I've always thought New Zealand's mixed-member proportional (MMP) voting system [1] is the least bad solution currently in use. I'm not from NZ so I'd be interested to hear what the locals think. [1] http://en.wikipedia.org/wiki/New_Zealand_voting_system_referendum,_2011 http://en.wikipedia.org/wiki/New_Zealand_voting_system_refer...
- lmkg 14y ago
  Not a local, but... Proportional voting systems suffer from the problem that voting "power" is not proportional to representation. Consider a parliament with 100 members and 3 parties. Suppose the breakdown is: A has 49 members, B has 48 members, and C has 3 members. Guess what... A, B, and C all have equal voting power! Any two parties are enough to reach a majority of 51 votes, and any one party is not. Despite A having, in theory, over 16 times the representation of C, it does not have any voting advantage. Keep in mind that any voting system based on parties will tend to have very partisan voting blocs. Representatives in the US are more independent and likely to break with the party because they are elected in geographically isolated elections. Representatives elected directly by a party generally have about as much independence as the Electors in the Electoral College.
  - NickNameNick 14y ago
    I'm from NZ... To form a government, the party with the most votes, or a coalition of parties which collectively holds a majority petition the governor general. For a single party this is quite straightforward. To form a coalition the member parties agree on a 'Confidence and supply agreement" This is basically a statement that in the event of a vote of no-confidence, all of the coalitions members will support the coalition, and also a broad agreement on the budget. Getting an agreement on confidence usually involves a certain amount of horse trading about ministerial and vice ministerial positions. Likewise, the agreement on supply will probably involve some intense budget and joint-policy negotiations. If you had a parliament of 101 seats, split into an opposition of 50 seats, and a government of 51, itself made up of a large party (48 seats) and a small party (3 seats) what you will probably see is the small party only has the tiniest influence on the coalition agreement. They probably traded everything else to get their senior member a ministerial position.
gabemart 14y ago
I found this article quite frustrating. >Condorcet formalized the idea that group preferences are also non-transitive. If people prefer Hanselman to me. And they prefer me to Guthrie. It does not necessarily mean they will prefer Hanselman to Guthrie. It could be that Guthrie would pull a surprise upset when faced head to head with Hanselman. I found this by far the most interesting assertion, but the examples under "Historical Examples" don't demonstrate this phenomenon at all. For instance, the author asserts that the Nader spoiler effect demonstrates nontransitive preference relationships. But from my reading, it wasn't the case that that group as a whole preferred (Gore over Nader) and (Nader over Bush) but (Bush over Gore). It was simply that due to the structure of the election, they happened to elect Bush. While this ties into the author's point about the "unfairness" of elections, it doesn't demonstrate nontransitive relationships in group preferences. Could someone post an example of a group preference configuration in which the group prefers (A over B) and (B over C) but (C over A)? I understand the concept of nontransitive relationships in general, but in the specific domain of fitness for office, I can't work out how this would come to be.
- jsharpe 14y ago
  I am wondering that too. He also gave the example of Ford beating Reagan (in the Republican primary), Carter beating Ford in the general election in 1976, and then Reagan beating Carter in 1980, but this is also not a great example since the Republican primary group is very different than the general electorate.
- Dove 14y ago
  Could someone post an example of a group preference configuration in which the group prefers (A over B) and (B over C) but (C over A)? Sure, that's easy to construct. Peter's preferences: A, B, C Paul's: B, C, A Mary's: C, A, B The group prefers A over B, by a 2-1 vote. Likewise B over C, and C over A.
- Nursie 14y ago
  It's late and I'm tired but I think in the following situation - 49% vote Bush, 42% vote Gore, 9% vote Nader. All Bush voters prefer Nader over Gore (unlikely!). All Nader voters prefer Gore over Bush. Half of Gore voters prefer Bush over Nader. - If the election was Gore:Bush, Gore would win 51:49 - If the election was Bush:Nader, Bush would win 70:30 - If the election was Gore:Nader, Nader would win 42:58 The group prefers Gore over Bush (A over B) and Bush over Nader (B over C) but Nader over Gore (C over A). That's my reading anyway.
jQueryIsAwesome 14y ago
Some of you are forgetting something; that even if you had some form of "stadistical fairness" (whatever that may be); you still have the biggest problem of most democracies: Uneducated people; people who think an atheist shouldn't be president, people who like to reinforce their biases more than they like to have deep discussions about the nation's issues, people who were never taught to do critical thinking... and without doing exceptions for their government, their parents, their religion and the law.
- bluedanieru 14y ago
  That's not really in scope for choosing a voting system that best represents the people. But yes, point taken.
  - deleted 14y ago
    [deleted]
Tloewald 14y ago
The article confuses two issues, one illustrated by Arrow's Theorem which is more relevant to parliamentary procedures (where any set of more than two choices has to be resolved as a series of binary choices, and the voting population is small and its preferences well understood) and first past the post electoral systems which are completely hopeless, especially when tiered, as in the US. Most of the article is essentially discussing an example of Arrow's Theorem where if you know people's preferences and can present them with binary options in an order of your choosing you can obtain any outcome except the least popular option. This is very artificial and not a real flaw of preferential and proportional electoral systems where (a) individual preferences are not known and (b) the entire vote is done in one step, not in a carefully chosen series of binary options. Great for gaming a committee, lousy for elections. As others have observed, the chief purpose of voting is allowing government transitions without violence and with the appearance of procedural fairness, but the fact remains voting works just fine when the population has a clear cut preference ("throw the bastards out"). Well, modulo corrupt redistricting. Americans who want to talk about voting really need to understand that there are other voting systems than the horse and buggy system used in the US and UK.
stretchwithme 14y ago
Winner-take-all elections, no matter how they operate, leave many people without the representation they prefer. Proportional representation is much less likely to do this. Proportional representation can used in the executive branch too. Switzerland does it.
fluxon 14y ago
Wasn't this issue addressed rather well in a recent hackernews-linked item which mathematically showed both that voting is not a sham, but that the Electoral College system is more fair than it has been represented? (sorry can't find the link!)

