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Imperfect Voting Systems

32 Post author: Yvain 20 July 2012 12:07AM

Stalin once (supposedly) said that “He who casts the votes determines nothing; he who counts the votes determines everything “ But he was being insufficiently cynical. He who chooses the voting system may determine just as much as the other two players.

The Art of Strategy gives some good examples of this principle: here's an adaptation of one of them. Three managers are debating whether to give a Distinguished Employee Award to a certain worker. If the worker gets the award, she must receive one of two prizes: a $50 gift certificate, or a $10,000 bonus.

One manager loves the employee and wants her to get the $10,000; if she can't get the $10,000, she should at least get a gift certificate. A second manager acknowledges her contribution but is mostly driven by cost-cutting; she'd be happiest giving her the gift certificate, but would rather refuse to recognize her entirely than lose $10,000. And the third manager dislikes her and doesn't want to recognize her at all - but she also doesn't want the company to gain a reputation for stinginess, so if she gets recognized she'd rather give her the $10,000 than be so pathetic as to give her the cheap certificate.

The managers arrange a meeting to determine the employee's fate. If the agenda tells them to vote for or against giving her an award, and then proceed to determine the prize afterwards if she wins, then things will not go well for the employee. Why not? Because the managers reason as follows: if she gets the award, Manager 1 and Manager 3 will vote for the $10,000 prize, and Manager 2 will vote for the certificate.  Therefore, voting for her to get the award is practically the same as voting for her to get the $10,000 prize. That means Manager 1, who wants her to get the prize, will vote yes on the award, but Managers 2 and 3, who both prefer no award to the $10,000, will strategically vote not to give her the award. Result: she doesn't get recognized for her distinguished service.

But suppose the employee involved happens to be the secretary arranging the meeting where the vote will take place. She makes a seemingly trivial change to the agenda: the managers will vote for what the prize should be first, and then vote on whether to give it to her.

If the managers decide the appropriate prize is $10,000, then the motion to give the award will fail for exactly the same reasons it did above. But if the managers decide the certificate is appropriate, then Manager 1 and 2, who both prefer the certificate to nothing, will vote in favor of giving the award. So the three managers, thinking strategically, realize that the decision before them, which looks like “$10 grand or certificate”, is really “No award or certificate”. Since 1 and 2 both prefer the certificate to nothing, they vote that the certificate is the appropriate prize (even though Manager 1 doesn't really believe this) and the employee ends out with the gift certificate.

But if the secretary is really smart, she may set the agenda as follows: The managers first vote whether or not to give $10,000, and if that fails, they next vote whether or not to give the certificate; if both votes fail the employee gets nothing. Here the managers realize that if the first vote (for $10,000) fails, the next vote (certificate or nothing) will pass, since two managers prefer certificate to nothing as mentioned before. So the true choice in the first vote is “$10,000 versus certificate”. Since two managers (1 and 3) prefer the $10,000 to the certificate, those two start by voting to give the full $10,000, and this is what the employee gets.

So we see that all three options are possible outcomes, and that the true power rests not in the hands of any individual manager, but in the secretary who determines how the voting takes place.

Americans have a head start in understanding the pitfalls of voting systems thanks to the so-called two party system. Every four years, they face quandaries like "If leftists like me vote for Nader instead of Gore just because we like him better, are we going to end up electing Bush because we've split the leftist vote?"

Empirically, yes. The 60,000 Florida citizens who voted Green in 2000 didn't elect Nader. However, they did make Gore lose to Bush by a mere 500 votes. The last post discussed a Vickrey auction, a style of auction in which you have have no incentive to bid anything except your true value. Wouldn't it be nice if we had an electoral system with the same property: one where you should always vote for the candidate you actually support? If such a system existed, we would have ample reason to institute it and could rest assured that no modern-day Stalin was manipulating us via the choice of voting system we used.

Some countries do claim to have better systems than the simple winner-takes-all approach of the United States. My own adopted homeland of Ireland uses a system called “single transferable vote” (also called instant-runoff vote), in which voters rank the X candidates from 1 to X. If a candidate has the majority of first preference votes (or a number of first preference votes greater than the number of positions to fill divided by the number of candidates, in elections with multiple potential winners like legislative elections), then that candidate wins and any surplus votes go to their voters' next preference. If no one meets the quota, then the least popular candidate is eliminated and their second preference votes become first preferences. The system continues until all available seats are full.

For example, suppose I voted (1: Nader), (2: Gore), (3: Bush). The election officials tally all the votes and find that Gore has 49 million first preferences, Bush has 50 million, and Nader has 5 million. There's only one presidency, so a candidate would have to have a majority of votes (greater than 52 million out of 104 million) to win. Since no one meets that quota, the lowest ranked candidate gets eliminated - in this case, Nader. My vote now goes to my second preference, Gore. If 4 million Nader voters put Gore second versus 1 million who put Bush second, the tally's now at 53 million Gore, 51 million Bush. Gore has greater than 52 million and wins the election - the opposite result from if we'd elected a president the traditional way.

