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Posted Mar 21, 2001 by Dogster
http://www.bbc.co.uk/h2g2/guide/A520372
"Arrow's Possibility Theorem" says that there is no perfect voting system. Is the idea of democracy doomed? What does he mean "perfect voting system"? Find out more inside...
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Posted Mar 21, 2001 by Crescent, ACE
Jings, that maths bitty was a bit hard to follow, but I think I managed it....I liked this Entry, and would hope that this should have little trouble with becoming an Edited Guide Entry  Well done Until later....
BCNU - Crescent
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Posted Mar 22, 2001 by Monsignore Pizzafunghi Bosselese
Oh, hi there!
I found your entry via the Writing Workshop and posted some comments there. And yes: shouldn't have any problems getting into the guide 
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Posted Mar 22, 2001 by Lonnytunes - Winter Is Here
Excellent work. It reminded me of Fermat's Last Theorem http://www.bbc.co.uk/h2g2/guide/A521966 which I recently spent a few hours on 
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Posted Mar 22, 2001 by Dogster
Hi everyone, glad you liked it, thanks for the approval!
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Posted Mar 22, 2001 by Gnomon [See A60420098 for details of new sign-in system]
Sorry to strike a jarring note, but I don't like it. I read the whole thing and found that the "maths" bit is just the same as the "non-maths" but with a few symbols added. Entire sentences in it are copied from the non-maths bit. It really doesn't give any more detail, it doesn't attempt to prove anything. It justs states the same thing in different terms. I expected it to provide some extra insight into understanding the theorem, but it didn't.
I think you would be better getting rid of the maths bit entirely. Mention at the start that the proof of the theorem involves some heavy mathematics and that you are not going to attempt it here. Then try and explain the intuitive bit in a little more detail.
Finally, in the closing paragraph, you could mention that although no system is perfect, there are some systems such as "proportional representation by the single transferable vote" which are generally reckoned to be much fairer than the "first past the post" system in use in the UK and the US. These systems are in use in most countries in Europe.
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Posted Mar 22, 2001 by Crescent, ACE
No, no, no - I would say leave the maths bit in. I think the whole point with it was that it was so similar to the intuitive section that it helps you get your head around the math. It also IS the actual Theorem, or at least part of it. As I said before I think this should have no bother getting into the Edited Guide, as is. Well, IMHO Until later....
BCNU - Crescent
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Posted Mar 22, 2001 by HenryS
I agree with Gnomon to some extent - the maths bits dont really add much beyond putting it into formal language in parts. Looks like it could be made much cleaner by numbering the conditions from the intuitive section, and just having the formal translations to each condition in the maths section. That way you avoid the repetitions.
It would be nice to see some sort of sketch proof in the maths section, though maybe its too long. Otherwise there doesn't seem that much point in the maths section. The intuitive section is pretty precisely defined as it is.
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Posted Mar 22, 2001 by Crescent, ACE
The Guide should have some actual stuff in it, not just comments on stuff. It should contain the Theorem, not just a comment on the Theorum and how it works. The author warns that there is heavy maths in it, if you do not like it, then don't read the maths bit. Dogster keep it as is, I say Until later....
BCNU - Crescent
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Posted Mar 22, 2001 by HenryS
Hey, I'm all for heavy maths  . I'm saying the maths bit should be there, and it should (ideally) do more than restate what's said in the intuitive section.
Oh, good entry btw
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Posted Mar 22, 2001 by Dogster
Hi there, I'm not sure of the wisdom of putting the entire proof in, although I could certainly add a bit about how the proof works. Essentially it's just Condorcet cycles, the proof just shows that Condorcet cycles are inevitable. Well, OK, it's a bit more complicated than that, but you get the idea.
Gnomon, the idea of the maths / non-maths sections was that people who were comfortable with the maths could read the maths section and not the intuitive section, and people who weren't could just read the intuitive section. Something for everyone. Perhaps I should make this more explicit in the introductory paragraph? Alternatively, I could do as HenryS suggests, perhaps put the formal definitions in footnotes?
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Posted Mar 22, 2001 by iaoth
Just a bit of nitpicking:
When you write "We have a society of citizens, C1, C2 and so on.", that could mean that we have an infinite number of citizens. Why not replace "and so on" with "up to Cn"? Obviously you'd need to use constants for policies and preference relations (maybe k, m and n?).
Also, I'd call that one citizen who changes his mind Ci.
Aparts from that, it's a really nice entry. However, I would really like to see a proof, if it's not too long and too hard to follow.
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Posted Mar 23, 2001 by Dogster
Yes, there will always be a finite collection of citizens, but I think that the policies could be infinite, I'll have to go back and check the proof to see if that's true or not. I'll have another look at the proof as soon as I get a chance and see if I want to include it...
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Posted Mar 23, 2001 by Dogster
Hi everyone, I've made a few changes to this entry, tell me what you think. The main changes are that I've included a sketch proof (some results which are intuitively obvious but strictly speaking require proof are left out since the proofs of these could easily double the length of the entry). The other main changes are structural, I've moved the sections around a bit so that all the intuitive stuff is at the beginning and the maths stuff at the end, so as not to frighten off people who don't like maths. Lastly, I added a couple of sentences saying that just because we can't have a perfect voting sytem doesn't mean we shouldn't try and get a better one, and added a link to an interesting web page about proportional representation.
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Posted Mar 23, 2001 by Gnomon [See A60420098 for details of new sign-in system]
That's better! Now that you have stated the proof, there is some excuse for including all the maths in the "Precise" discussion.
Well done!
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Posted Mar 23, 2001 by iaoth
Cool. Much better now that the proof is in there.
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Posted Mar 23, 2001 by HenryS
Yep. I'd heard of the result before but not seen the proof, but I can see the idea now. Where's them scouts?
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Posted Apr 9, 2001 by Crescent, ACE
Congratulations, your fine Entry has passed through Peer Review, with flying colours, and is on its way to a SubEd, as we speak The SubEd is the next stage of becoming an Edited Guide Entry, and it can take some time, so patience is needed However saying that, sometime, fairly soon, in the future your Entry should make it to the Front Page Again, congratulations - THIS THREAD IS NOW CLOSED
BCNU - Crescent
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Posted Apr 11, 2001 by BBC auto-messages
Editorial Note: This thread has been moved out of the Peer Review forum because this entry has now been recommended for the Edited Guide.
If they have not been along already, the Scout who recommended your entry will post here soon, to let you know what happens next. Meanwhile you can find out what will happen to your entry here: http://www.bbc.co.uk/h2g2/guide/SubEditors-Process
Congratulations!
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