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The Condorcet method of voting requires that each voter rank the candidates from best to worst. It's generally a good system, but has been criticised for being hard to understand (maybe not for those of us on /., but for the stupid voters). Another interesting voting method is range voting, which assigns a number value to each candidate based on that candidate's desirability.

Rated voting, which is a special case of range voting, was generally the best method (i.e., it maximised voter happiness) in a test of various voting systems. Also see ElectionMethods.org.

An improved voting system would certainly make lots of things better (though due to Arrow's paradox, a perfect system is impossible). I think we also need to improve the voters. The most heard criticism of Condorcet's method is that it's hard to understand, and it's really not all that complex at all.

Ya, I'd like to get my Graphical Voter Interface GVI into a distribution or two. I think it's pretty cool. Check it out.

I prefer Approval Voting. It has significant advantages over Plurality, IRV and (IMO) other ranking methods:

1. It's simple to explain
2. It's a strict superset of plurality, so anyone who votes the old way will still be valid
3. It's supported by voting machines designed for plurality
4. There are no paradoxes, and no situations where voting against your favorite candidate is a good strategy
5. It encourages consensus rather than polarization

Check out ElectionMethods.org. (Is it down for anyone else right now?)

All kinds of great info on the types of voting methods and which is best.

Search for condorcet. He's right, none are perfect, but some are less un-perfect than others.

Don't believe the hype about IRV, in a lot of ways it worse than plurality voting. The only reason I don't jump up and down about: these people are pushing for ranked ballots, which is required for Condorcet.

Yes, Approval Voting is the next step in democracy.

See ElectionMethods.org.

I'm an optimistic realist. In reality it might never happen, but I have to keep hoping and trying. :)

Eliminating commercials during the news might be a good idea, but I doubt that would help much either. I get very little of my news from the mainstream outlets anymore. With the internet, there's little need to. Most of the media is biased, and I don't care for its agenda.

Approval voting is too easy to rig. Honest conservatives (for example) might vote for Republicans and some other right-leaning parties, but you'll always have the die-hard partisans that won't "approve" anyone but their own party - Republican in this case. Result: the dominant Duopoly will retain their supremacy, but out of "brand loyalty" and ignorance, not because they actually deserve it. As long as it is possible to "lie" at the ballot box to gain an advantage, there are people that will do so. Condorcet's method is the only strategy-proof system I know of.

Condorcet is just as easy to vote as Approval, and is much more precise about who the winner is because preferences are expressed about who amongst the approved set is the best. Approval only tells you that those in the approved set beat those in the non-approved set. It doesn't tell you which of the approved candidates you really want. Some examples:

• It's possible, though improbable, that everybody would approve the same 3 of 8 candidates (for example), leaving the winner ambiguous. (I suppose it's technically possible for every voter to rank every candidate in a tie, so this would happen in Condorcet too. But the probability of absolutely zero preference in the electorate is, well, zero.)
• Similarly it's possible, though extremely improbable, for one voter to overturn the will of the people. Suppose that everybody's approved list contains A, the preferred candidate if we were using a ranking system, and B, the "merely acceptable" candidate (some other candidates may be approved by individual voters in this example, but everybody approves A and B) - except for one guy who approves only B. So this one voter tosses out the candidate that should clearly win, and 99.99999% of us are stuck with a guy who is merely "second best". Sure, 100% can tolerate him, but is that the best criterion for winning an election?

A good voting method shouldn't do these things. I'm sure there are web sites that can make a much better case for Condorcet than I can here, with better examples and more alternative systems to compare against.

Call me pessimistic, but I doubt this would help. I think the root problem is that too many Americans ARE actually afraid, paranoid, uninformed, and vindictive. Whether you represent them in large blocks or small blocks is not important - the percentages don't lie.

I think the only way to address this is to reduce the power of the mainstream media, while enhancing their independence. For example, if elected, I would propose eliminating advertising during the news hour, which would eliminate the incentive to dramatize the news to get better ratings and sell commercials. I would also introduce legislation aimed at preventing administration officials from giving reporters they don't like the cold shoulder (maybe by seating reporters randomly at press conferences and not pre-screening them).

One other thing we should do now: implement approval voting . This is a no-brainer, and will go a long way towards fixing the artificial advantage enjoyed by the two major parties.

I think you should strike the "closed-source" part. Even if you have the source, you cannot prove that this source corresponds to the binaries running on the machine.

Yes you can, but it's hard, and requires specialized hardware.

What is really needed is a system where everyone can prove that the system works. The easiest way to do that is manually counted paper ballots.

That's one option. Personally, I prefer the idea of easy-to-use touch-screen systems that print a paper ballot with both human-readable and machine-readable sections. The voter can verify the human-readable part before dropping it in the ballot box, and the machines can quickly and reliably total up all of the votes. In the case of a dispute, all of the ballots can be recounted by machine. In the case of a continued dispute, a statistical sample of the ballots can be checked to verify that the human and machine readable parts match. The ballots can also be made available for complete hand recounts if necessary.

