[EM] Borda- Young example

[Paul Dumais]

I'm going to try Paul's Borda Count #2 on this:

DEMOREP1 at aol.com wrote:
> 
> "Condorcet's Theory of Voting" by H.P. Young (82 American Political Science
> Review 1231 (1988) has the following Borda example by Prof. Young--
> 
> Table 5  A Voting Matrix of Six Alternatives and 100 Voters
>         a      b       c       d       e       f     Borda Scores
> a     --     51     54     58     60    62     285
> b     49     --    68     56     51    58      283
> c     46     32    --     70     66     75     289
> 
> d      42     44    30    --   41      64     221
> e     40      48    34    59    --    34      215
> f      38      42    25   36     66    --      207
> 
> a, b and c each beat d, e and f
> 
> Borda produces cabdef.

BN = 500, eliminate d,e,f because they have BC<BN/2
BN = 200, BC: A:105, B:117, C:78 eliminate c because BC < BN/2
BN = 100, BC: A:51 B:49 eliminate b because BC < BN/2

We have a ranking of A>B>C.

We could continue to rank the lower candidates in the same way.
BN = 200, BC: D:105 E:93 F:112 eliminate e
BN = 100, BC: D:64 F:36 eliminate f

final ranking: A>B>C>D>F>E
 
> If only a,b,c were the choices (the upper left part of the matrix) then the
> Borda result would be b 117, a 105, c 78 or bac (the opposite of the first
> Borda count).
> 
> Prof. Young says in effect that introducing inferior alternatives may/can
> manipulate the Borda choices among the superior alternatives.
> 
> Choice a is the Condorcet winner (beats each alternative head to head).

Paul's Borda Count #2 (PBC2) appears to yield a condorcet winner if one
exists. It also seems that inferior candidates do not affect the ranking
of superior candidates. This method is only one day old (provided it
doesn't already exist). I think it needs more tests to see how it
measures up. Does anyone like it?

-- 
Paul Dumais