95 points by eibrahim 14y ago

mtgx 14y ago

Approval Voting mostly solves the "strategic voting" part that almost forces you to choose the "most likely to win" candidate, or if you hate that one, the one closest to him, while eliminating the spoiler effect, and giving 3rd party candidates a much higher chance of winning than with current traditional voting systems. http://www.electology.org/approval-voting http://www.electology.org/approval-voting http://en.wikipedia.org/wiki/Approval_voting http://en.wikipedia.org/wiki/Approval_voting

DennisP 14y ago
Plus it doesn't run into trouble with Arrow's theorem, since it's not a "rank-order voting system," unlike plurality, instant runoff, and various others. Range voting has the same advantage. In computer simulations measuring how well the election result matches voter preferences, either range or approval is as much an improvement over plurality as plurality is over picking someone at random (or, if you like, monarchy). http://rangevoting.org/BayRegsFig.html http://rangevoting.org/BayRegsFig.html
- gus_massa 14y ago
  I'm not sure about the definitions, but if the Arrow theorem doesn't apply to the Approval Voting sistem them I think that it must not be applicable to the "majority rules" criterion. In this two system the idea is that you get very little information from the voters (best candidate / a set of candidates) and don't know all the information about the order of preference and the relative strength. So I don't understand why having less information is better (theoreticaly).
  - Empact 14y ago
    > I don't understand why having less information is better (theoreticaly). A ranked-choice ballot only encodes the orders the candidates against one another, whereas approval and score votes also encode the candidates' positions within the voter's range of subjective preferences. That is, if we have 3 candidates (A, B, C) and a few voters which each voters has a range from love to hate for each candidate, like so: Love Hate |-A--B-------------------C-| |-A-------------B-----C----| |-------------------A-B-C--| |-A-B---C------------------| Under ranked choice voting, every one of these voters' ballots would look the same: 1)A, 2)B, 3)C Ranked choice voting encodes the ordering of the preferences, but the intensity of those preferences is lost when the ballot is cast. Whereas under approval and score voting, every one of these voters represents their preferences differently, because they're reflecting their personal response to each candidate: Approval | Disapproval |-A--B-----|-------------C-| |-A--------|----B-----C----| |----------|--------A-B-C--| |-A-B---C--|---------------| Of course, some information is lost in the fact that we only have 2 values approval/disapproval to encode positional preferences. But I would argue this information is already more meaningful than a fully-expressed ranked ballot. And if necessary, score voting can capture more of that information by offering > 2 levels to divide the candidates into.
    - gus_massa 14y ago
      OK, this method recollect some information that the ranked choice voting ignores. But I still don't understand why the Arrow's theorem doesn't apply. If in a hypothetic population everyone loves/hates each candidate equally spaced, then in that population it is possible to apply the Arrow's theorem and prove that for that population this method doesn't work. But the method should be useful for every population, even the pathological ones.
- jivatmanx 14y ago
  Don't know if anyone is going to read this, but I was reading about ordinal vs. cardinal utility, which are interesting because they seem to correspond to Ranked Choice vs. Approval voting, with the various voting systems simply being a different algorithm of calculating the winner from these. Anyway, apparently, with "Inter-temporal choice", or, different utility of the same thing measured in different time periods, Cardinal Utility needs to be used. I wonder if the same applies to grouping utility of different people together in order to get an aggregate. If so, it's an argument for the use of Approval/Score voting as opposed to Ranked choice. The quote is "Models of utility with several periods, in which people discount future values of utility, need to employ cardinalism in order to have well-behaved utility functions." an appears in the cardinal utility article.
bhauer 14y ago
Score voting is actually slightly superior to Approval Voting (which is Score Voting with a range of 0 to 1). To my understanding, the Center for Election Science ("electology.org") is the preeminent organization championing Approval and Score Voting. http://www.electology.org/score-voting http://www.electology.org/score-voting Eric Sanders of that same organization has written a few articles on the subject, including the following: http://bigthink.com/action-in-action/why-the-republicans-lost http://bigthink.com/action-in-action/why-the-republicans-los... I've personally been trying to campaign for the adoption of score voting: https://usa.brianstaskforce.com/task/362/score-voting-for-national-elections https://usa.brianstaskforce.com/task/362/score-voting-for-na...
- jivatmanx 14y ago
  I think that, over time, people would drift towards using only 0 and 10 and none of the middle scores, similar to how, over time a plurality voting system drifts towards only having two political parties (Duverger's Law). 0 And 10 are the "strategic votes" of score voting as 2-major-parties are the "strategic votes" of plurality voting. A possible counter-argument to this is that score voting doesn't have a reinforcing feedback loop (each election, the minor parties get weaker until they remain at around 1%)