Use of an OCR-able font could make it so the human and machine readable portions are one and the same, but in the absence of a very high level of confidence that slight tweaks to the letters couldn't convince a machine to read it one way while a human reads it another, I'd prefer to have two sections. With an OCR-able font it would be possible to automatically check all of the ballots to see if the sections agree (while still allowing for manual checks as a backstop).

All the people who vote for any of the losers in a US presidential election had their vote thrown away. With a proportional voting system, a small error is not so disastrous. Of course, you cannot elect a president with a proportional voting system.

No, but there are other methods you can use to elect a president and which do not just ignore the "losing" votes. The best of the bunch is Condorcet Voting. It's a little complicated, but understandable with a bit of effort, and allows you to vote your true preferences without worrying about throwing your vote away on a sure loser.

Plus, proportional voting sucks if you're interested in voting for the individual, rather than the party.

Well put. Before America gets significantly better, we need a better election method, otherwise we'll end up with the two-party bullshit we have now.

However, the grandparent post wasn't completely off. It advises voting in primaries; that is, you can vote for which Mr. Righty or Mr. Lefty will be in the final election. Maybe they're all corporate sellouts, but some to a lesser degree than others.

The difficulty is that those who voted for Nader gave Bush the 2000 election, by splitting the anti-Bush vote. If Nader had not run, it is likely that the majority of Nader voters would have voted for Gore, rather than Bush, handing Gore the election. Note that this is not the fault of those who voted for Nader, who, as ubikkibu notes, thought they were doing The Right Thing(tm) by voting for the candidate they preferred. Rather, the fault is due to the plurality voting system, in which to get a result most in accordance with his desires a voter is sometimes best served by voting for someone other than the candidate he prefers--in this case, "whatever half-assed corporate whore the Democrats put up," instead of Nader. In 2000, a vote for Nader was a vote for Bush, which was likely not the intent of the voter (again, as ubikkibu notes). (And it works both ways--in 1992 Perot probably took enough votes from Bush I for Clinton to win.)

Other voting systems exist that are much more fair to the wishes of the electorate; one that receives high marks in this regard is the Condorcet system, in which the voter states his preferences pairwise among the listed candidates. The drawback of this method is its complexity, which may be a problem in a country in which the "butterfly ballot" is beyond the capabilities of the voter.

If properly implemented, a combination of electronic and paper ballots can provide much better integrity than either mode can provide by itself. See Ensuring the Integrity of Electronic Voting

The main reason is, it's simple game theory that our current election system leads to two major parties. The only way for another party to get popular support is for it to supplant one of the current major parties, and we'll still have a two-party system. We need a better election method.

This could be accomplished by having representatives use an ordinal voting system such as Condorcet to vote on bills.

The bill with pork could be on the ballot right next to the bill without pork, and representatives would be able to pass the bill whether or not they felt the pork was worthwhile.

This would obviously require a constitutional amendment.

I think the main reason we're in this mess is because we have such a flawed voting system, one that essentially forces you to vote for whichever of the two major parties you hate less. We need a better election method.

You want to go back to the days when the State Legislatures rubber stamped the majority party's choice for Senator,

That's why we need voting method reform, so that there is no such thing as a "majority party" and this problem simply goes away. The 17th Amendment was passed as a way to combat a procedural issue (difficulties in filling vacant seats), but instead it drastically changed one of the fundamental power balance triangles of government.

It also increased the amount of money in politics, as senate candidates had to campaign across a whole state rather than just amongst the state legislature. The primary rationale for the supposed "campaign finance reform" was that there is "too much money" in politics. Well, limit senators to campaigning a smaller group then, don't limit every citizen's ability to participate financially!

It also makes senators less responsive to their home states - do you really think California's senators feel more accountable to 50 million individuals than they would to a couple hundred (or whatever the number is) in it's legislature? The citizenry is better served by indirect senatorial elections than direct. A senator doesn't care about you, other than that it is easy to sway the emotions of a herd (which includes you) to keep himself in power. If he had to campaign to a smaller group someone might *gasp* force him into an intelligent reasoned debate, he might have to take a position on issues, he might have to actually take a stand for principles.

Most people are uninformed on state level issues, but the 17th gave them power to elect a federal representative for six years! One of the reasons the House has short terms is so that if the general public's (relatively uninformed) choice for office doesn't work out, he's quickly removed. One of the reasons the Senate has long terms is because it was assumed that the states' legislatures would be composed of thoughtful cool-headed people that could make a more responsible choice. The system was supposed to protect us against ourselves.

and the people had little direct say in the process? I don't think you'll find a lot of people agreeing with you there.

People should not have that much (direct) say in selection of US senators. (See above.) The Senate represents the States, therefore the States - as the political entities they are - should select those senators. The power of the states was supposed to serve as a check against the power of the central government. Without any representation in the federal government, how are the states supposed to do that? Like you said, "It's really unfortunate, since many things are really best handled on a state-by-state basis," and I fully agree with that.

That also seriously hurts third party power.

Third parties currently have no power, so I don't see how this could hurt it. We need to implement Condorcet voting in as many elections as we can, so minority (ideology, not race!) viewpoints can be heard.

