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Gabu
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Posts: 28,386
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Political Matrix
E: -4.32, S: -6.52

« on: January 03, 2005, 07:19:35 PM »
« edited: January 04, 2005, 11:10:41 PM by Senator Gabu »

Okay, well, I looked into it given that Peter Bell isn't around, so here's my split up version of the previous amendment.  Since they're closely related, I'm putting them both on the same post.  I've also included the other stuff StevenNick suggested regarding the definition of an "active voter" as well as a few other bits (see the "Notes" at the bottom).  It is okay to have two pieces of legislation in the same thread, right?  If not, I'll stick the statute in its own thread.

Election and Voter Policy Specification Amendment

§ 1. Article II, Section 2, Clause 4 is hereby amended by appending to the end of it the following text: "For the purposes of this clause, the amending of one's vote is defined to be the editing of the post containing the vote."

§ 2. The amended version of Article II, Section 2, Clause 4 shall hereby be applied to all federal elections.

§ 3. The following text from Article V, Clause 4 is hereby stricken: "No one who has attained eighteen posts, is an active member of the forum, and has established an avatar from the United States for at least the time span of the election shall be denied the right to vote. An active member is defined as a person who has participated in other threads at the forum and has not joined for the purpose of trolling."  It shall be replaced with the following text: "No one who has attained eighteen posts shall be denied the right to register to vote.  No one who is registered to vote, who is an active member, and who has established either an avatar from the United States or a statement declaring his or her registration in his or her signature for at least the time span of the election shall be denied the right to vote.  For the purposes of this clause, an active member is defined to be one who has posted at least twenty-five times since the last federal election in which he or she voted.  The burden of proof shall be placed on the Secretary of Forum Affairs to prove that a registered voter has not posted twenty-five or more times; if it cannot be proven, the voter shall be assumed to be active.  If a person is registered to vote, and no federal election has passed since registering to vote, that person shall be counted as an active member."

§ 4. The parts in Section 3 pertaining to the requirement of registered voters to be active members shall not be enforced on voters who have registered prior to the passage of this bill until they have voted in at least one federal election.

§ 5. The following text from Amendment II, Section 2, is hereby stricken: "Every registered vote at the forum who has acquired eighteen posts, is an active member of the forum, and are registered with an avatar from the United States".  It shall be replaced with the following text: "Every person who fulfills the requirements to vote in Article V, Clause 4 of the Constitution".

§ 6. Article II, Section 2, Clause 5 of the Constitution is hereby stricken.



Statute of Election Procedure, Certification, and Challenges

§ 1.

  Clause 1. No election results shall be deemed to be official except those which have been certified.

  Clause 2. The certification of election results that occur following the passage of this amendment as official shall consist of the Secretary of Forum Affairs releasing an official statement, signed by that official, displaying the uncertified results in question and declaring them to be hereby certified.

  Clause 3. All election results in place prior to the passage of this amendment are hereby declared to be certified without requiring a statement from the Secretary of Forum Affairs.

§ 2.

  Clause 1. No election results shall be challenged except those which are awaiting certification or those which have been certified less than seven days prior to the challenge and which have occurred following the passage of this statute.

  Clause 2. To challenge an election result, a formal statement of challenge must be brought before the Supreme Court indicating the challenged result and the reason for challenging the result.

  Clause 3. In considering the challenge, the Supreme Court shall examine relevent parts of the Constitution and Atlasian law, and each member of the Court shall determine whether or not the challenge is legitimate.

  Clause 4. In the event that a majority of the Supreme Court concurs that the challenge is legitimate, appropriate action shall be taken to rectify the challenged section of the result:

    a. If the challenged section is a vote that has been counted, it shall be stricken from the official count.
    b. If the challenged section is a vote that has been disregarded, it shall be entered into the official count.
    c. If the challenged section is the procedure of the election, the election shall be declared invalid and a new election shall be scheduled for the Friday following the declaration of the invalidity of the election.

§ 3.

  Clause 1. In the case that a tie arises in the last round of preferential voting, the candidate in the tie who has received the greatest number of first-preference votes shall be declared the winner.

  Clause 2. In the case that a tie arises in the last round of preferential voting and no candidate in the tie has received a greater number of first-preference votes, non-first-preference votes shall be included one level at a time (second-preference votes first, then third-preference votes, etc.) until one candidate has a greater number of votes than anyone else.