Another system called Condorcet voting also uses a list of all candidates ranked in order, but uses the information to run mock runoffs between each of them. So a Condorcet system would use the ballots to run a Gore/Nader match (which Gore would win), a Gore/Bush match (which Gore would win), and a Bush/Nader match (which Bush would win). Since Gore won all of his matches, he becomes President. This becomes complicated when no candidate wins all of his matches (imagine Gore beating Nader, Bush beating Gore, but Nader beating Bush in a sort of Presidential rock-paper-scissors.) Condorcet voting has various options to resolve this; some systems give victory to the candidate whose greatest loss was by the smallest margin, and others to candidates who defeated the greatest number of other candidates.

Do these systems avoid the strategic voting that plagues American elections? No. For example, both Single Transferable Vote and Condorcet voting sometimes provide incentives to rank a candidate with a greater chance of winning higher than a candidate you prefer - that is, the same "vote Gore instead of Nader" dilemma you get in traditional first-past-the-post.

There are many other electoral systems in use around the world, including several more with ranking of candidates, a few that do different sorts of runoffs, and even some that ask you to give a numerical rating to each candidate (for example “Nader 10, Gore 6, Bush -100000”). Some of them even manage to eliminate the temptation to rank a non-preferred candidate first. But these work only at the expense of incentivizing other strategic manuevers, like defining “approved candidate” differently or exaggerating the difference between two candidates.

So is there any voting system that automatically reflects the will of the populace in every way without encouraging tactical voting? No. Various proofs, including the Gibbard-Satterthwaite Theorem and the better-known Arrow Impossibility Theorem show that many of the criteria by which we would naturally judge voting systems are mutually incompatible and that all reasonable systems must contain at least some small element of tactics (one example of an unreasonable system that eliminates tactical voting is picking one ballot at random and determining the results based solely on its preferences; the precise text of the theorem rules out “nondeterministic or dictatorial” methods).

This means that each voting system has its own benefits and drawbacks, and that which one people use is largely a matter of preference. Some of these preferences reflect genuine concern about the differences between voting systems: for example, is it better to make sure your system always elects the Condorcet winner, even if that means the system penalizes candidates who are too similar to other candidates? Is it better to have a system where you can guarantee that participating in the election always makes your candidate more likely to win, or one where you can be sure that everyone voting exactly the opposite will never elect the same candidate?

But in practice, these preferences tend to be political and self-interested. This was recently apparent in Britain, which voted last year on a referendum to change the voting system. The Liberal Democrats, who were perpetually stuck in the same third-place situation as Nader in the States, supported a change to a form of instant runoff voting which would have made voting Lib Dem a much more palatable option; the two major parties opposed it probably for exactly that reason.

Although no single voting system is mathematically perfect, several do seem to do better on the criteria that real people care about; look over Wikipedia's section on the strengths and weaknesses of different voting systems to see which one looks best.

Comments (86)

Comment author: bryjnar 20 July 2012 08:44:03AM 28 points [-]

I think people often dismiss systems like STV/IRV by essentially saying "Arrow's theorem implies you can still vote tactically, so it's just as bad". But there's a big difference: in STV it's much harder to figure out how to vote tactically.

In First Past The Post systems, tactical voting is blindingly obvious: if there are two candidates you like, but you don't think that your favourite has enough popularity to win outright, then you should vote for the other one, to avoid splitting the vote. This is easy to understand, and it's also easy to detect circumstances where it would be beneficial for you to vote other than your preferences.

OTOH, even though there are times where you can vote tactically in STV, they're harder to understand, and crucially, it's much harder to recognise such opportunities: you need a lot more information.

This means that, in general, STV would cut down on tactical voting a great deal, simply because it makes it harder.

Comment author: Kaj_Sotala 20 July 2012 09:12:50AM *  11 points [-]

This. In FPTP, tactical voting will have a major influence on the results, since it's so obvious and thus lots of people will end up doing it. In STV, most people won't even realize that the opportunity for tactical voting exists, so the amount of people doing it will be much smaller.

Comment author: TraderJoe 20 July 2012 11:41:36AM *  3 points [-]

[comment deleted]

Comment author: Luke_A_Somers 21 July 2012 01:33:38AM 4 points [-]

Because in electoral politics, you are not a unique snowflake. Failure to take into account collective action of people thinking along the lines you're thinking drastically understates the influence of those thoughts.

Comment author: TraderJoe 24 July 2012 08:38:02AM *  0 points [-]

[comment deleted]

Comment author: Luke_A_Somers 30 July 2012 02:40:39PM *  0 points [-]

It's not that your decision affects the others. That's messed up causality. It's that your decision shares a lot of its causes with other decisions in other people. If you take yours as typical of a particular subset, and decide not to vote, then that suggests that others in that subset might as well. Gathering a large bloc of equivalent voters raises the voting power from approximately 0 to... well, some nontrivial number. If it's really large, it's exactly 1 (voting power is not probability, so 1 is a legit answer).