  - bhauer 14y ago
    An interesting point. Since you're speaking about strategy and honesty, I would defer to those who have done research, where I can only speak for myself. http://ScoreVoting.net/Honesty.html http://ScoreVoting.net/Honesty.html I know I would not hesitate to vote my actual opinion and I suspect others would not either. I would be happy to give a score to each candidate, and it would not necessarily be binary. Just as I am happy today to vote for a third-party candidate though that is not a strategic move. Again speaking just for myself, if nothing else, having the ability to score candidates would reduce my feeling of regret or disappointment with the outcome because it's less polarizing.
bradbeattie 14y ago
Let's say there are two head-line candidates: A and B. I hate A, am neutral towards B, and love the less popular of the three candidate C. So do I vote 0/0/1 or 0/1/1? Well, that depends on how popular the three are and is very much an example of strategic voting. When proposing an alternative, one should probably be up-front with its flaws.
- jivatmanx 14y ago
  That's not strategic voting according to the definition. In both cases you're still voting for C, the candidate you like the most. "In voting systems, tactical voting (or strategic voting or sophisticated voting or insincere voting) occurs, in elections with more than two candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.[1]" If you mean it in the larger sense of using strategy when voting, Gibbard–Satterthwaite theorem shows that no voting system is strategy free unless it's either dictatorial or nondeterministic.
  - bradbeattie 14y ago
    My decision to vote either 0/0/1 or 0/1/1 is explicitly to prevent my desire for B over A from causing B to win when C might have a chance. Whenever you have to consider the ballots of other voters, you're dealing with tactical voting.
    - lmkg 14y ago
      Approval voting is immune to a particular definition of tactical voting, which is somewhat weaker than the traditional one. Which isn't perfect, but it's better than most other methods can offer. Most traditional voting methods are preference systems: You take your N candidates and rank them from 1 to N. Every voter is assumed to have a "ground truth" preference of ranking. Tactical voting means that a rational voter may sometimes be encouraged to vote with a ranking other than their true preference. The weaker criteria that approval voting satisfies is this: A rational voter can always make a rational vote by writing down their true preference ranking in order, drawing a line, and approving everyone above that line. In other words, there is no situation where a rational voter would want to vote A > B when their true preference is B > A. This is a significant bound on the effects of tactical voting. As you correctly point out, the rationally optimal place to draw that line can be tactical. Nonetheless, there is a strong argument that this is "less tactical" than many other systems allow.
Steko 14y ago
Approval voting suffers the largest number of "Especially Intolerable Failures" in the comparison here: http://en.wikipedia.org/wiki/Comparison_of_instant_runoff_voting_to_other_voting_systems#Voting_system_criteria http://en.wikipedia.org/wiki/Comparison_of_instant_runoff_vo...
- Empact 14y ago
  If you examine these supposed failures of Approval voting, you'll find that the bulk of them can be attributed to the divide between a "Majoritarian" or a "Consensus-driven" perspective. That is, many of the criteria suppose that the most-preferred candidate of the majority should win, but should that be the case? Imagine there are 3 candidates, one who is adored by the super-majority, a second who is very well-liked by that super-majority and a third who is hated. Meanwhile the minority hates the first and third candidates, but well-likes the second. We can visualize this like so: # Approval | Disapproval 80 |-1--2----|--------------3-| 20 |-2-------|-----------3--1-| So while the first candidate is the favorite candidate of the super-majority, the second candidate has the unanimous approval of population. Which is preferable? I would say the second candidate. So you see, the criteria themselves incorporate an ideological perspective - a majoritarian bias - rather than articulating some absolute objective truth. Also I have to take issue with the basis for the "Especially Intolerable Failures" explanation - does it make sense to reject a system for being theoretically capable of producing a result, "regardless of the probability that these paradoxes may occur"? Given 2 systems, one which exhibits several flaws often, and another which rarely exhibits flaws but is theoretically capable of exhibiting a certain offensive flaw, does it make sense to reject the better-behaving system because of a theoretical result? I think not.
  - chimeracoder 14y ago
    > Given 2 systems, one which exhibits several flaws often, and another which rarely exhibits flaws but is theoretically capable of exhibiting a certain offensive flaw, does it make sense to reject the better-behaving system because of a theoretical result? I think not No, but if we want to go on the basis of how likely it is to produce those outcomes, Instant-runoff voting beats approval voting by a long shot. Amartya Sen has shown that, not only is IRV is highly unlikely to produce an outcome which violates transitivity and independence, but if ideologies are assumed to be relatively linear[1], then it never violates those conditions. [1] Ie, very few people would rank Nader > Bush > Gore

