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Author Topic: Condorcet Voting Method  (Read 17575 times)

JasonPSorens

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Condorcet Voting Method
« on: May 04, 2003, 01:35:46 pm »

The new Condorcet's Method practice poll is up:

http://www.freestateproject.org/condorcet/

It hasn't been announced on the website yet, in case there are still some unforeseen glitches.  Go ahead and stop by to cast your vote on the top libertarian thinkers of all time.  You may want to take a look at the results first, then cast your vote, to see how your vote changes the results.
« Last Edit: September 13, 2003, 06:56:40 pm by Elizabeth »
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JasonPSorens

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Re:Condorcet poll up!
« Reply #1 on: May 06, 2003, 01:32:01 pm »

The poll results show how unlikely it is that we'd have to move to the tie-breaker to get a Condorcet winner.  Thomas Jefferson is currently creaming everyone else.  If TJ is eliminated, Ayn Rand is a runaway winner.  If TJ & Ayn Rand are eliminated, then Milton Friedman is the runaway winner.  If TJ, Rand, and Friedman are eliminated, then and only then is it close to a cyclical result - with Mises just avoiding a defeat to Thoreau and therefore coming out the undisputed winner.  

And we have only 126 votes so far...
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paul

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Re:Condorcet poll up!
« Reply #2 on: May 06, 2003, 04:36:11 pm »

Now it is just a matter of voting correctly. ;)
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Eric

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Re:Condorcet poll up!
« Reply #3 on: May 06, 2003, 06:11:08 pm »

Now it is just a matter of voting correctly. ;)

Then consider this much-needed training for the state vote.  I don't know about you, but I don't want anybody trying to interpret my vote for state selection -- my intent should be crystal clear.   We should be using this and followup polls to get everyone up to speed on how to vote properly.  If the membership can't get this poll correct now, the actual vote will be a disaster.


eric
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LeRuineur6

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Condorcet is a Points System?
« Reply #4 on: June 30, 2003, 08:11:25 am »

I've been doing some thinking about Condorcet's method and how it calculates votes and have come to a conclusion.

Correct me if I'm wrong, but isn't Condorcet's just a point system?  Just assign values to the votes and you'll see what I mean:

A > B > C > D > E > F
A=6, B=5, C=4, D=3, E=2, F=1

This makes the entire problem so much more simplified and the calculations create identical solutions to the horrible matrices I've seen floating around.   ;)

Is this obvious common knowledge or have I actually simplified the calculation system here?

Hehehe, you can call my Condorcet-plagiarized point system LeRuineur's Method.   :D
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LibertyLover

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Re:Condorcet is a Points System?
« Reply #5 on: June 30, 2003, 05:15:08 pm »

Correct me if I'm wrong, but isn't Condorcet's just a point system?  Just assign values to the votes and you'll see what I mean:

A > B > C > D > E > F
A=6, B=5, C=4, D=3, E=2, F=1

This makes the entire problem so much more simplified and the calculations create identical solutions to the horrible matrices I've seen floating around.   ;)

Since I've been spending so much time figuring out exactly how Condorcet works, I've become a big admirer of the method.

It is definitely NOT a points system. A points system encourages people to try to vote strategically by giving a lower ranking to choices they think may be rivals to their top choice. Since Condorcet measures each choice only by higher/lower rankings with every other choice, there is no advantage in trying to vote strategically.

In your above example vote, A beats B just the same as it beats F and E beats F the same as A beats F. This is the main reason why people don't need to try to vote strategically. As long as people vote honestly (i.e., their honest opinions), Condorcet will give the result that reflects the preferences of the greatest number of voters. And if individual voters try to vote strategically, they only undermine their own true preferences.

With Condorcet, the state that gets a plurality of the #1 votes won't necessarily win, because the winner will be the state that is ranked higher than all the other states by the most people. This means that all the rankings of all the votes count. In other words, if you don't get your first choice, you are more likely to get your second or third choice than if a points system were used. Even if your opinions about the relative rankings are in the minority, the winner will probably be higher in your rankings than if a point system were used.

It looks like the Condorcet method was chosen to give the most fair and accurate result rather than to be easily understood and calculated. :o
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JasonPSorens

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Re:Condorcet is a Points System?
« Reply #6 on: June 30, 2003, 08:45:51 pm »

The points system is technically referred to as "Borda," which was actually one of the methods under consideration when we moved from Cumulative Count.  Borda has severe strategic voting problems, and its designer admitted that, "My system is for honest men."  There's an old thread somewhere on the "Which state?" forum comparing IRV, Borda, Condorcet, and Cumulative Count.  Interestingly, you'll find that I at first supported IRV until I and my fellow researcher Steve Cobb (who liked Borda!) were persuaded of the overwhelming superiority of Condorcet. ;)
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LeRuineur6

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Re:Condorcet is a Points System?
« Reply #7 on: July 01, 2003, 11:02:07 am »

I'm trying to figure out the difference between Condorcet's method and my explanation of it, and I'm having quite a difficult time.