Comment author: TraderJoe 31 July 2012 06:59:11AM *  0 points [-]

[comment deleted]

Comment author: Luke_A_Somers 31 July 2012 02:10:19PM *  -1 points [-]

It's not 'will be the same regardless of which side I come down on', like we're in a state

A |Luke votes & Joe votes> + B|Luke doesn't vote & Joe doesn't vote>

It's 'Is this a good plan of action? Let's look at its consequences. First order (if I do it): OK. Second order (if everyone does it): not OK.'

Comment author: TraderJoe 02 August 2012 06:52:07AM *  0 points [-]

[comment deleted]

Comment author: framsey 20 July 2012 01:46:40PM *  7 points [-]

I imagine that if polls showed that we were in a situation where strategic voting might be useful for people with certain preferences, the news media would report on it and people would learn about it.

I can see the headline now: "Mathematician says that if your preferences are 'A > B > C', you should vote 'B > A > C' in November!"

Such situations could be recognized by poll questions like "What is your preference ordering over these 3 candidates?" Candidate B's campaign would have a large incentive to publicize this information.

Comment author: bryjnar 20 July 2012 02:15:54PM 3 points [-]

I think the more important point is that you simply require too much information about too many people's preferences to be able to do that, except in rare cases. The amount of data you'd need would be tantamount to just knowing how everyone would vote. If you know that, then this sort of thing might be feasible, but that's a big ask!

Comment author: Luke_A_Somers 21 July 2012 01:44:32AM *  2 points [-]

In IRV, cases of clear opportunity for strategic voting are not at all rare, nor are they hard to detect. All you need is to see that a compromise candidate is in third place by lead preference, and that your wing candidate would probably lose in the runoff. This is hardly inaccessible information, requiring only one horse-race poll and the most obvious head-to-head poll.

What you face is a flat cost in terms of settling for a non-first-choice, in return for bolstering your chances of avoiding a strongly non-preferred outcome. It's a chicken strategy, rather than the berserker strategy that's your only opportunity with Condorcet.

In effect it pulls IRV back towards FPTP in terms of voting behavior. Not all the way, to be sure - you're perfectly safe putting the extremely silly party on the top of your ticket, and if there are more than three major parties, each with a credible chance at winning, it gets to be sufficiently difficult to project consequences that the benefits of defensive strategy are no longer clear.

Comment author: roystgnr 24 July 2012 04:44:54AM 6 points [-]

in general, STV would cut down on tactical voting a great deal, simply because it makes it harder

Possible counterexample:

In the USA, tactical voting for President is usually completely impossible, due to the electoral college system. Your vote only affects the election outcome if the election as a whole is a toss-up and if your home state is in play. But for a Texan like me, that will never occur, not even relative to the one-in-a-million odds you'd normally expect from a national election. If the Democratic candidate stands any chance of winning here, they'll be winning the rest of the country in a landslide. Likewise for a Californian: any situation in which the Republican might win California is a situation where they've surely already won nearly everywhere else. Likewise for most of the country; only a handful of states, known well in advance, are "swing states" in a given election.

Yet, other than a few weirdos like me, does anyone use this freedom-means-nothing-left-to-lose situation to vote for a third party and thereby at least influence news results? Granted that most people usually prefer the two leading parties' candidates, but I haven't seen any statistics which would suggest that the minority of voters who disagree are likely to vote their consciences except in the swing states.

It may be that, even if many Democratic/Republican voters would legitimately prefer other alternatives, they appear to vote tactically due to some other bias: the human desire to "vote for a winner" tempered by the desire to avoid voting for a completely unpalatable candidate, or the desire for group affiliation expressed in this case via political party identification, perhaps.

What baffles me is that even the news media here does first-past-the-post polling! Asking people to give ranked preferences to generate official election results might be a serious legal undertaking, but why in the world doesn't a single major news company or polling organization ask for ordered preferences either, even for primary elections when there are often a half dozen serious contenders in play?

Comment author: Ezekiel 20 July 2012 10:56:08AM 1 point [-]

OTOOH, the people who do figure it out effectively get more power over choosing the result than people who don't. In most democracies, this would be considered a negative. Not that real-life elections are totally fair either, of course.

Comment author: Luke_A_Somers 20 July 2012 01:37:50PM *  8 points [-]

It's even harder to see when you ought to strategically vote in Condorcet systems than under STV. The strategic voting style you'd aim for in Condorcet is to 'bury' a second-favorite candidate.

Case: A Blue. Thinks the Reds have some serious problems, but those problems are nowhere near as bad as the White party.

The honest vote here is to vote Blue - Red - White. The strategic vote is Blue - White - Red.