streptomycin 14y ago

Also, there's this: http://papers.nber.org/papers/w15220 http://papers.nber.org/papers/w15220

saraid216 14y ago

> Voting is a method that a group of people use to pick the “best choice” out of a set of candidates. It’s pretty obvious, right? And like many other pieces of "common sense", this isn't correct. Wikipedia says, "Voting is a method for a group such as a meeting or an electorate to make a decision or express an opinion—often following discussions, debates, or election campaigns. Democracies elect holders of high office by voting." This is very different from "picking the best choice". I realize that the American public has been indoctrinated for the past few decades that voting is the only way you make yourself heard, but this isn't true and never has been. I recently learned about Wellstone Action ( http://en.wikipedia.org/wiki/Wellstone_Action http://en.wikipedia.org/wiki/Wellstone_Action ); I encourage everyone to look into enrolling. (I haven't done so myself yet. I probably will at some point, though.) > On one hand, this seems to be an endorsement of the two-party political system we have in the United States. Actually, what it's an endorsement of is all of our other voting systems where the choice is between APPROVE and REJECT. You have to endorse the existence of political parties in the first place before you can endorse a two-party system, and Arrow's theorem goes nowhere near that.

derleth 14y ago
> I realize that the American public has been indoctrinated for the past few decades that voting is the only way you make yourself heard This has never been true. Americans have always protested, signed petitions, and even joined special interest groups like the ACLU and the NRA. Americans have a very long tradition of things like that.
- saraid216 14y ago
  Tell that to the next person who complains that their vote doesn't count.
  - derleth 14y ago
    It's entirely possible to be active in the ACLU, for example, and still be annoyed that since you live in Montana your vote for a Democratic presidential candidate is basically pointless.

basseq 14y ago

> A voting system can only, at times, choose the most preferred of the options given. But it doesn't necessarily present us with the best candidates to choose from in the first place. Reminds me of HHGTTG: "Anyone who is capable of getting themselves made President should on no account be allowed to do the job."

aprescott 14y ago

In this case, Hanselman is the clear winner with three votes, whereas the other two candidates each have two votes. This is how our elections are held today. This is dependent on the exact election taking place. With the US presidential elections, my understanding is that a plurality of electoral college votes is not enough to win, you need an actual majority. In the event of a simple plurality win with no majority, the result is decided by the House of Representatives (which may itself be tied).