  Clause 3. In the case that no candidate with a greater number of votes than anyone else emerges once every level of preferencing is considered, this event shall be declared an "unbreakable tie".  Differing procedures shall be followed depending on the type of election that contains an unbreakable tie:

    a. If the election is for the presidency, the Senate shall vote on who shall be President.  No candidates may be voted upon except for those who are present in the tied vote.  A majority in the Senate shall be needed to elect a candidate as President.
    b. If the election is for the Senate, the President shall choose from the candidates in the tied vote one candidate who shall be Senator.
    c. If the election is for any other new office created in the future, no procedures shall be set in place upon passage of this amendment, but no new office shall be established without specifying the procedures of handling an unbreakable tie.

§ 4. This statute shall be applied to all federal elections.


I think that covers everything.

Notes:

1. I realized that Article V, Clause 4 does not at all differentiate between the requirements to register to vote and the requirements to actually vote.  I've made that differentiation.

2. Amendment II, Section 2 effectively duplicated the requirements to vote, which would require that it be amended every time we amend Article V, Clause 4.  I've changed it to effectively say "see Article V, Clause 4" instead, to prevent that hassle.
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Gabu
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Posts: 28,386
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Political Matrix
E: -4.32, S: -6.52

« Reply #1 on: January 04, 2005, 12:57:26 AM »
« Edited: January 04, 2005, 02:05:02 AM by Senator Gabu »

So, basically, the idea is that we skip the consideration of each level of preferencing and go straight to breaking the tie?

I could live with that.  I see your point about it not correcting what preferential voting is supposed to correct, which is the idea that one vote is more important than another.
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Gabu
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*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #2 on: January 04, 2005, 07:30:52 PM »
« Edited: January 04, 2005, 11:15:11 PM by Senator Gabu »

One problem with both Gabu's bill and WMS' change, and also the reason we got the first preference rule:
What to do with a tie in the earlier rounds?
For example, we had an election where
Keystone Phil received 5 first pref. votes
Umengus received 3 first pref. votes
Migrendel received 3 first pref. votes

Migrendel beat Umengus on second pref.s*, and went on to beat Phil 6-5.
In this kind of situation (which Gabu's bill doesn't address), a tie-breaker is needed, while in a tie in the final tally, you can have a revote instead.


*in a fashion I thoroughly abhor: Republicans boycotted preferential voting, absurdly claiming not to see any difference between Migrendel and Umengus. All Umengus voters had put Migrendel at second, but only two Migrendel voters had put Umengus at second as the third one, HockeyDude, hadn't understood the election law and cast a vote that looked like DemoHawk's original one. In essence, Umengus got punished for having the most informed and sensible voters of the lot. The current rules place a premium on ignorance. Of course, the only way to fix this would be to require voters to list all candidates, in which case Umengus would probably have won with Rep. 2nd prefs, or to switch to Condorcet in which case there would have been an unbreakable tie, and a revote, between Umengus and Migrendel.

Yes, that's a excellent point to bring up.  I hadn't thought about ties occurring before the final round... I'll have to think about that one.

EDIT: I thought that maybe we could require that people list every candidate, as you said, but then we'd still have to make higher preferences worth more, and that doesn't address WMS' concerns.  Hmmm...

For the purposes of this clause, an active member is defined to be one who has posted at least twenty-five times since the last federal election in which he or she voted.  If the person has not voted in any federal election since registering to vote, that person shall be counted as an active member.

The language of these two sentences needs to be changed.  This would allow a member to register and potentially sit out every election and still be classified as an active member.

Wouldn't they be removed from the list of registered voters after missing two elections, though?

I see your point, though.  I'll change that.

PS: I also added a tidbit saying that the burden of proof will be on the Secretary of Forum Affairs to prove that someone has not posted 25 times since the last federal election.  I figured that this is fair due to the "innocent until proven guilty" protocol that is standard.  As I suggested in another topic a while back, it wouldn't be that difficult for the SoFA just to record the number of posts each voter has at the time of voting for future reference.

If there's any argument with that part, we can change it.

PPS: I also added another section in the amendment below that section clarifying what will happen with people who are already registered to vote before the passage of this amendment.