Unfortunately, I still feel obligated to cast my votes for the most freedom-oriented Republicans (or Democrats), until the Libertarian Party has a chance of winning, but how can you knock the party that advocates more FREEDOM?

You can't knock them - you join them. (Or if you happen to believe that rights derive from God and not from man, join the CP like I did.) Until you start voting for them, then of course they will never win. My question to you is will you stand up for what you believe in, even when the going is rough, or will you cave in to pressure?

The problem is that the voting system is rigged in favor of the two major parties. A simple plurality vote, with only one vote to express preference between candidates, will always lead to people sacrificing their principles in order to vote for the "lesser of two evils". That's why we need Condorcet voting, to restore liberty of conscience. (Ask yourself this: If you have to sacrifice your conscience in order to feel like you're having an impact on an election, is it truly a free country?) There's absolutely no reason that we cannot have a diverse range of viewpoints in a race together, instead of being stuck with two parties that squeeze to the center so tight that they're essentially the same with different rhetoric. The laws these guys make is going to govern our lives, you know - darn right I want some real debate and some real choice between candidates.

I've posted about this many times in the past, with more explanation than I have time for now. If you search Slashdot for my nick and "condorcet" or "voting" you should be able to find it. Condorcet's method trashes every other voting method I've heard of, including Instant Runoff Voting (also called Single Transferable Vote), Approval, Borda Count, and definitely Plurality.

Another problem is ballot access laws. Again, the major parties shape this to favor the status quo. Why is it so hard for challengers to get in the race? Obviously, the major parties don't want competition. If collecting a half million signatures is "good enough" for a minor party, why don't we require the same thing of a major party?

We just talked about this in history class! This was already tried in renaissance Italy. It does not work, because people are selfish. They will try to maximize their influence by not voting fairly.

Actually, the Condorcet method used by the Debian project is pretty much immune from manipulation, in contrast to our current system which *strongly* discourages people from voting "honestly" if their preferred candidate isn't one of tha major parties.

The Condorcet method is less than 100 years old, and the proofs the show exactly why it has the characteristics it does rely on some fairly modern mathemetics, so you can be certain it wasn't tried in the 15th century.

For example, someone who supports Bush would be best off putting Bush first and Gore last even if Gore is their second choice. By putting Gore last, they help Bush by giving the expected second place candidate less votes.

Pairwise evaluation makes all of that irrelevant, because the absolute positions you choose in the ranking list have no effect: what matters is the *relative* order. So if Bush is higher than Gore on the ballot, that ballot ranks Bush over Gore, regardless of whether they're one step apart or 10.

For more information about Condorcet and other methods, look here.

No, Debian uses Condorcet voting.

The ordinal ballot, however, is identical to IRV.

TCL is a command language for TK. For that purpose it is excellent, but for general scripting it is awkward at best. If you have a GUI intensive application to write, use TCL/TK, otherwise use another language, such as Python.

By the way, check out GVI, the Graphical Voter Interface, which I wrote in TCL/TK.

Because the most states have a "winner take all" system, any candidate that doesn't have enormous numbers of backers to begin with isn't going to win anyways.

"Winner takes all" only applies in presidential elections. There are a number of other problems which apply in all elections. The plurality voting system is chief among them.

So, if no candidate gets a majority, you have a run-off among the top contenders.

Bad idea. Learn about the problem with Instant Runoff Voting. The same problem applies in any runoff, instant or not. Sometimes the best "compromise" candidate may get eliminated first, and you're stuck voting between two bad choices - exactly what we have now. Yes, plurality voting is bad, but IRV isn't really any better (even though it seems to be). The system you want is Condorcet voting. Same ranking method, but you consider all preferences simultaneously rather than sequentially.

Now that I think about it, getting rid of the electoral college would have the same effect as insisting on proportional represntation of electoral college seats.

Not really. True proportional representation by popular vote forgets that the states, as political entities, should be represented in the federal government too. (That's what federal government means, the federation of individual states.) In Congress we have one house that represents the states (at least we did until that lousy 17th Amendment) and one that represents the people. The EC is an attempt to unify the interests of the states and the people when voting for a singular office (president). That's why the number of EC votes a state has is the total number of Senators and Representatives from that state.

I do agree that "winner takes all" is a broken system. The legislators that put it in place were very short-sighted - in giving more power to "their state's party" in presidential elections, they didn't think that the balance of power in their state might swing another way in the future and end up hurting "their party". NE and ME allocate their EC votes (less two) proportionally by congressional district to the plurality winner of that district. That's a good attempt at compromise. I think it would be better if we used Condorcet, better still if the last two EC votes were decided in the state legislature (if they are supposed to represent the state's interest) and we scrapped the 17th Am. while we're at it. Remember, these issues are decided by your state legislators, not DC. This gives you much greater ability to make a change to the system. It's closer to you, and hence more responsive.

I've also heard people say that we don't have enough representatives in Congress. With only 435, each has far too many constituents to respond to. The Constitution originally called for a 1:30k ratio. Maybe several thousand would be a tad excessive, but with modern technology I don't see why the number couldn't be increased without hampering the ability to debate. This means you'd have more chance of your view being represented in Congress, and combined with the idea of allocating EC votes by CD, a better chance of picking the president too.