rjzzleep 14y ago
is it? the actual candidates already get preselected. even if youre right, which is likely, it doesn't matter, because any majority was previously generated by pluarility.

wam 14y ago

Learning about Arrow's theorem definitely changed the way I think about elections in the US. It also changed the way I think about election news coverage. I used to be an ardent "horse race news" hater. I still am, in terms of how utterly it dominates election news, but now I see some utility in it as well. Arrow and these others have focused how I look at the game-theoretic underpinnings of elections and the importance of being up to speed on exactly how candidates and interested parties are crafting strategies around the complexities built into the game. When people conflate the "message" of the candidate with the strategy (which is always) I still get irritated. I have a tendency toward partisanship and that kind of thing clouds my judgment. But the day-in day-out workings of the campaigns and PACs are more interesting to me now, because they shed light on what's fundamentally "broken" (from my point of view) in the underlying system, as opposed to what I simply find distasteful or disappointing. Math!

saraid216 14y ago
Social choice theory is One Of Those Things which everyone (myself included) needs to spend more time learning about.

hcarvalhoalves 14y ago

If you look at Brazil, which has multiple parties and plurality voting, the problems are pretty clear. In this year's elections, the candidate with 28% of the votes was elected mayor in my city.

Noughmad 14y ago

I find it interesting that in all those discussions about voting systems, which are mostly focused on USA president elections, nobody mentions two-round voting, also known as run-off voting. This is what we have in Slovenia for electing our president. In the first round, there are many candidates, and each voter can vote for one. If any candidate gets at least 50% of votes, he automatically wins. If, on the other hand, there is no majority winner, the two best candidates compete head-to-head in the second round. Such a system allows you to always vote for your favourite candidate in the first round, and if your candidate doesn't make it into the second round, you can vote for the fallback one. Details: https://en.wikipedia.org/wiki/Two-round_system https://en.wikipedia.org/wiki/Two-round_system

kscaldef 14y ago
I don't believe this satisfies the Condercet criterion either. Consider these rankings of preferences: 20% A ... 20% B ... 15% C ... 15% D C ... 15% E C ... 15% F C ... In a two-round run-off, one of A or B will be elected, despite the fact that 60% of voters prefer C over either A or B.
- im3w1l 14y ago
  And in the real world, people would second guess this, and enough people would tactic vote for C that it would't be a problem. "But then they can't vote for their prefered candidate which was the whole point" Well, some people can. D, E, F could still get a few percentage points. More importantly, I don't think we would see convergence to a 2-party system. Unless I am missing something, it looks like at least 3 parties could be sustained.

gradstudent 14y ago

Preferential voting solves all these problems. You vote by ranking the candidates on order of preference. If your top candidate does not win the vote goes to next guy down the line until eventually it ends up for one of two candidates.

Pinckney 14y ago
Preferential voting does not satisfy the Condorcet criterion. http://en.wikipedia.org/wiki/Instant-runoff_voting#Voting_system_criteria http://en.wikipedia.org/wiki/Instant-runoff_voting#Voting_sy...
- bradbeattie 14y ago
  To demonstrate this, consider the following. 80 people: A, C, B 50 people: B, C, A 35 people: C, B, A IRV eliminates C (as it has the fewest first-place votes) and elects B. But voters on the whole prefer C over B (115 to 50). This is the failure that Pinckney refers to.
  - deleted 14y ago
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- finnw 14y ago
  You mean IRV does not satisfy the Condorcet criterion. IRV is not the only preferential voting system. There are others, e.g. ranked pairs[1] which do. Under ranked pairs, each pair of candidates is considered individually, largest majorities first. In bradbeattie's example we have: C > B: 115 votes C > A: 85 votes B > A: 85 votes So the group preference is C > B > A and C wins. Ranked pairs fails the participation criterion[2], but it is still possible to vote tactically in a way that guarantees you will not harm your first-choice candidate by participating (since if your first choice is A you can rank A first and all the others joint second. Similarly if your goal is to prevent C from winning, you can rank C second and all others joint first.) [1]:http://en.wikipedia.org/wiki/Ranked_pairs http://en.wikipedia.org/wiki/Ranked_pairs [2]:http://en.wikipedia.org/wiki/Participation_criterion http://en.wikipedia.org/wiki/Participation_criterion

bo1024 14y ago

This is a very nice summary of/intro to the classic/standard mathematical approach to voting and Arrow's Theorem.