PPPS: I added a small phrase to the end of Section 2, Clause 1 of the statute that says that only future elections may be challenged.  I just realized that the wording of "those which have been certified less than seven days prior to the challenge" meant that any idiot who decided to get extremely technical could actually challenge any election in Atlasian history in the time span of seven days following the passage of that statute, given that the statute automatically certifies them all.
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Gabu
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Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #3 on: January 04, 2005, 10:35:20 PM »

Finally some action from the Senate when it comes to Election Reform!

I comend Senator Gabu. Smiley

Thank you, Mr. President, but StevenNick should take at least half of the credit; I was following the recommendations in his report.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #4 on: January 04, 2005, 11:45:04 PM »

One problem with both Gabu's bill and WMS' change, and also the reason we got the first preference rule:
What to do with a tie in the earlier rounds?
For example, we had an election where
Keystone Phil received 5 first pref. votes
Umengus received 3 first pref. votes
Migrendel received 3 first pref. votes

Migrendel beat Umengus on second pref.s*, and went on to beat Phil 6-5.
In this kind of situation (which Gabu's bill doesn't address), a tie-breaker is needed, while in a tie in the final tally, you can have a revote instead.


*in a fashion I thoroughly abhor: Republicans boycotted preferential voting, absurdly claiming not to see any difference between Migrendel and Umengus. All Umengus voters had put Migrendel at second, but only two Migrendel voters had put Umengus at second as the third one, HockeyDude, hadn't understood the election law and cast a vote that looked like DemoHawk's original one. In essence, Umengus got punished for having the most informed and sensible voters of the lot. The current rules place a premium on ignorance. Of course, the only way to fix this would be to require voters to list all candidates, in which case Umengus would probably have won with Rep. 2nd prefs, or to switch to Condorcet in which case there would have been an unbreakable tie, and a revote, between Umengus and Migrendel.

Yes, that's a excellent point to bring up.  I hadn't thought about ties occurring before the final round... I'll have to think about that one.

EDIT: I thought that maybe we could require that people list every candidate, as you said, but then we'd still have to make higher preferences worth more, and that doesn't address WMS' concerns.  Hmmm...

Crap. Lewis has a point. I'll be thinking about tie-breaker procedures on rounds before the final one as well, although I am still opposed to using the preference rule. Would Condorcet being used on a tie before the final round work out?

How would the Condorcet method work?  I can't think of anything that doesn't value higher preferences above lower preferences at this moment, so I'm open to suggestions.
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Gabu
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Posts: 28,386
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Political Matrix
E: -4.32, S: -6.52

« Reply #5 on: January 04, 2005, 11:48:01 PM »

Seems kind of long-winded to have a whole new vote just to break a tie for second place, though.  Isn't there anything else?

Maybe not; I dunno.
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Gabu
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Posts: 28,386
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Political Matrix
E: -4.32, S: -6.52

« Reply #6 on: January 04, 2005, 11:50:44 PM »

Come to think of it, wouldn't having an entirely new vote just be basically the exact same as just considering the second preferences if we required everyone to give everyone a preference?  A vote between the second-place tying candidates would be asking, "Which of these two would you prefer to have as president?", which is basically the exact same as preferencing one higher than the other.
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Gabu
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Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #7 on: January 05, 2005, 12:01:20 AM »

Well, maybe we should make it so that everyone has to preference each candidate.  I don't think that it would be a lot to ask of the voters and it would certainly provide the simplest solution.
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Gabu
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*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #8 on: January 05, 2005, 12:11:51 AM »

Well, maybe we should make it so that everyone has to preference each candidate.  I don't think that it would be a lot to ask of the voters and it would certainly provide the simplest solution.

As long as there are no preferencing rules used in the final round, this might work. Of course, there are some voters who are extremely resistant to this, judging by past voting controversies, and we haven't heard from them yet...(looks at the Vice President) Smiley

Okay, so what we have is this:

1. If there is a tie in any round that has at least three or more candidates in it for last place, lower preferences are considered until a person with more votes than anyone else emerges.
2. If there is a tie in the last round, Clause 3 in Section 3 in the statute is applied.

There's one other issue, however: what happens when there's an unbreakable tie for last place?  I just thought of that.
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Gabu
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Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #9 on: January 05, 2005, 12:32:02 AM »
« Edited: January 05, 2005, 12:36:45 AM by Senator Gabu »

2. Is this where the President chooses someone, or is this part undefined yet? In the last round, I support a tie leading to a runoff election.