But that is a very risky move. It only helps if this vote-bury helps the White party beat the Red by direct preference, AND the Red beat the Blue, AND the Blue beat the White party by direct preference, - so we just helped make a cycle - AND the cycle-resolution system, whatever that is, ends up favoring the Blues.

If you get the first and the second but not both of the other two... congratulations, you just elected the White party (or you made a cycle, and though the Red won, you made the Whites gain reputation and power relative to where they'd be being eliminated).

Unless you can know a great deal about the ballots that have been cast, this is far more likely to backfire and get you something you really don't want (White winning) than to get you something you want (Blue winning).

Comment author: Luke_A_Somers 17 August 2012 01:15:33PM 0 points [-]

I just remembered another style of strategic offensive voting - this one involves burying your favorite candidate under the second favorite in order to induce a cycle and then win it.

This one is even more insane than the other one, for obvious reasons. I just wanted to point out that it exists.

Comment author: shminux 20 July 2012 01:36:17AM 6 points [-]

Stalin once (supposedly) said that “He who casts the votes determines nothing; he who counts the votes determines everything “

The original Russian and a better translation together with some background on the Stalin quote can be found here. Of course, this is not from an official record, and so could have been made up or mis-remembered.

Comment author: steven0461 20 July 2012 01:34:01AM 21 points [-]
Comment author: GLaDOS 03 August 2012 02:31:42PM 2 points [-]

Yeah this article was pretty much screaming blue team.

Comment author: [deleted] 24 July 2012 05:42:45PM 0 points [-]
Comment author: Xachariah 27 July 2012 06:22:25AM *  -2 points [-]

I'm not seeing what she should have changed specifically. Politics is the mindkiller is mostly a suggestion to avoid politics unnecessarily. In this case, wouldn't it be necessary?

It seems kind of impossible to discuss voting systems without discussing politics.
Edit: Nevermind, it seems the offending comment in the OP was edited out before I read it.

Comment author: jacobt 20 July 2012 07:28:53AM 13 points [-]

I vote for range voting. It has the lowest Bayesian regret (best expected social utility). It's also extremely simple. Though it's not exactly the most unbiased source, rangevoting.org has lots of information about range voting in comparison to other methods.

Comment author: [deleted] 20 July 2012 07:33:36PM *  5 points [-]

I like Majority Judgement, which is like range voting except instead of sorting candidates by the sum of the scores each of them gets, you use the median of the scores. IIUC it's been proven that it's the system where tactical voting is hardest (for a certain definition of “hardest”).

Comment author: wedrifid 21 July 2012 04:51:19AM 1 point [-]

Majority Judgement link is dead.

Comment author: [deleted] 21 July 2012 10:35:22AM 4 points [-]

Fixed (both by changing the URL in the parent, and by creating a redirect on Wikipedia from the spelling with the E to the spelling without it).

Comment author: Luke_A_Somers 22 July 2012 03:55:28PM 0 points [-]

I hadn't encountered this one before.

It seems to me like it'll essentially be approval voting with the ability to give half a point of approval. There will be no distinction between 'Excellent' and 'Good'. What are the chances that two parties would make it up to 'good' median rating in an election, anyway? Maybe that's just the present-day US, but I have a hard time seeing people being that happy with politics.

But if they are, then there's suddenly no distinction between 'fair' and 'poor'. It's like since I don't like either of them I'm not allowed an opinion between them. I'll take Nixon over Hitler, please!

Comment author: Yvain 21 July 2012 03:54:02AM -1 points [-]

I also like Majority Judgment.

Comment author: shminux 20 July 2012 01:38:57AM 29 points [-]

The 60,000 Florida citizens who voted Green in 2000 didn't result in Nader for President (they did result in a nadir for the presidency, but that's different)

The parenthetical statement, while mildly funny, is unnecessarily political and detracts from the substance of your post.

Comment author: Gastogh 20 July 2012 04:15:26PM 15 points [-]

Upvoting for capturing the remark for those of us who didn't catch it before it was edited out. Yvain has the best puns.

Comment author: smijer 22 July 2012 02:39:21PM *  4 points [-]

My morning coffee hasn't kicked in... I wonder what the significance is that no voting system can be "perfect". Is it a fluke of math, or does it say something about the coherence of our value systems as they pertain to electoral systems?

I should also express my view that a plurality voting system that allows only two parties to thrive in practice is probably the worst of all worlds where it concerns voting systems. I believe the polarizing effects of a system that requires exactly two parties are a large component of the set of difficulties that make it so politics is the mind-killer.

Comment author: fubarobfusco 20 July 2012 01:10:22AM 8 points [-]

The 60,000 Florida citizens who voted Green in 2000 didn't result in Nader for President (they did result in a nadir for the presidency, but that's different) . However, they did make Gore lose to Bush by a mere 500 votes.

The same could be said for the 562 voters for James Harris of the Socialist Workers Party.