Because the most states have a "winner take all" system, any candidate that doesn't have enormous numbers of backers to begin with isn't going to win anyways.

"Winner takes all" only applies in presidential elections. There are a number of other problems which apply in all elections. The plurality voting system is chief among them.

So, if no candidate gets a majority, you have a run-off among the top contenders.

Bad idea. Learn about the problem with Instant Runoff Voting. The same problem applies in any runoff, instant or not. Sometimes the best "compromise" candidate may get eliminated first, and you're stuck voting between two bad choices - exactly what we have now. Yes, plurality voting is bad, but IRV isn't really any better (even though it seems to be). The system you want is Condorcet voting. Same ranking method, but you consider all preferences simultaneously rather than sequentially.

Now that I think about it, getting rid of the electoral college would have the same effect as insisting on proportional represntation of electoral college seats.

Not really. True proportional representation by popular vote forgets that the states, as political entities, should be represented in the federal government too. (That's what federal government means, the federation of individual states.) In Congress we have one house that represents the states (at least we did until that lousy 17th Amendment) and one that represents the people. The EC is an attempt to unify the interests of the states and the people when voting for a singular office (president). That's why the number of EC votes a state has is the total number of Senators and Representatives from that state.

I do agree that "winner takes all" is a broken system. The legislators that put it in place were very short-sighted - in giving more power to "their state's party" in presidential elections, they didn't think that the balance of power in their state might swing another way in the future and end up hurting "their party". NE and ME allocate their EC votes (less two) proportionally by congressional district to the plurality winner of that district. That's a good attempt at compromise. I think it would be better if we used Condorcet, better still if the last two EC votes were decided in the state legislature (if they are supposed to represent the state's interest) and we scrapped the 17th Am. while we're at it. Remember, these issues are decided by your state legislators, not DC. This gives you much greater ability to make a change to the system. It's closer to you, and hence more responsive.

I've also heard people say that we don't have enough representatives in Congress. With only 435, each has far too many constituents to respond to. The Constitution originally called for a 1:30k ratio. Maybe several thousand would be a tad excessive, but with modern technology I don't see why the number couldn't be increased without hampering the ability to debate. This means you'd have more chance of your view being represented in Congress, and combined with the idea of allocating EC votes by CD, a better chance of picking the president too.

Two choices isn't a choice, it's a coin flip and a mockery of representative republican values. Both parties have tried for years to convince the public that having 10-190 people officially registered on the ballot is irresponsible because it creates chaos somehow. Having two people on the ballot is akin to having only one choice in most races.

I couldn't agree more. And as a member of an American third party, one of the issues I promote is voting reform. (Not campaign finance reform, which just restricts your ability to participate financially in the political process.) We need Condorcet voting or some other method that allows to express a preference between more than only two candidates.

Look at it this way. The ideal political system runs on a foundation of honesty and truth. If the voting system compels you to sacrifice your conscience and vote for the "lesser of two evils" then your choice in the ballot box is a lie. Our system is rotten at its core. If we lie when we put officials into office, how can we expect the system to work truthfully and honestly? If you vote for a third party, any third party, I applaud you for standing true to your beliefs. To the rest of you: stop compromising what you believe in. Do the right thing, investigate all the parties and candidates in the race, and vote for the one you agree with the most even if "popular wisdom" says "he can't win". Even better, get off your butt and get involved in a party. Stop complaining and get involved.

Remember, having two parties on the ballot is only one more than they had in Soviet Russia. As ShatteredDream said, that's not a choice at all.

• Approval voting, where you cast one vote for every candidate you approve of, and the results are added up;
• The Borda count, where you rank the candidates in order of preference;
• The Condorcet method, similar to Borda but the results are counted differently.

Plurality voting is the source of most of the election problems we have in the US. We don't need "campaign finance" reform, we need voting method reform! The problem isn't that Democrats and/or Republicans spend a lot of money, the problem is that we can't effectively vote against both of them!

Glad to see someone else posting useful Condorcet links. Condorcet is so superior to other methods, and IRV so flawed, I'm surprised that IRV is still mentioned as a possible replacement for plurality.

ElectionMethods.org

Instant Runoff Voting Problems

IRV is great for letting you cast "protest" votes for unpopular parties, but once a third party becomes popular you end up with the same strategic voting problems that plurality voting has. Don't get me wrong, sticking with plurality is insane, but IRV would be a placebo; we need approval or Condorcet voting instead.

One last thing... ask a local Green what IRV is.

Condorcet, Condorcet, Condorcet! I can't say this enough. IRV has so many pitfalls that I can't believe anyone seriously recommends it as an alternative. Its faults in the vote-counting method so overwhelm the improvements in its vote-casting method as to make any benefit in using IRV completely illusory. Condorcet uses the same vote-casting method, but the vote-counting method actually does what IRV purports to do.

One last thing... ask a local Green what IRV is.