Undefined, for the most part.  That was just an idea I threw out that is not in any way set in stone; we can resolve what to do about an unbreakable tie later.

(3.) Last place? Do you mean before we've reached two candidates?

Well, consider this possibility:

We have candidates A, B, and C.

First preferences look like this:

A: 9
B: 3
C: 3

But B and C both get 6 second preferences (say, 6 from A's voters for B and 3 from A's voters and 3 from B's voters for C) and 6 third preferences (say, 3 from A's voters and 3 from C's voters for B and 6 from A's voters for C).  That leads to an unbreakable tie for last place.
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Gabu
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*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #10 on: January 05, 2005, 12:43:22 AM »

Understood. This would bring us back where we started on this one, huh?

I suppose, though, let me check the logic of the situation that I gave; something about it doesn't seem quite right...
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #11 on: January 05, 2005, 12:47:38 AM »

Understood. This would bring us back where we started on this one, huh?

I suppose, though, let me check the logic of the situation that I gave; something about it doesn't seem quite right...

Well, tell me what you come up with.

Geez, the entire electoral system is going to be designed by three people... ;-P

Well, if anyone else wants to chime in, they're more than welcome to. Tongue

Okay, I've figured it out.  Suppose we have five votes for candidates A, B, and C, as follows:

Vote 1: A, B, C
Vote 2: A, B, C
Vote 3: A, C, B
Vote 4: B, C, A
Vote 5: C, A, B

This results in the following situation:

A: 3
B: 1
C: 1

with both B and C having 2 second- and third-preference votes, leading to an unbreakable tie.

Okay!  Good.  I just wanted to make sure that the situation I thought of actually can happen, and so it can.

Now we need to figure out what to do about it...
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #12 on: January 05, 2005, 12:55:16 AM »

Actually, come to think of it, a new vote might work... if you look at the votes that I gave, 3 people preferenced B over C while only 2 people preferenced C over B, so even though counting every preference results in an unbreakable tie, it would appear to me that a new vote would make B win 3-2.

I need one more bit of information: is an unbreakable tie for last place possible with an even number of voters?  If it's not, then I think we have our solution.
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Gabu
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Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #13 on: January 05, 2005, 12:59:55 AM »

Offhand, I can't think of a scenario in which it could... if it did, I think it would definitely need more than 3 candidates.

I wonder if there's a mathematical way of figuring this out; there probably is, but I can't think of it at the moment.  Maybe I should sleep on it and see what I can come up with.
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Gabu
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*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #14 on: January 05, 2005, 01:01:28 AM »

Using your votes:
Vote 1: A, B, C
Vote 2: A, B, C
Vote 3: A, C, B
Vote 4: B, C, A
Vote 5: C, A, B
Vote 6: A, C, B

Err, is this an unbreakable tie?

No, it isn't; C has 3 second-place votes while B only has 2, so B would be eliminated.

For it to be an unbreakable tie, every candidate in the tie must have equal numbers of every level of preferencing.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #15 on: January 05, 2005, 01:06:53 AM »

Edited Part: If there's a mathematical way to determine this, I yield the floor to you. Smiley

There must be one, but I'm too tired at the moment to think mathematically.

Given that this isn't incredibly urgent, I think I'm gonna head to bed and see what I can come up with regarding this tomorrow.  If we can prove that it's impossible to have an unbreakable tie with a number of voters divisible by the number of candidates in the tie (for whatever reason, I feel like that assertion is true, but I don't know why), then we can go with a new vote to resolve an unbreakable tie.

This issue was a lot more complicated than I thought it would be when I started. Smiley
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #16 on: January 05, 2005, 01:08:18 AM »

Using your votes:
Vote 1: A, B, C
Vote 2: A, B, C
Vote 3: A, C, B
Vote 4: B, C, A
Vote 5: C, A, B
Vote 6: B, A, C
Vote 7: C, A, B

Err, is this an unbreakable tie?

No, it isn't; C has 3 second-place votes while B only has 2, so B would be eliminated.

For it to be an unbreakable tie, every candidate in the tie must have equal numbers of every level of preferencing.
Edited: Well, it can sure happen with an odd number of voters...

Yes, but with an odd number of voters in a 2-candidate tie, it's impossible to have a tie between the two candidates in a new vote, so that wouldn't be a problem.