Comment author: hairyfigment 20 July 2012 01:18:27AM 10 points [-]

I've used this as an example of the problem with 'Highlander thinking', or the claim that there can be only one cause. Seems to me that any number of changes to the timeline would hand Gore the Presidency.

Comment author: CronoDAS 20 July 2012 12:16:02AM 6 points [-]

The two theorems you quoted technically don't apply to range voting...

Comment author: Yvain 20 July 2012 12:21:45AM 2 points [-]

Arrow doesn't, Gibbard-Satterthwaite still does to some degree.

Comment author: dmr 23 July 2012 09:17:22PM 2 points [-]

How? GST is for rank voting and RV isn't rank

Comment author: Pentashagon 22 July 2012 05:55:10AM 4 points [-]

I'm moderately in favor of randomly sampling members of legislative bodies from the represented population. The U.S. would only need a thousand citizens in Congress to have the national opinions and beliefs represented with the same accuracy as a Gallup poll. The period from November to January could just be a crash course in parliamentary procedure and the legal system.

Comment author: beoShaffer 22 July 2012 06:11:27AM 1 point [-]

The Athenians tried something like that. I don't know enough about ancient greek history to say how effective it was.

Comment author: TimS 22 July 2012 12:51:36PM 3 points [-]

They randomly selected from citizens, but not everyone in the city was a citizen. The qualifications for citizenship (essentially wealthy landowner) made it relatively likely that random citizens would have the skill to legislate.

Comment author: Strange7 25 July 2012 04:12:11PM 0 points [-]

Might be sensible to gather up more than strictly needed and then have some further filtering criteria, as with jury duty.

Comment author: Solvent 23 July 2012 07:11:16AM 2 points [-]

Do these systems avoid the strategic voting that plagues American elections? No. For example, both Single Transferable Vote and Condorcet voting sometimes provide incentives to rank a candidate with a greater chance of winning higher than a candidate you prefer - that is, the same "vote Gore instead of Nader" dilemma you get in traditional first-past-the-post.

In the case of the Single Transferable Vote, this is simply wrong. If my preferences are Nader > Gore > Bush, I should vote that way. If neither Bush nor Gore have a majority, and Nader has the least number of first preferences, my vote contributes towards Gore's total. In no way does voting Gore > Nader > Bush instead help Gore (in the case where Nader obviously has a small number of votes), but it does make it less likely that Nader will get elected, which I presumably don't want.

The link describes how if your preferences are A > B > C > D, it is sometimes best to vote C > A > B > D because this will help get A elected, which is different to voting Gore ahead of Nader to get Gore elected.

Comment author: prase 23 July 2012 10:17:56AM *  6 points [-]

What about this situation: You and your friend are the last people to vote (having the same preferences for Nader over Gore over Bush) while the standings are:

  • 1,000,001 votes Gore first, Bush second
  • 1,000,002 votes Bush first, Nader second
  • 1,000,003 votes Nader first, Gore Second

Giving your two votes to Nader first + Gore second would mean that Gore is eliminated and his votes now support Bush, which gets Bush elected. If you instead vote Gore first and Nader second, Bush is eliminated and his votes are transferred to Nader who gets elected, which is much better outcome regarding your preferences.

Comment author: Solvent 23 July 2012 10:39:10AM 1 point [-]

You're right. My mistake. The standard "that doesn't really apply for real world situations" argument of course applies, with the circular preferences and so on.

Comment author: prase 23 July 2012 11:34:44AM 3 points [-]

The standard "that doesn't really apply for real world situations" argument of course applies

I am not sure. Quite a realistic, although a bit different situation may be this: There are three candidates - White, Gray and Black. White and Black are opposed to each other while Gray is somewhere inbetween. Thus the preferences of White supporters are W > G > B and the preferences of Black supporters are B > G > W. The Grays are split equally between G > B > W and G > W > B.

Now suppose that the distribution of supporters is 40 for White and 30 - 30 Gray and Black. You are a White supporter. If you vote according to you real preferences, i.e. first W, second G, you make it likely that Gray makes it to the second round where he wins due to the transferred Black votes. So you should instead vote tactically first B, second W, which would help Black into the second round where he will be eliminated by White who has stronger overall support.

Comment author: Strange7 25 July 2012 04:05:58PM 2 points [-]

That's not a safe strategy with less than perfect information. If as few as 5 of those gray-supporters vote black secondary when you thought they'd vote white, you've just handed the election to your worst enemy, when by voting honestly you could have had the moderate, agreeable-to-all candidate.

As a wider assortment of fringe parties become involved, perhaps emboldened by their nonnegligible first-round numbers, that sort of strategy becomes more sensitive to secondary (and tertiary, etc.) preferences. As part of that same increasing complexity, secondary preferences become more difficult to meaningfully survey in advance.

Comment author: prase 25 July 2012 06:55:58PM 2 points [-]

Sure, but you can be nearly indifferent between Gray and Black, or simply take the risk.