Condorcet, Condorcet, Condorcet! I can't say this enough. IRV has so many pitfalls that I can't believe anyone seriously recommends it as an alternative. Its faults in the vote-counting method so overwhelm the improvements in its vote-casting method as to make any benefit in using IRV completely illusory. Condorcet uses the same vote-casting method, but the vote-counting method actually does what IRV purports to do.

Check out GVI, the Graphical Voter Interface, which I wrote in Tcl/Tk. I think it's pretty cool.

I therefore have no reason to believe that either major party has any intention of reforming the Code, and the only way I can see the Code being changed is for third parties to gain enough votes to be a threat to the majors.

As I'll keep saying until it happens, the better alternative is to enact Condorcet voting. It is not enough for third parties to act merely as "spoilers". If you think about it, a single vote can represent your true preference between, at most, two people. As soon as you introduce a third option, there's an amibuity: are you really for the person you vote for, are are you against his most popular opponent? We need a system that allows you to express preferences between candidates in this way, one that eliminates incentives for "strategic" voting.

That's Condorcet. Conceptually it is only slightly more difficult than single-vote plurality vote (current US system). Think of it this way: in a multi-way race, the "true winner" is the one that would win all (or at least a majority) of head-to-head races against all contenders. A single vote can determine only one head-to-head race - Condorcet provides a ranking method that allows all head-to-head winners to be determined simultaneously. Do not confuse this with an iterative approach to counting such as IRV. The iterative approach is flawed because it eliminates candidates before they've had a chance to be paired off with all other contenders. It is trivial to demonstrate this once you understand how the vote counting for both methods works.

Write your legislators. Write your editors. Explain to your neighbors and friends. Better yet, run for office. Imagine running on a platform that says, "I intend to make it easier for you to vote me - and other politicians - out of office if you don't like what we do".

I therefore have no reason to believe that either major party has any intention of reforming the Code, and the only way I can see the Code being changed is for third parties to gain enough votes to be a threat to the majors.

As I'll keep saying until it happens, the better alternative is to enact Condorcet voting. It is not enough for third parties to act merely as "spoilers". If you think about it, a single vote can represent your true preference between, at most, two people. As soon as you introduce a third option, there's an amibuity: are you really for the person you vote for, are are you against his most popular opponent? We need a system that allows you to express preferences between candidates in this way, one that eliminates incentives for "strategic" voting.

That's Condorcet. Conceptually it is only slightly more difficult than single-vote plurality vote (current US system). Think of it this way: in a multi-way race, the "true winner" is the one that would win all (or at least a majority) of head-to-head races against all contenders. A single vote can determine only one head-to-head race - Condorcet provides a ranking method that allows all head-to-head winners to be determined simultaneously. Do not confuse this with an iterative approach to counting such as IRV. The iterative approach is flawed because it eliminates candidates before they've had a chance to be paired off with all other contenders. It is trivial to demonstrate this once you understand how the vote counting for both methods works.

Write your legislators. Write your editors. Explain to your neighbors and friends. Better yet, run for office. Imagine running on a platform that says, "I intend to make it easier for you to vote me - and other politicians - out of office if you don't like what we do".

It's also the corporations' fault. Every time they try to levy a standard tax the lobbyists come out and beg, wheedle, and bribe to get loopholes in the law. They should just set a standard import/ export tax, no exceptions.

True, that's what they (corps) do. But it's our fault for voting such pushovers into office. Elect some people that stand for principle over politics and you'll get fair across-the-board standards.

As long as the 16th Amendment allows the gov't to squeeze "the rich" for whatever they want to give it to "the poor", they can continue to buy their votes in November. As long as they have the power of office, they will continue to get money from corps for these special favors. And as long as the 17th Amendment removes State gov'ts from having any balancing influence at the federal level, nothing will change. Money and power are powerful and perverse incentives.

However, the solution isn't "campaign finance reform" or "term limits". Some of the most expensive races are US Senate, which removing the 17th Amendment would solve. Besides, we ought to be able to spend our money how we please. There's been more money in politics now since the "reforms" of the 70's than before. And we already have term limits - you get to "vote the bums out" every November. What we need is voting method reform so that we have a real choice, so that non-Dem/Rep votes make a difference.

Instant runoff voting is definitely the wrong way to go if you want to reform the voting system. I won't go into depth on it here but its flaws, and the virtues of alternatives such as approval and Condorcet voting systems, are discussed on this site.

I'm not sure there's a difference...it all depends on your definition of "difficult" vs. "expensive". More below...

> I have no clue about how to [motivate and educate the public], but simply forcing the parties to find new ways to get money isn't going to do much.

I totally agree. My preference would be to have more robust competition so that the "market forces" created by the quest for votes trump the market forces created by the quest for dollars. If we create genuine opportunites for third, fourth, and fifth parties to compete against the big two, they all would need to be more careful about where they accept money from or lose votes to a more cleanly-financed party in the same approximate position in the political spectrum. In a robust multi-party system, we could probably loosen up on traditional "campaign finance reform" laws, because the incentives built into the system would keep it honest enough. Note that I'm not arguing for traditional multi-party parliamentary systems, but a new style of multi-party system as described here.

