Welcome Guest!
 Ranked Pairs
 Previous Message All Messages Next Message 
Re: Bringing proportional representation to ranked pairs  Blake Cretney
 Nov 16, 2000 22:14 PST 
"Bram Cohen" <br-@gawth.com>, on the subject of 'Re: Bringing
proportional representation to ranked pairs', is quoted as:

 Here's a quick rundown of how Weighted Ranked Pairs meets (or
doesn't) various standards and criteria -
--snip--
 Consistency Criterion - I'm pretty sure it passes this one just fine.

That seems unlikely. The Consistency criterion says that if you divide
the electorate into two arbitrary groups, and find the winner for each
group, and the winner is the same, then this should also be the winner
for the combined groups. That's obviously true of a method like
plurality, or in fact, any positional method. It is impossible to meet
both the Condorcet and Consistency criteria. It's pretty obvious which
I choose. I think I describe why in the Average Ratings section of my
Ranked Pairs site. Anyway, I'll sketch the outline of a proof that no
method can pass Condorcet and Consistency.

40 A B C
35 B C A
25 C A B

Now, the method has to select one of these 3 candidates. Let's say it
picks A. Notice that C beats A pairwise. Add votes like this,

51 A C B -- group 1 winner , candidate beating group 1 winner, other
candidate
49 C A B -- candidate beating group 1 winner, group 1 winner, other
candidate

When you add them together, you'll find that C is the CW. However, for
consistency A must win. To complete the proof, you have to form a new
group 2 for each other possible winner of group 1, which are B and C.
By proving that the winner can't be any of them, you know that Condorcet
and Consistency are in contradiction.

IRV also fails consistency in this example.

---
Blake Cretney
	
 Previous Message All Messages Next Message 
  Check It Out!

  Topica Channels
 Best of Topica
 Art & Design
 Books, Movies & TV
 Developers
 Food & Drink
 Health & Fitness
 Internet
 Music
 News & Information
 Personal Finance
 Personal Technology
 Small Business
 Software
 Sports
 Travel & Leisure
 Women & Family

  Start Your Own List!
Email lists are great for debating issues or publishing your views.
Start a List Today!

© 2001 Topica Inc. TFMB
Concerned about privacy? Topica is TrustE certified.
See our Privacy Policy.