Comment author: [deleted] 20 July 2012 09:00:10AM 2 points [-]

You confuse AV ('Instant Runoff') with STV (AV in multi-member constituencies). The incentives for STV and AV are very different.

"The Liberal Democrats, who were perpetually stuck in the same third-place situation as Nader in the States, supported a change to a form of instant runoff voting which would have made voting Lib Dem a much more palatable option; the two major parties opposed it probably for exactly that reason."

Actually, most studies showed that if anything the support for the Lib Dems would drop slightly rather than rise under AV (the system that was voted on, which is different from STV, which is the system that the Lib Dems actually support), because there'd be less tactical voting. While electoral reform is tempting for the Lib Dems in part because the current system is biased against them and any other small parties, there's also the fact that a lot of people joined the Lib Dems because they are the only major party supporting electoral reform -- for a lot of Lib Dems getting the party into government is at least in part a means to the end of getting the electoral system changed, rather than changing the electoral system being a means to the end of getting the party into government.

Comment author: Salemicus 20 July 2012 01:59:21PM 2 points [-]

I wish this post would have more gone into the issues of what you are voting for, and how the appropriateness of the voting system depends on that. Counting the votes is not an end in itself, but a reflection of actual decisions to be made, often including further votes.

For example a British MP does not have authority in his own right; he only exercises power through his vote in Parliament. Few would argue that choosing ones own MP is an end in itself; the important thing is that the voter should be able to influence the decisions of the government as a whole. Indeed, it seems quite wrong to suggest, in the context of Parliamentary elections, that a "fair" voting system is the one that minimises tactical voting, as that will merely mean that the "tactical voting" will go on in Parliament itself, in terms of building coalitions of parties rather than coalitions of voters.

Electoral design needs to be looked at in terms of the whole system, not merely candidate selection.

Comment author: matabele 23 July 2012 03:37:48PM *  1 point [-]

It would appear that many of these problems would be circumnavigated, if voters were permitted to save their votes. In the case that none of the candidates were to my liking, I could then save up my vote for any forthcoming election. When, after a 50 years of waiting, I am finally offered a candidate of my liking, I may then have an opportunity to spend all 50 of my votes at once (great for minorities who are never offered a meaningful choice.)

A system based upon non expiring votes would likely be sufficiently unpredictable to discourage strategic voting (manipulation), as the total number of votes cast in any one election is variable. This could be extended to different types of election; perhaps, an initial equal allocation of 10 votes per year each, to be cast on any election of my choice, whenever I choose. I might just get to spend all of my 500 votes, saved up from 50 years of not voting for local and regional representatives, on a referendum to make one meaningful change to the system itself.

Sorry, this is a hobby horse of mine: the goods market offers bountiful choice, but unfairly allocates the number of spendable votes; the political market fairly allocates the number of votes, but never offers any choice of when and what these may be spent on. Does not appear that either system is democratic in any meaningful sense.

Comment author: Eugene 30 July 2012 03:00:24AM 0 points [-]

One problem with this system is that it can violate the "non-dictatorship" criteria for fairness, since a single voter (or small group of allied voters) could strategically withhold votes during potential landslide elections and spend them during close elections. With the right maneuvering among a well-organized block of voters, I could imagine a situation where the system becomes a perpetual minority rule.

Comment author: matabele 30 July 2012 12:28:36PM -2 points [-]

Votes can not be counted more than once, and every vote counts (according to the voter.) As all voters have an equal opportunity to withhold or spend votes - how can this be unfair?

In current systems, a minority voter may never be offered a candidate worth a vote - all such votes don't count (according to the voter.) This is clearly unfair, and has only an appearance of proportional representation.

With the right maneuvering among a well-organized block of voters, I could imagine a situation where the system becomes a perpetual minority rule.

And this does not happen now?

This is likely the reason for low turn outs in many elections - the voters simply do not care.

Comment author: Eugene 17 August 2012 03:41:17AM *  1 point [-]

That's just the problem. It does happen now, in a system where everyone is throttled at only one vote to spend per election. In a system where you can withhold that vote till another election, increasing the power of your vote over time, it only exacerbates this behavior.

Is the better fairness on a micro level worth the trade-off of lesser fairness on a macro level?

Comment author: Strange7 25 July 2012 03:35:07PM 0 points [-]

Downside is there would be a lot more bookkeeping involved, and a powerful incentive to compromise the secret ballot. Someone with a lot of "none of the above" votes saved up is obviously not a fan of the current government, and willing to stockpile resources toward an attempt to overthrow it, but has no actual elected representatives in that government. If some legislator proposed a program to monitor potential domestic terrorists with a level of scrutiny proportional to the cube of the suspect's reserved votes, who would oppose that program?

Comment author: matabele 27 July 2012 03:05:14PM 2 points [-]

There are numerous systems of verifiable secret ballot, for example this one.