Approval voting is both simpler and mathematically superior to Instant Runoff Voting (though not as good as Condorcet).

IRV has serious problems. IMHO it is worse, not better, than the existing system of plurality voting. Read this and this.

For those not farmiliar with it, the Condorcet method works roughly like this. Voters rank each candidate. If one candidate wins a majority of the vote in every head-to-head pairing they belong to, they win (i.e. A is ahead of B in 65% of ballots, ahead of C in 90% of ballots, and ahead of D in 51% of ballots). If no candidate win every head to head matchup, there are a couple of methods for deciding the winner that give roughly equal results. Basically the winner is the candidate who wins the most head-to-head matchups between candidates that win at least one head-to-head matchup. A complete description of the Condorcet method along with comparisions to other methods can be found at electionmethods.org.

The only real drawback to the Condorcet system is its complexity, both in that voters must rank every candidate and that the methods used to determine the winner in close races is difficult to understand. Personally I like methods that require voters to understand all of the candidates, so I do not think the ranking process is a drawback.

I also thought that the article failed to mention a serious fault with the Borda count. By allowing the candidate rankings to count as points rather than as head-to-head matchups, voters are encouraged to place viable second best choices last to improve the standing of the first place candidate. In the Condorcet system there is no advantage to this, ranking candidate B second or tenth makes no difference if the race comes down to A vs. B if A is ranked first on your ballot, A wins the head-to head matchup the same either way. In this manner the Condorcet method is the only method I know of that truly makes the voter vote their conscience, rather than voting strategically to elect the lesser of evils (e.g. voting for Gore when you really like Nader but really hate Bush). Instant runoff has the right idea in this sense but is fundamentally flawed, as the article states due to an increase in support for a candidate possibly causing that candidate to lose.

and overplayed what is arguably the worst -- instant runoff voting (IRV), which not only has the ability to lead to more counterintuitive situations than plurality voting, but also becomes very complex to manage for large elections, because ballots are not "summable". You can't add up all the votes from one voting precinct and send a total on to the next tier up (ultimately you do want to collect all of the physical ballots together, but summability allows decentralized counting for faster results).

But the article completely ignored the Condorcet voting method, which is pretty universally considered to be the best system from a technical point of view. Like IRV and Borda, Condorcet voting asks voters to rank their choices, which is very important because it allows a voter's entire set of preferences to be applied, but unlike them it has far better mathematical properties (mainly because it "discards" almost *no* information from the ballots); is much more "stable" in the sense that changes to votes don't do counterintuitive things; manages to satisfy a slightly relaxed version of Arrow's criteria, which no other voting system can do; and is "summable".

In fact, it's quite arguable that Arrow's criteria were overstated and that the slight weakening of one of his axioms is correct, even though it destroys his proof. Thus it's possible there *is* a perfect voting system, and, arguably Condorcet is it.

Condorcet's clever idea was "pairwise" evaluation. When you only have two candidates, simple majority is a perfect system, so Condorcet applied majority voting to multiple candidates by just taking them two at a time. Since each voter ranks all of the candidates(*), each ballot expresses a choice about any pair of candidates, and you can easily tally up the public's actual preference between that pair.

If one of the candidates is preferred over each of his opponents, then that candidate is the winner, which is very logical if you think about it. It's easy to show that this will happen most of the time, the only time it won't happen is in a three or more-way race where the candidates are all fairly close and where the electorate is seriously divided. What happens is you get a "cycle".

For example, suppose you have three candidates, A, B and C and suppose a majority of the voters ranked A over B, a majority ranked B over C and a majority ranked C over A. Mathematicians have devised some moderately complex but very accurate ways of resolving such issues, basically by looking at how badly the candidates were beaten in their losses. The result is a very stable, very predictable system that accurately reflects the electorate's will and pretty much completely eliminates any possibility of successfully "gaming" the system by casting an insincere vote.

If you'd like to read more about Condorcet and a technical evaluation of the various methods, look here. If you'd like to play with it a bit, I have a Java implementation that you can find here. It's very rough, since I just hacked it together a couple of days ago to evaluate votes for a new name for a SCUBA diving club I'm involved in, but it works pretty well. Just make a file called "rawballots.txt" that contains one ballot per line, with the candidates listed in order, separated by commas (there's a sample on the web site), place the file in the same directory as Condorcet.java, and compile and run (javac Condorcet.java; java Condorcet). My code also abuses the Condorcet system a little by trying to construct a complete ranking of all candidates rather than just finding the winner (it does this by finding a winner, then adjusting the defeats matrix to make him a loser, then finding another winner, until all candidates have "won").

(*)It actually isn't necessary for every voter to rank every candidate. Essentially, any candidates a voter chooses to leave off the ballot are considered as ranked equally and below all of the candidates that were listed. For example, if there are candidates A through E, and I cast a ballot like:

A,B,C

That means I prefer A over everyone, B over C-E, C over D and E and I don't have a preference between D and E.

Actually, although it would probably make voting interfaces to complicated, the method even allows me to express the fact that I don't have a preference between higher-ranked candidates. Something like:

A, (B|C), D

Would mean I like A over everyone, prefer either B or C over D or E, and prefer D over E.