The only problem that would arise is when you have a number of voters divisible by the number of candidates in the unbreakable tie.  If it's not possible to have an unbreakable tie under those circumstances, as I said before, then a new vote will work.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #17 on: January 05, 2005, 01:11:08 AM »

Using your votes:
Vote 1: A, B, C
Vote 2: A, B, C
Vote 3: A, C, B
Vote 4: B, C, A
Vote 5: C, A, B
Vote 6: B, A, C
Vote 7: C, A, B

Err, is this an unbreakable tie?

No, it isn't; C has 3 second-place votes while B only has 2, so B would be eliminated.

For it to be an unbreakable tie, every candidate in the tie must have equal numbers of every level of preferencing.
Edited: Well, it can sure happen with an odd number of voters...

Yes, but with an odd number of voters in a 2-candidate vote, it's impossible to have a tie, so that wouldn't be a problem.

The only problem that would arise is when you have a number of voters divisible by the number of candidates in the unbreakable tie.

Ah! Recognition Dawns! That's what you meant! I feel smarter now. Cheesy Good luck with this one...

Thanks; I'll probably need it. Tongue

Good night, I'll post here tomorrow with what I've got at that time.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #18 on: January 05, 2005, 10:39:44 AM »

Once again, this draft amendment contains provisions that really ought to be statutory. The 25-post rule should not be in the Constitution as I can see us getting about a month down the line and then everybody suddenly thinking - Thats too much or thats not enough. This once again leads us on the labourious endeavour of amending the Constitution (which frankly I'm really tired of now).

The 25 post rule is fine as part of the statute as it simply defines what the word active in the constitution means and is subject to further revision by the Senate at a later date.

So, your suggestion is that we just remove the current Constitutional definition of "active" and then redefine it later in the statute?

Okay, I'll change that in the next version of this legislation.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #19 on: January 05, 2005, 10:42:42 AM »

Well, in your 9-3-3 or 3-1-1 scenarios, there is no need to break the tie since candidate A already has a majority of the vote.

Oh.  Right.  Eh heh.

Getting back to the 5-3-3 scenario that really happened, therefore (it was Bono btw, not Keystone - mea culpa) and amending it this way...
Hockeydude had a second preference.
One Bono voter did not exist.
Of the other four, two sec.pref Umengus, two Migrendel.
Leaves us with
ABC
ABC
ACB
ACB
BCA
BCA
BCA
CBA
CBA
CBA
and an unbreakable tie for last place, except by tossing a coin.
So it certainly still could happen.
Under Condorcet, you cast a ballot as under IRV. You're not required to list all candidates.
You then draw up a matrix in which all candidates are compared to each other.
in this case:
   A   B   C
A x   4   4
B 6   x   5
C 6   5   x
6 voters prefer B to A, 4 voters prefer A to B
6 voters prefer C to A, 4 voters prefer A to C
5 voters prefer B to C, 5 voters prefer C to B

There are three different possible results really:
1 (by far the most common, would have happened in our presidential elections): One candidate beats all other candidates in one-on-one matchups and is the winner.
2 : There is a circular chain, A beats B, B beats C, C beats A. In that case, the margin of these defeats is used as a chain-breaker.
3: Two (or more) candidates beat everybody else, and tie among themselves. That's what happens in the above example, and frankly I don't have a clue what's supposed to happen.
Here's what would have happened in the original example (B being Umengus):
   A   B   C
A x   5   5
B 5   x   3
C 6   3   x
A and B tie, B and C tie, C beats A. I honestly don't know what happens in this case actually. At first glance I guess it would also count as a Migrendel victory. (Hey, don't blame me. I'm writing this from memory.)

I'm going to need to put aside more time than I've currently got to study what's going on in this Condorcet business, as I currently don't quite understand it.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #20 on: January 05, 2005, 10:51:18 AM »

So, your suggestion is that we just remove the current Constitutional definition of "active" and then redefine it later in the statute?

My suggestion would be to strike the present definition of active and then say that the Senate shall have power to define what an active voter is by appropriate legislation. Then get the Senate to do it by appropriate legislation.

It should be noted that as a scholar of this sort of stuff I have a bias towards a constitutional structure that leaves as much to the legislature as possible. I'm a great believer that the constitution provides the skeleton of the law and the legislature provides the flesh of it. There are certainly viewpoints out there that disagree with my methods, so don't necessarily defer to me all the time (but certainly don't let me stop you!)

