User talk:Waisbrot

Arrow's theorem[edit]

if Dave is ranked dead last by each individual voter, then the example will not violate IIA in any popular balloting system [1]

Under the Borda count, it is possible that introducing a candidate who is ranked last by every voter will change the winner from one preexisting candidate to another.

CRGreathouse (t | c) 19:35, 20 February 2008 (UTC)[reply]

I don't see it. Can you elaborate? There are n voters, who have ranked two candidates A and B. A has a votes and B has b votes where a > b. Add a third candidate C, ranked last by every voter. C therefore has n points. Vote counts for the other candidates are also altered as their score increases: A has a + n points, and B has b + n. Nate (talk) 00:59, 21 February 2008 (UTC)[reply]

Suppose ACB has 60 votes, CBA has 18 votes, and BCA has 22 votes. The Borda scores are A: 120, B: 122, and C: 58. Suppose now that candidate D, the Devil incarnate, enters the race. Every voter ranks the Prince of Lies last, because his platform involves roasting everyone alive. The new Borda totals are A: 220, B: 162, C: 218, D: 0. Now A is the winner instead of B.

I encourage you to total these yourself. Using 3/2/1 gives the same results as using 2/1/0 as I have done, but there's no need to trust me on that -- the example speaks for itself. There are actually many more examples of this kind of nonsense in the Borda count, many of which don't require the numbers to be so close.

CRGreathouse (t | c) 01:34, 21 February 2008 (UTC)[reply]

... A B C..... A.. B.. C


60: 2 0 1 -> 120.. 0. 60
18: 0 1 2 -> ..0. 18. 36
22: 0 2 1 -> ..0. 44. 22
TOTALS ......120. 62 118 A WINS

... A B C D..... A.. B.. C.. D
60: 3 1 2 0 -> 180. 60 120.. 0
18: 1 2 3 0 ->. 18. 36. 54.. 0
22: 1 3 2 0 ->. 22. 66. 44.. 0

TOTALS........ 220 162 218.. 0 A WINS

What am I doing wrong? It looks to me that there was an error in the original example, purporting to show B winning. As expected, adding 1 to all vote values does not change the relative outcome. --Abd (talk) 03:33, 21 February 2008 (UTC)[reply]

Abd's numbers look correct to me (except that C's subtotal from the first row is 60). How are you calculating the scores for B and C?Nate (talk) 08:05, 21 February 2008 (UTC)[reply]

I fixed the error mentioned above. Notice that all that adding D does is to add 100 to each total for A, B, and C. It is adding D into the middle for some voters that causes problems with Borda. The Devil doesn't cause any problems if everyone rejects him! --Abd (talk) 21:30, 21 February 2008 (UTC)[reply]