When we're figuring out who won in the pairwise election between B and C, this ballot is a "tie" and effectively doesn't give a vote to either. When counting up the election between B or D and any of the other candidates, however, this ballot expresses a preference.

Here's a fun example from John Allen Paulos' excellent book A Mathematician Reads the Newspaper:

55 voters are voting in a primary between 5 candidates.

18 of them prefer Tsongas to Kerrey to Clinton to Harkin to Brown
12 of them prefer Clinton to Harkin to Kerrey to Brown to Tsongas
10 of them prefer Brown to Clinton to Harkin to Kerrey to Tsongas
9 of them prefer Kerrey to Brown to Harkin to Clinton to Tsongas
4 of them prefer Harkin to Clinton to Kerrey to Brown to Tsongas
2 of them prefer Harkin to Brown to Kerrey to Clinton to Tsongas

Who should win?

Under our current plurality, "winner-take-all" system, Tsongas would win because he had the most first place votes.

If a single runoff election was held between the top two candidates, Clinton would win the runoff by a landslide.

If instant runoff was used, dropping the candidates from the running one at a time depending on who had the fewest first place votes, then Brown would end up winning.

If a Borda count was used, giving each candidate 5 points for a 1st place vote, 4 points for 2nd place, etc., then Kerrey would win.

Finally, if Condorcet voting was used, Harkin would win, since he would win a one-on-one election against any of the other candidates.

Who do you think should win, and why?

This, by the way, fails to illustrate why I think we need Condorcet voting: not because it's criteria necessarily produces the best candidate, since in an election like the above it isn't clear by any means who is the "best". The appeal of Condorcet voting is that in all but the most degenerate cases (e.g. where most people prefer A to B, most people prefer B to C, and most people prefer C to A) Condorcet removes any incentive to make the election even worse by not "throwing your vote away"; in every other method mentioned, there are voters who can improve the outcome of the election (according to their own preferences) by voting something other than their own honest rankings. There's a nice discussion of Condorcet voting and the criteria like this that it meets on electionmethods.org.

I heartily second the recommendation to visit electionmethods.org. That site has much more information and analysis than the rather skimpy article. The arguments for Condorcet voting are incredibly compelling. I believe Debian uses it for its elections.

And if it is done with three candidates all of whom are fairly popular, it gives you just as much incentive to "spoil" your vote as plurality does. An explanation of circumstances in which this can occur (as well as a lot of other good information about voting systems and in particular Condorcet voting) is at electionmethods.org.

IRV isnt as good (IMHO) as Condorcet

please, have a read.

Arrow's Theorem doesn't draw any such conclusion. Sure, there's no perfect system (by Arrow's set of criteria), but there are systems that are much better than what we've got. Moreover, all that Arrow did was define a set of criteria, and proved that the criteria couldn't be met. He didn't prove that his criteria were correct, because that's a subjective decision that can't be proven.

For more on this, read this rebuttal of Arrow's theorem-based fatalism.

Ensuring the Integrity of Electronic Voting

Ensuring the Integrity of Electronic Voting

Normally I don't comment on sigs, but...

You mean Condorcet voting. IRV has serious problems once you look closely at it that make it unsuitable. With Condorcet, voting is the same, but the counting method is better.

Take a look at the links. If I ever run for office, changing the election method to something fair will be one of my planks.

Normally I don't comment on sigs, but...

You mean Condorcet voting. IRV has serious problems once you look closely at it that make it unsuitable. With Condorcet, voting is the same, but the counting method is better.

Take a look at the links. If I ever run for office, changing the election method to something fair will be one of my planks.

I would scream it from the rooftops if I felt it would do any good: CAMPAIGN FINANCE REFORM!

It would do harm, not good. There are two types of campaign finance reform:

1. Reform where the only limits are on financial donations to political campaigns, and donors can still purchase advertising for candidates or issues themselves. This could be called, "ineffectual reform", or even "counterproductive reform" if it's effect is simply to shut out the voice of people who could previously have pooled their efforts in lobbying groups but who are not wealthy enough to buy a single advertisement.

2. Reform where people are restricted as to what amount or what venues of political speech they can purchase with their own money. This is called "unconstitutional reform", and moreover will simply ensure that elections get decided by the news media instead of by political organizations and other industries.

I'm a Democrat, but if McCain had been on the ballot I would have voted for him in a heartbeat.

In that case, I suggest screaming for a different kind of reform, election method reform. Plurality voting is designed to force all voters to pick between two parties, and so ensures that the most important factor in an election is the party apparatus and it's funding. Anyone succeeding in the Democrat or Republican ranks has already been "bought", so if you want candidates who haven't to be electable then we need a fairer way to run elections.

Yes, and as in much election theory, I found the stated criteria filled with universal quantifiers ("must never," "must always," etc.) which as a practical matter refer to extremely rare events.

Right, just like how problems that crop up in plurality voting are extremely rare events.

The discussion at the end concerning the difficulty of counting IRV ballots is contrary to the actual experience of districts in Massachussets, Louisiana, Ireland, Australia, and many other places which use IRV.