Why should those whom are not 'fans' of any current member of the ruling regime, never be offered a meaningful vote? That is the point of non expiring votes, that minorities will have representation at least some of the time. The fundamental test of any democracy, is whether the incumbent regime can be peacefully overthrown.

Comment author: MileyCyrus 20 July 2012 03:37:38AM 1 point [-]

You can solve the domination problem by just picking a vote at random, and having that vote be the deciding vote. So if 49% of people vote for Bush, and 49% vote for Gore, and 2% vote for Nader, then Bush, Gore and Nader have a 49, 49 and 2% chance of winning respectively. In this system, you can always vote for your favorite candidate without worrying about how electable they are.

Comment author: Alicorn 20 July 2012 03:50:12AM 10 points [-]

(one example of an unreasonable system that eliminates tactical voting is picking one ballot at random and determining the results based solely on its preferences; the precise text of the theorem rules out “nondeterministic or dictatorial” methods).

Comment author: MileyCyrus 20 July 2012 08:08:19AM 3 points [-]

That's what happens when you skim articles before work :P

Comment author: [deleted] 24 July 2012 05:14:26PM 2 points [-]

This. I used to be a prolific lesswrong contributor on another account until I realized that everything I wrote felt insufficiently edited and researched and I devolved into lurkerhood. It would be much easier posting here if I had not someone recieved the impression this was actually a high status site.

Comment author: jimrandomh 20 July 2012 01:09:48AM 1 point [-]

I'm a big fan of approval voting, because while it does have strategic voting concerns, the way they work is intuitive. Instant-runoff's occasional non-monotonic results seem like inviting a scandal, and Condorcet seems too opaque and to ask for too many decisions.

Comment author: Luke_A_Somers 20 July 2012 01:17:51PM 2 points [-]

What do you mean by 'too many decisions'?

Comment author: jimrandomh 20 July 2012 06:08:52PM 2 points [-]

I just mean that picking an ordering over options is harder than picking a preferred subset of those options, since there are n! choices rather than 2^n choices, and the simple criteria voters tend to come up with ("any candidate who supports policy X") tend to be boolean classifiers.

Comment author: wedrifid 23 July 2012 07:52:40AM 2 points [-]

I just mean that picking an ordering over options is harder than picking a preferred subset of those options

The reverse is true. Picking a subset is hard. For each of the candidates you have to consider whether the less preferred option that you predict has more potential is worth selecting despite the fact that it reduces the chances of your most preferred options. The same difficulty as with picking a single vote for a preferred candidate except multiplied and with much more challenge in second guessing the rest of the voters. Picking rankings completely removes that problem. Then, for any pairing that you don't have a clear preference ordering for you can put down randomly or arbitrarily and lose nothing.

Comment author: prase 23 July 2012 10:35:38AM *  2 points [-]

If you account for the difficulty of picking candidates only, then yes. Practically the difficulty of navigating and filling the ballot should be considered too. People would quickly become angry when confronted with a task to check half of the 870 checkboxes printed on a ballot when choosing among 30 candidates/parties in an election. Even if it weren't mandatory to decide on all pairs, merely finding all of the 29 pairs your favourite takes part in would be a frustrating task for most citizens.

Comment author: Luke_A_Somers 22 July 2012 03:21:12PM 0 points [-]

In many Condorcet systems, you don't need to provide a total ordering - you can have ties. In those systems and IRV, you can use a truncated ballot - any name not on the list is ranked at the bottom.

I don't have anything against Approval - I think it's a fine system, and easier to build hardware for - but I don't think ranking systems are all that problematic.

Comment author: sketerpot 23 July 2012 05:21:49AM *  7 points [-]

I think you underestimate how difficult it is to create a voting system that won't utterly baffle a large portion of the electorate. People in general aren't good about reading instructions, and they often get confused about the simplest of things. While I like both Condorcet and approval voting, I prefer approval voting for being stupidly simple. "Vote for the people you think would do a good job; the person with the most votes wins," is a very easy thing to understand, so most people will probably get it.

(Think I'm being too cynical? Try writing non-trivial instructions aimed at ordinary people. You'll see.)

Comment author: Strange7 25 July 2012 04:36:42PM 1 point [-]

What about a bubble-fill, with multiple bubbles per candidate? Instructions, beyond the standard how-to-darken-a-bubble stuff, amount to "fill in more bubbles for the candidate(s) you really like, fewer bubbles for the candidate(s) you don't like so much, and no bubbles for the candidate(s) you don't like at all." Maybe some examples. Vote-reader filters out the noise of exactly which bubbles were filled, then normalizes each ballot into a preference ranking, plus some implied trivia about preference strength.

Comment author: Jost 22 July 2012 09:54:32PM 1 point [-]

Another example for the influence of voting systems:

In Germany, the voting system was recently changed due to some very problematic edge cases. While the new voting system has its own problems (of a similar severity), a newspaper used the opportunity to compare the distribution of seats in parliament among the political parties according to the 2009 election (under the old voting system) with the distributions that would have resulted from the same voting behavior under many different voting systems.