It seems logical to me; if we screwed something up that desperately needs to be changed, it would be a serious pain and time-waster if we needed to go through the process of amending the whole Constitution yet again.
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Gabu
Atlas Star
*****
Posts: 28,386
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Political Matrix
E: -4.32, S: -6.52

« Reply #21 on: January 05, 2005, 06:25:15 PM »

Well, I've examined the mechanisms behind Condorcet, and as far as I can tell, it unfortunately won't resolve unbreakable ties, as far as I can tell:

Getting back to the 5-3-3 scenario that really happened, therefore (it was Bono btw, not Keystone - mea culpa) and amending it this way...
Hockeydude had a second preference.
One Bono voter did not exist.
Of the other four, two sec.pref Umengus, two Migrendel.
Leaves us with
ABC
ABC
ACB
ACB
BCA
BCA
BCA
CBA
CBA
CBA
and an unbreakable tie for last place, except by tossing a coin.
So it certainly still could happen.
Under Condorcet, you cast a ballot as under IRV. You're not required to list all candidates.
You then draw up a matrix in which all candidates are compared to each other.
in this case:
   A   B   C
A x   4   4
B 6   x   5
C 6   5   x
6 voters prefer B to A, 4 voters prefer A to B
6 voters prefer C to A, 4 voters prefer A to C
5 voters prefer B to C, 5 voters prefer C to B

(snip)

3: Two (or more) candidates beat everybody else, and tie among themselves. That's what happens in the above example, and frankly I don't have a clue what's supposed to happen.

From what I can tell, an unbreakable tie in IRV will result in an unbreakable tie in Condorcet, as well.  If all candidates in the tie have exactly the same amounts of first-, second-, third-, etc. preferences, then each candidate is prefered over the other candidates the exact same amount.

Unless someone can prove me wrong on this, I think it's back to the examination of the possibility of a new vote to break an unbreakable tie.

PS: JFK, is there any way to have this get postponed for debating time?  I think we're gonna need longer than what we'll get if it takes its place in the queue.
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Gabu
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*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #22 on: January 05, 2005, 07:05:02 PM »
« Edited: January 05, 2005, 08:41:33 PM by Senator Gabu »

Well, damn.  It isn't true that it's not possible to have an unbreakable tie with an even number of voters.  Here's a scenario where that happens:

ABC
ABC
ACB
ACB
BCA
BCA
BCA
CBA
CBA
CBA

First-preference results:

A: 4
B: 3
C: 3

Second-preference results:

A: 0
B: 5
C: 5

Third-preference results:

A: 6
B: 2
C: 2

If put to a vote between B and C, the final results would be 5-5 because 5 voters placed B above C and 5 voters placed C above 5, and we're at yet another unbreakable tie.  This would still be an unbreakable tie using Condorcet, because B would beat C 5 times and C would beat B 5 times.

So, neither a new vote between the tying candidates nor Condorcet will always work to resolve an unbreakable tie.

Back to the drawing board...

EDIT: I should add that there are, in fact, an infinite number of examples of votes that will create this.  Let's number the vote types:

1: ABC
2: ACB
3: BAC
4: BCA
5: CAB
6: CBA

If we let n be the total number of voters and vk be the number of votes of type k cast, then my mathematical analysis of this situation says that we will have an unbreakable tie if and only if

v3 + v4 = v5v6
v1 + v6 = v2v4
v3 + v4 < n/3
v5v6 < n/3
v1 + v2 < n/2

If you find a set of votes that satisfies those conditions, they will provide an unbreakable tie.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #23 on: January 05, 2005, 08:23:48 PM »

I think we're going to have to resort to something less scientific (along the lines of flipping a coin or having someone else make the call) than what we've considered so far to break a tie of this sort. Smiley  I am at an absolutely total loss to think of anything that involves the voters and am beginning to think that there isn't one.
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Gabu
Atlas Star
*****
Posts: 28,386
Canada


Political Matrix
E: -4.32, S: -6.52

« Reply #24 on: January 05, 2005, 08:42:39 PM »

Perhaps ties should be broken by a vote of the Senate?

Given the pace that the Senate has been known to move on things, I'm not sure if that would be a good idea.  Plus, I don't like the idea of the Senate voting on its own members.

If it's all we've got, though, we maybe could go with something like that.
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