Good point. If you write them about that section, please let me know what their response was.

Who picked these criterion, anyway? They are certainly not from the American Political Science Association, which uses IRV to elect its officers.

Your pet voting system doesn't pass the criteria, so you attack the criteria by it's source? I'm not sure who came up with it, some goat in Italy could have scratched paragraphs out in the dirt for all I know. Do they make sense? "Oh, that is rare that that would happen anyway" is a simple brush-off and is about as convincing as "Does not!". Need a real world example? You mentioned that Australia used IRV and hasn't had any troubles. Australia is *still* essentially a two-party country today. So apparently there are a few more troubles with it than you think there are. Look at the criteria again, do you not think they are valid points? What's wrong with, say, Summability Criterion? The webpage presents good arguments for it. I'd like some more detail on why you think each one of them isn't essential to a good voting system.

Oh, and "Appeal to Authority" is also a logical fallacy.

The answer could not be simpler than with IRV: Rank A first and B second. When A is eliminated, your support will transfer to B. Under no conditions will your ballot be counted in support of C.

Allow me to ask the question again:

What would the average voter do? What have they done in Australia? You know, plurality voting isn't all that terrible of an idea in theory. But people aren't honest enough at the polls to make it work. Heck, if it wasn't a common practice most people would read about it and think "You know, those problems would be really rare. The answer couldn't be simpler! Just tell people to vote for who they want." That's why you have to account for such things in the design of or when choosing any voting system. The webpage went into a lot more detail about why it doesn't work in practice than I did here. If you need to, refer to it again here. Remember, people won't vote honestly if they think they can beat the system. Why wouldn't they do it in IRV if they do it in plurality?

Contrast that to the Approval method, where you would be forced to support B to the same extent that you support A if you want to counter C at all.

Yes. You vote for who you approve of, or at least could tolerate. It is a nice way to work out a compromise without the problem of voters screwing themselves over. Anyway, if your purpose of going to the polls is to vote against someone, that's how you do it right there. Approval voting allows for no special manipulation that keeps systems like plurality and IRV down. To make an analogy, most people would keep antifreeze locked up in a cupboard than place it in a dish next to the rest of sparky's food. People are not much different from other animals -- if the temptation is there and it seems like a good idea at the time, people will do it. You'd need nearly as much effort to to educate people enough to use IRV honestly as it would to fix how people vote in the current system. If we're going to reform voting, why don't we do it right the first time?

Surely you can see from that simple case that you can send much more information about your preferences to be used for election with an IRV ballot than with an AV ballot.

Come again? You did research all the criteria that voting systems should pass, right? Simple tests, such as the Generalized Strategy-Free Criterion (Voters must not be able to shoot themselves in the foot by falsely ranking how they prefer candidates in an attempt to manipulate the outcome. See the example below). IRV fails all of them. Even plurality manages to pass two of them.

No, it does not. You can see from a purely information-theoretical perspective that IRV is more powerful than AV.

More information does not ensure a more accurate result when the voting system itself is almost certain to return bad information. In addition, the whole "more information" argument fails to regard whether the way the system processes the votes is sure to lead to an accurate result. From an information-processing-theoretical perspective, IRV is the least powerful voting system.

Example: So you step up to the polls. You know candidate B (who you could stand) is neck and neck with candidate C (who you really hate). You really prefer candidate A, but are scared to death that C could get in if you don't give B your top support.

What would the average voter do in this situation?

As for the simplicity of implementation, the Australian and Irish parliments have been doing just fine for a long time, and after a recent sudden conversion to IRV, respectivly.

Good for them, they managed to switch with no troubles. Approval works with existing voting equipment, so the change can be made quickly without waiting for new equipment. A whole country could change at the same time without a hitch.

Surely you can see from that simple case that you can send much more information about your preferences to be used for election with an IRV ballot than with an AV ballot.

Come again? You did research all the criteria that voting systems should pass, right? Simple tests, such as the Generalized Strategy-Free Criterion (Voters must not be able to shoot themselves in the foot by falsely ranking how they prefer candidates in an attempt to manipulate the outcome. See the example below). IRV fails all of them. Even plurality manages to pass two of them.

No, it does not. You can see from a purely information-theoretical perspective that IRV is more powerful than AV.

More information does not ensure a more accurate result when the voting system itself is almost certain to return bad information. In addition, the whole "more information" argument fails to regard whether the way the system processes the votes is sure to lead to an accurate result. From an information-processing-theoretical perspective, IRV is the least powerful voting system.

Example: So you step up to the polls. You know candidate B (who you could stand) is neck and neck with candidate C (who you really hate). You really prefer candidate A, but are scared to death that C could get in if you don't give B your top support.

What would the average voter do in this situation?

As for the simplicity of implementation, the Australian and Irish parliments have been doing just fine for a long time, and after a recent sudden conversion to IRV, respectivly.

Good for them, they managed to switch with no troubles. Approval works with existing voting equipment, so the change can be made quickly without waiting for new equipment. A whole country could change at the same time without a hitch.