[EM] Democratic symmetry

[Rob Lanphier]

On Tue, 7 Mar 2000, Craig Carey wrote:
> At 21:50 06.03.00, Rob Lanphier wrote:
>  >The method that Dr. Saari purports as the fairest method, the Borda count,
>  >presupposes a very narrow definition of fairness.  While focusing on
>  >abstract concepts of symmetry and cancellation, he misses the boat on more
>  >important criteria, such as the "Majority Winner Criterion", which states
>  >that if a strict majority of the voters rank a particular alternative as
>  >their first choice, then the voting method must select that alternative
>  >as the unique winner [2].  Nearly all other methods proposed by electoral
>  >reformers pass this criterion, not to mention first-past-the-post.  The
>  >Borda count is one of the few methods that doesn't.
> 
> Standard(?) Borda would actually pass that test. The Economist article was
>   quoted as saying: "Also if voters are not familiar with all candidates, and
>   do not rank them all, the unassigned points must be divided up evenly
>   between the unranked candidates.".

That doesn't matter, does it?  Very simple example:  4 candidates (A, B,
C, and D), 3 voters.  Here's the ballots:

           Points for A    Points for B    Points for C    Points for D
A>B>C>D         4               3               2               1
A>B>C>D         4               3               2               1
B>C>D>A         1               4               3               2

Totals:         9              10               7               4


B wins under Borda, even though B would lose in FPTP, IRV, Condorcet, and
most other methods.

Rob
------
Rob Lanphier
robla at eskimo.com
http://www.eskimo.com/~robla