frozenport 14y ago

This is why we have a 2 party system :-)

maratd 14y ago

This is off. Voting is not a system for selecting the best candidate. Voting, in whatever forms it exists, is a system to avoid violence and conflict. Each side feels it had a fair shot, regardless of outcome. The purpose of voting is to leave you with that feeling, to avoid unpleasant behavior from the losing party. The best person for the job almost never gets it. That's why we don't vote people in when hiring somebody at a company.

diego 14y ago
Yes, and in addition it's also a system to ensure that elected officials and their parties have accountability. If you win an election and then "betray" your voters, you won't be reelected. If you can't be reelected, you could damage the chances of your party. In essence, democracy in its current form is not so much about choosing the right/best candidate. It's more about making sure the winner cannot become a despot.
- bad_user 14y ago
  In addition, people do not even try voting for the best candidate. People usually vote for the candidate whose interests best align with their own interests and if we're talking about that, then we can't avoid talking about compromises. Which is why it's easy to see why preferences between candidates may be non-transitive, as the space we're talking about is no longer one-dimensional so candidates don't have a natural order.
- ontheotherhand 14y ago
  "If you win an election and then "betray" your voters, you won't be reelected." That ain't accountability, that's a joke. If you pay me 5000$ to do a job, and I don't lift a finger, and your "punishment" is that we won't do that a second time, then I have free money and you're a fool. It doesn't hurt the party one bit either; that's the whole point of corporatism, you can swap out individuals while the "brand" rolls on, saying "whoops, bad apple" every 5 seconds, with people forgetting after 2. "It's more about making sure the winner cannot become a despot." Correction: it replaces a single despotic individual with a tag team of people who basically can do whatever they want - within boundaries, sure, they at least have to be somewhat slick about it, and know how to make a puppy face, too; but certainly not within boundaries defined by the actual will of the people who handed their power as souvereigns over to their representatives. Having despotic entities control you is not one iota better than despotic humans, not in the long run. Despotism is marked by the control going only down, accountability going only up -- period. Not by angry men on podiums necessarily, and not by bloodshed. (Not that there isn't plenty bloodshed, but that's besides the point) If you seriously see a huge difference or improvement there, you've fallen for it I'm afraid.

mmphosis 14y ago

Mixed Member Proportional (MMP) Representation solves some of the problems. http://www.youtube.com/watch?v=QT0I-sdoSXU&feature=relmfu http://www.youtube.com/watch?v=QT0I-sdoSXU&feature=relmf... The problem with MMP is when the parties choose the ranking of their list of representatives. I think it would be even better if rather than use a party generated list, instead the representatives are determined by people's votes.

nikatwork 14y ago

I've always thought New Zealand's mixed-member proportional (MMP) voting system [1] is the least bad solution currently in use. I'm not from NZ so I'd be interested to hear what the locals think. [1] http://en.wikipedia.org/wiki/New_Zealand_voting_system_referendum,_2011 http://en.wikipedia.org/wiki/New_Zealand_voting_system_refer...

lmkg 14y ago
Not a local, but... Proportional voting systems suffer from the problem that voting "power" is not proportional to representation. Consider a parliament with 100 members and 3 parties. Suppose the breakdown is: A has 49 members, B has 48 members, and C has 3 members. Guess what... A, B, and C all have equal voting power! Any two parties are enough to reach a majority of 51 votes, and any one party is not. Despite A having, in theory, over 16 times the representation of C, it does not have any voting advantage. Keep in mind that any voting system based on parties will tend to have very partisan voting blocs. Representatives in the US are more independent and likely to break with the party because they are elected in geographically isolated elections. Representatives elected directly by a party generally have about as much independence as the Electors in the Electoral College.
- NickNameNick 14y ago
  I'm from NZ... To form a government, the party with the most votes, or a coalition of parties which collectively holds a majority petition the governor general. For a single party this is quite straightforward. To form a coalition the member parties agree on a 'Confidence and supply agreement" This is basically a statement that in the event of a vote of no-confidence, all of the coalitions members will support the coalition, and also a broad agreement on the budget. Getting an agreement on confidence usually involves a certain amount of horse trading about ministerial and vice ministerial positions. Likewise, the agreement on supply will probably involve some intense budget and joint-policy negotiations. If you had a parliament of 101 seats, split into an opposition of 50 seats, and a government of 51, itself made up of a large party (48 seats) and a small party (3 seats) what you will probably see is the small party only has the tiniest influence on the coalition agreement. They probably traded everything else to get their senior member a ministerial position.

