[EM] Fw: borda count

Rob Lanphier robla at robla.net
Sat Nov 6 23:00:58 PST 2004

Steve Eppley wrote:

>Mike (R?) asked:
>>Here's a similar question: Does it matter if we use 
>>a Borda count of 3-2-1-0 (Highest score wins) or 0-1-2-3
>>(lowest score wins)? I thought I read somewhere they
>>weren't necessarily symmetric, but I can't think of 
>>any counterexamples so I might be mistaken. 
>Again, as Stephane pointed out for 4-3-2-1 vs 3-2-1-0,
>it depends on how non-strict orderings are handled.
>Assuming all votes are strict orderings, "3-2-1-0 
>highest wins" elects the same winner as "0-1-2-3 
>lowest wins."
Based on my recollection of how Saari's version of Borda works, I 
believe the points allocated are actually the square of the previous 
rank (e.g. 8-4-2-1), or some other non-linear method which mitigates 
some of the truncation problems.   It's been so long since I've paid any 
attention at all to Borda, and I've only understood it well enough to 
feel satisfied that I've given it a fair look, so I could be mistaken.

In reading some of Saari's stuff, I've become convinced that he has 
figured out a proper application of Borda, which is in artificial 
intelligence type applications (e.g. reconciling multiple sensors with 
different readings).  In environments where "voters" can be trusted not 
to engage in strategic manipulation, it probably does pretty well, and 
may indeed outperform Condorcet-compliant methods as Saari claims.  
However, it's prety clear that "voters" can't be human or agents of 
humans with a stake in influencing the result.


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