<html><head></head><body>I ran some sims to compare L1 and L2 distance. This is still using a uniform<br>
distribution, and I'm still debugging, so these are very preliminary<br>
results (and there are only 500 random trials so there's still a significant<br>
error margin). But a funny thing happened when I did the L2 sims.<br>
The success rate for both Plain Condorcet and SSD went from about<br>
96% to 100%. Borda and Approval also improved, while IRV and<br>
Plurality got worse.<br>
<br>
I suspect that the improvement results from a lower incidence of tied<br>
rankings with L2 distances. This is because the population of voters<br>
and candidates both have integer policy values, so L1 distances are<br>
always integers. Restricting the distances to integers makes tied ratings,<br>
and hence tied rankings, much more likely. I suspect if I rounded the<br>
L2 distances to integers I would see the success rates go back down.<br>
<br>
I still don't know if L1 or L2 is more typical of how voters think, but<br>
I'm leaning towards L1. If you disagree with a candidate only on one<br>
issue, that's one strike against the candidate. If you disagree with him<br>
on three issues, that's three strikes. But I also think there's a point of<br>
saturation, where if you disagree with him on nine issues, a tenth isn't<br>
going to make a big difference. So for a small number of issues, I<br>
still prefer L1.<br>
<br>
I didn't see any difference between PC and SSD, even with L1 distances.<br>
I suspect I haven't run enough trials for a case of different results to turn<br>
up. Non-uniform distributions might differentiate these too, as well,<br>
but I can't really predict what effect they will have.<br>
<br>
It shouldn't be surprising that Condorcet methods do so well, since<br>
the standard being used here, majority potential, is a majoritarian<br>
standard (another difference from SU).<br>
<br>
-- Richard<br>
<br>
<br>
Anthony Simmons wrote:<br>
<blockquote type="cite" cite="mid:3.0.5.16.20010522151449.0877df0a@krl.org"><pre wrap="">I think what you're more likely to find is factors that are<br>correlated, but not perfectly. I once heard a sociologist<br>say that if you're doing sociology, always be sure to include<br>socio-economic class as one of the variables, because it's<br>correlated with everything. In an election for something<br>like legislative office, I'd expect everything to be<br>correlated with political party. Problem is, they won't be<br>colinear, and they won't be independent.<br></pre>
</blockquote>
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