gabemart 14y ago

I found this article quite frustrating. >Condorcet formalized the idea that group preferences are also non-transitive. If people prefer Hanselman to me. And they prefer me to Guthrie. It does not necessarily mean they will prefer Hanselman to Guthrie. It could be that Guthrie would pull a surprise upset when faced head to head with Hanselman. I found this by far the most interesting assertion, but the examples under "Historical Examples" don't demonstrate this phenomenon at all. For instance, the author asserts that the Nader spoiler effect demonstrates nontransitive preference relationships. But from my reading, it wasn't the case that that group as a whole preferred (Gore over Nader) and (Nader over Bush) but (Bush over Gore). It was simply that due to the structure of the election, they happened to elect Bush. While this ties into the author's point about the "unfairness" of elections, it doesn't demonstrate nontransitive relationships in group preferences. Could someone post an example of a group preference configuration in which the group prefers (A over B) and (B over C) but (C over A)? I understand the concept of nontransitive relationships in general, but in the specific domain of fitness for office, I can't work out how this would come to be.

jsharpe 14y ago
I am wondering that too. He also gave the example of Ford beating Reagan (in the Republican primary), Carter beating Ford in the general election in 1976, and then Reagan beating Carter in 1980, but this is also not a great example since the Republican primary group is very different than the general electorate.
Dove 14y ago
Could someone post an example of a group preference configuration in which the group prefers (A over B) and (B over C) but (C over A)? Sure, that's easy to construct. Peter's preferences: A, B, C Paul's: B, C, A Mary's: C, A, B The group prefers A over B, by a 2-1 vote. Likewise B over C, and C over A.
Nursie 14y ago
It's late and I'm tired but I think in the following situation - 49% vote Bush, 42% vote Gore, 9% vote Nader. All Bush voters prefer Nader over Gore (unlikely!). All Nader voters prefer Gore over Bush. Half of Gore voters prefer Bush over Nader. - If the election was Gore:Bush, Gore would win 51:49 - If the election was Bush:Nader, Bush would win 70:30 - If the election was Gore:Nader, Nader would win 42:58 The group prefers Gore over Bush (A over B) and Bush over Nader (B over C) but Nader over Gore (C over A). That's my reading anyway.

jQueryIsAwesome 14y ago

Some of you are forgetting something; that even if you had some form of "stadistical fairness" (whatever that may be); you still have the biggest problem of most democracies: Uneducated people; people who think an atheist shouldn't be president, people who like to reinforce their biases more than they like to have deep discussions about the nation's issues, people who were never taught to do critical thinking... and without doing exceptions for their government, their parents, their religion and the law.

bluedanieru 14y ago
That's not really in scope for choosing a voting system that best represents the people. But yes, point taken.
- deleted 14y ago
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Tloewald 14y ago

The article confuses two issues, one illustrated by Arrow's Theorem which is more relevant to parliamentary procedures (where any set of more than two choices has to be resolved as a series of binary choices, and the voting population is small and its preferences well understood) and first past the post electoral systems which are completely hopeless, especially when tiered, as in the US. Most of the article is essentially discussing an example of Arrow's Theorem where if you know people's preferences and can present them with binary options in an order of your choosing you can obtain any outcome except the least popular option. This is very artificial and not a real flaw of preferential and proportional electoral systems where (a) individual preferences are not known and (b) the entire vote is done in one step, not in a carefully chosen series of binary options. Great for gaming a committee, lousy for elections. As others have observed, the chief purpose of voting is allowing government transitions without violence and with the appearance of procedural fairness, but the fact remains voting works just fine when the population has a clear cut preference ("throw the bastards out"). Well, modulo corrupt redistricting. Americans who want to talk about voting really need to understand that there are other voting systems than the horse and buggy system used in the US and UK.

stretchwithme 14y ago

Winner-take-all elections, no matter how they operate, leave many people without the representation they prefer. Proportional representation is much less likely to do this. Proportional representation can used in the executive branch too. Switzerland does it.

fluxon 14y ago

Wasn't this issue addressed rather well in a recent hackernews-linked item which mathematically showed both that voting is not a sham, but that the Electoral College system is more fair than it has been represented? (sorry can't find the link!)