This example predicts the correct winner:

45 A B C
 A=135, B=90, C=45
6 B C A
 A=6, B=18, C=12
14 B A C
 A=28, B=42, C=14
35 C B A
 A=35, B=70, C=105

A = 204, B = 220, C = 176
B wins.

------

This example also predicts the correct winner:

40 A B C
 A=120, B=80, C=40
5 A C B
 A=15, B=5, C=10
6 B C A
 A=6, B=18, C=12
14 B A C
 A=28, B=42, C=14
31 C B A
 A=31, B=62, C=93
4 C A B
 A=8, B=4, C=12

A = 208, B = 211, C = 181
B wins.

------

This example, however, does not.  Under Condorcet's Method, this creates a Conflicting Majority phenomenon.  Under my theoretical "points system" explanation of Condorcet's, it produces C as a winner.

2 A B C
 A=6, B=4, C=2
3 B C A
 A=3, B=9, C=6
4 C A B
 A=8, B=4, C=12

A = 17, B = 17, C = 20
C wins.

I've cracked an encryption algorithm before, by hand, in only 13 hours, but simplifying Condorcet's Method is frying my brain!
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JasonPSorens

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Re:Condorcet is a Points System?
« Reply #8 on: July 01, 2003, 11:18:26 am »

Under our method of resolving cyclical majorities, C also wins in that last example, because B's 5-4 victory over C is eliminated first.
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LeRuineur6

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Re:Condorcet is a Points System?
« Reply #9 on: July 01, 2003, 01:35:29 pm »

Quote
Under our method of resolving cyclical majorities, C also wins in that last example, because B's 5-4 victory over C is eliminated first.

Really?  Woohoo!

Other than the conflicting majorities problem (which apparently creates the same outcome as your solution), I have not yet been able to create a situation in which calculations under the modern Condorcet method differ from my simplification of that method.

I'll keep trying the numbers but hopefully somebody will help me out.  hehe
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JasonPSorens

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Re:Condorcet Question
« Reply #10 on: July 01, 2003, 03:10:23 pm »

No, there's no reason to do that.  Condorcet is different from a points system.  LeRuineur has been trying to discover how far the similarities go, but I can direct anyone who's interested to demonstrations of how Borda Count (points system) sometimes does not pick the Condorcet winner.
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Re:Condorcet Question
« Reply #11 on: July 01, 2003, 03:16:16 pm »

Quote
Is there any logical reason to do this unless one believes that New Hampshire is the worst choice among the ten states?

I certainly don't believe New Hampshire is the worst among the 10 states.  But I do think it has the most support in the east.  So if one truly wants to live in the west it seems like putting the strongest contender from the east at the bottom would make it more likely that you would end up in the west.  

I have nothing against New Hampshire.  I just would prefer to live in the west.
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JasonPSorens

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Re:Condorcet Question
« Reply #12 on: July 01, 2003, 03:21:43 pm »

No, Radar, with the Condorcet system, putting NH at the bottom won't help any Western state, but it will help VT, DE, and ME vis-a-vis NH.  So if you're more comfortable with VT, DE, or ME winning than you are with NH winning, by all means rank them higher.  But by not voting your true preferences you could end up shooting yourself in the foot, and you do no good for your top state(s).

The flip side of this is that you can't really hurt any candidate that badly by voting strategically under Condorcet.  Let's say NH was really your #7 choice, but you put it #10, behind a couple of states that you liked less but thought less likely to win.  Well, all this does is hurt NH relative to those states less likely to win.  So it's unlikely to really hurt NH at all, assuming few others vote "strategically" (I put it in quotes because it's a bad strategy!).  If many people vote "strategically," then AK, ND, or ME could win the vote. ;)
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JasonPSorens

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Re:Condorcet is a Points System?
« Reply #13 on: July 01, 2003, 03:29:11 pm »

Here's an empirical analysis of how often Borda, IRV, and other systems pick the Condorcet winner:

http://accuratedemocracy.com/c_data.htm

Here is a description of different voting methods and the kinds of strategy that arise with each (Condorcet is called "Ranked Pairs" here):

http://condorcet.org/emr/methods.shtml
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JasonPSorens

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Re:Condorcet Question
« Reply #14 on: July 01, 2003, 03:37:04 pm »

Most dangers in using Condorcet rules come from the notions held by voters  and politicians accustomed to bad voting rules. A prime one comes from voters who might think they can manipulate a Condorcet rule in the usual ways: with decapitation and punishing votes.