The results of this comparison can be found here. (Use the buttons saying “Niederlande”, “Türkei”, … to switch between different voting systems. The picture on the left is the actual distribution of the seats.) This is a nice illustration of how strongly a voting system changes the result, even without the influence of strategic votes. (For example, the conservative party (in black) would receive between 34 and 73 per cent of the vote.)

(And for any German-speaking folks who are interested, here's a description of the different voting systems in that comparison.)

Comment author: enoonsti 29 July 2012 07:54:57AM *  0 points [-]

Here is a 30-minute Great Course starring Professor Scott P. Stevens: The science of election methods

tldw: at 28:53, he recommends Range Voting.

Comment author: TraderJoe 20 July 2012 06:40:43AM *  0 points [-]

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Comment author: [deleted] 20 July 2012 09:03:58AM 0 points [-]

Also,. I was one of the most active pro-AV campaigners in that referendum, and it seemed to me that a large number of people made their decisions based on political grounds rather than on what they thought of the system -- the single question I got asked the most by people when campaigning was "Will it make it more easy for X to get in?"

But it certainly wasn't a case of just Lib Dems and no-one else supporting AV -- AV got 33% in the referendum while the Lib Dems only got 17% on the same day's council elections (and indeed while campaigning I met quite a few Lib Dem voters who were going to vote against AV).

Comment author: TraderJoe 20 July 2012 11:37:31AM *  1 point [-]

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Comment author: [deleted] 20 July 2012 01:42:02PM 3 points [-]

No, you didn't -- I was just saying that while a majority, probably nearly everyone, did vote on similar lines to what you talked about ("how does it affect the party I support?"), not everyone did -- even assuming that everyone in the 28% of people who didn't vote for one of the two biggest parties followed their party's line and supported AV in the referendum (and of course not all those parties did support it), that still leaves 5% of people who voted either Tory or Labour but still voted yes in the referendum.

Which is a rather comforting thought, as it suggests that at an absolute minimum 5% of voters can be trusted to make their minds up on an issue independently of what the party they support thinks of it. Probably more than that.

Comment author: roystgnr 25 July 2012 01:33:32AM 1 point [-]

look at the rationality of voting and observe that a forced voting system like Australia's increases the power of rationalists?

I just ran across an old interesting three part look at the rationality and psychology of voting.

Comment author: TraderJoe 27 July 2012 10:25:39AM *  1 point [-]

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Comment author: [deleted] 20 July 2012 08:53:45AM -1 points [-]

Given that the referendum wasn't on STV, but on AV, perhaps it's a good thing you didn't vote.

Comment author: TraderJoe 20 July 2012 11:38:58AM *  1 point [-]

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Comment author: [deleted] 20 July 2012 01:36:17PM 1 point [-]

The whole point of the distinction is that STV doesn't have a single winner. AV is used for elections with a single winner, STV for elections in multi-member constituencies. Because it's only used in single-member constituencies, AV can never be proportional, while STV in multi-member constituencies usually produces a roughly proportional outcome.

Comment author: TraderJoe 23 July 2012 08:18:35AM *  2 points [-]

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Comment author: [deleted] 23 July 2012 01:22:38PM 0 points [-]

The point is that the incentives for tactical voting linked to in the OP are not there for STV but are for AV, and that when you're talking about a Parliamentary election, electing 600 individuals by AV gives VASTLY different results to having 120 constituencies each elect five members by STV. You might as well say "I don't see a need for a separate name for subtraction -- it's just another name for addition to specify addition of negative numbers". When two processes have very different outcomes, even if the processes are similar, that's sufficient reason to distinguish them.

Comment author: TraderJoe 24 July 2012 08:40:39AM *  -1 points [-]

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Comment author: [deleted] 24 July 2012 11:16:00AM 0 points [-]

You are missing something. There is no such thing as STV 'under a single winner per constituency model'. STV is a system for deciding winners in multi-member constituencies.

There are two main axes for voting systems -- preferentiality and proportionality. STV is both preferential and proportional. AV is preferential but can't be proportional because it's for electing single members. First Past The Post is neither preferential nor proportional, and the bloody stupid d'Hondt system we use for European elections is proportional but not preferential.

This is not a matter of semantics. In AV you're voting for a single representative, in STV for multiple representatives. In AV if one candidate gets over 50% on first preferences that's the end, in STV preferences continue to count until all members have been elected. STV produces proportional results, AV exaggerates swings. They're similar in that the voter gets to rank candidates by order of preference, but the process of counting, and the results, will be wildly different.

Comment author: TraderJoe 24 July 2012 02:02:43PM *  -1 points [-]

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Comment author: [deleted] 24 July 2012 05:20:27PM 0 points [-]

That's neither STV nor AV, just some random mad system you've made up yourself where you've changed the rules half-way through!