Steve Eppley wrote:
Mike (R?) asked: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.
Here's a similar question: Does it matter if we use a Borda count of 3-2-1-0 (Highest score wins) or 0-1-2-3Again, as Stephane pointed out for 4-3-2-1 vs 3-2-1-0,
(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.
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."
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.
Rob
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