For example, Bob, a Bush supporter, may think he can help Bush by ranking Gore below Nader. That has no affect on Bush in his comparisons against Gore or Nader; Bush always wins Bob's vote no matter how he ranks the other candidates. But the change does help Nader in his 1 on 1 against Gore. If many Gore supporters also rank Nader second, he may beat both Bush and Gore -- because of strategic votes that had negative strategic value!

That strategy is called a "punishing vote" (against Gore) or "raising turkeys", giving high ranks to hopeless losers. Sincere but uninformed voters also may put a little-known candidate in between their favorite and her major rival. In this way a candidate could be elected almost by accident! She might be a political weakling without a mandate to govern, a strong base of support or the respect of a majority on the council.

When voters become familiar with the strength of Condorcet's rule they will not make that mistake. A quicker solution requires each candidate to win 5 or 10 percent of the first-choice votes to qualify for the Condorcet tally. This threshold excludes very small parties from the tally just as the thresholds for proportional representation do. A threshold pushes some voters to decapitate a weak first choise in order to help a lower choice reach the threshold.

Unfortunately a threshold motivates a candidate to focus narrowly on a few voters; that 10% is her first priority. Her second is to position her policies between the big parties -- and that might not require a broad appeal. As the council's swing voter, she might push a selfish agenda to serve her narrow base of support.

So Condorcet's rule would need a threshold low enough to include several central candidates; then all voters may choose the 1 with the broadest appeal. Instead of a percentage, the threshold could be a number of slots for the [5] candidates with the most first-place votes.

<http://accuratedemocracy.com/Rule_Chair_300.gif>

Speaking of uninformed voters, most candidates give speeches full of vague, feel-good symbolism but avoid offering detailed solutions to controversial issues. This lets voters fill in what they want to hear and imagine the speaker is suggesting. Sometimes the candidates as a group don't even raise important but formidable problems -- making the campaign an empty ritual. These strategies seem to win votes under all rules but critics claim the centrism of Condorcet rules might make it worse, more likely to elect candidates who "sit on the fence".

<http://accuratedemocracy.com/Rule_Chair_300.gif>

Several dangers have more to do with the psychology of politicians than of voters. A chief executive must have a clear sense of direction and be strong willed to make the bureaucrats pull together. These qualities may be stronger in the IRV winner than in the middle-of-the-road Condorcet winner.

But when electing a council, the question "Do we want 'bold leadership' OR 'the best moderator'?" is a false dichotomy. We can have several reps who are strong advocates for various interest groups AND a chairperson who excels at building consensus. Her role is very different from the chief executive's.

Many democratic reformers prefer the "council and manger" form of government in which a Chief Administrative Officer is hired by the council to execute its decisions and run the bureaucracy. This CAO has great influence through reports and testimony to the council. But the broad-based council has all final power.

<http://accuratedemocracy.com/Rule_Chair_300.gif>

The process of governing presents another danger: often the way to find the best course is to go a little to the right, then a little to the left. Plurality and IRV tend to do that when electing successive chief executives. Condorcet winners change course only as much as voters do; small shifts in the electorate do not lead to policy flip flops. Which is usually a good thing, but occasionally some organizations may need sweeping changes.

Condorcet rules might exacerbate a problem some Latin American countries have when the combination of a PR legislature with an independent president results in deep gridlock (see Gary Cox, p. 59 of "Instability? A response to Robert Richie and Steven Hill's "The Case for Proportional Representation" ) The president's veto power is key; absent that, this gridlock can not occur.

Part of the solution, according to Cox, is tightly linking the election of the president with election of the legislature, so the president's "coattails" help give her a legislative majority and make reps seek her favor in coming campaigns. Their elections should be simultaneous and should use equally eccentric voting rules so the president and most reps come from the same party or at least from the same side -- so electing this president by IRV is usually best.

(Another part of the solution is to limit the number of effective parties the president must negotiate with by limiting the number of reps elected from any district. Three-seat districts are safest here because they usually produce one or two reps from each of the two major parties and none from smaller parties.)

<http://accuratedemocracy.com/Rule_Chair_300.gif>

The chance of a tie (or "voting cycle") may run about 10% in most electorates. It is easily fixed by any of the numerous "Condorcet-completion rules" such Schulze's, Tideman's Ranked Pairs, or I.D. Hill's use of IRV.


http://accuratedemocracy.com/c_anti.htm
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