<br><br><div class="gmail_quote">2010/6/8 Kevin Venzke <span dir="ltr"><<a href="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</a>></span><br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
Hi Warren,<br>
<br>
--- En date de : Mar 8.6.10, Warren Smith <<a href="mailto:warren.wds@gmail.com">warren.wds@gmail.com</a>> a écrit :<br>
<div class="im">> comments by WDS<br>
><br>
> 1. I think using utility=-distance<br>
> is not as realistic as something like<br>
> utility=1/sqrt(1+distance^2)<br>
><br>
> I claim the latter is more realistic both near 0 distance<br>
> and near<br>
> infinite distance.<br>
<br>
</div>Why would that be? Do you mean it's more intuitive?<br>
<div class="im"><br>
> 2. It has been argued that L2 distance may not be as<br>
> realistic as L1 distance.<br>
> L2=euclidean<br>
> L1=taxicab<br>
<br>
</div>That's interesting. I wonder what arguments were used.<br></blockquote><div><br>I haven't seen anyone else argue this, but I've always found taxicab distance more reasonable. Separate issue dimensions add linearly. If somebody's going to put/take $3 in/from my left pocket and $4 in/from my right pocket, that's a total of $7, not $5.<br>
</div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div class="im"><br>
> 3. Your "candidates bolted in place" (in locations selected<br>
> manually)<br>
> at some point needs to be replaced by an outer loop which<br>
> chooses<br>
> their locations from some distribution, and finds average<br>
> bayesian<br>
> regret over all candidate locations.<br>
> If I manually choose locations, I can probably make nearly<br>
> any method look like<br>
> "the best" or "worst" method... that is<br>
> kind of anecdotal evidence<br>
> versus real evidence.<br>
> (Not that the anecdotes are uninteresting.)<br>
<br>
</div>Well, it would be better to cycle over some of the locations, but taking<br>
the average over all possible locations would not be very good evidence<br>
either, since not all locations are equally likely.<br></blockquote><div><br>OK, so you need to have some probability density function. But systematically, not just by picking scenarios that seem reasonable. <br></div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<br>
On the other hand if you select a scenario that seems likely to occur<br>
in practice, I think that is good and useful evidence, especially if you<br>
can't refute your conclusion by changing the scenario slightly.<br>
<br>
If you stick to reasonably realistic scenarios I really doubt you could<br>
find a way to make any method you like best or worst.<br>
<div class="im"><br>
> 4. your results look interesting but I do not know what a<br>
> lot of your<br>
> voting methods are, e.g. QR, VFA, SPST, C//A, etc. <br>
> Too abbreviated.<br>
> Need to supply a key.<br>
<br>
</div>Of these:<br>
C//A: Elect the CW if extant, else the Approval winner.<br>
(Condorcet//Approval)<br>
VFA: This is what you have called Venzke Disqualified Plurality.<br>
Elect the FPP winner except that when more than half of the voters<br>
rank this candidate strictly last, instead elect the second-place FPP<br>
candidate.<br>
SPST: This is the same as VFA except that when the FPP winner is<br>
disqualified, his supporters' preferences are transferred, instead of<br>
simply electing the second-place candidate.<br>
QR: This is a new method by me called Quick Runoff. Elect the candidate<br>
with the most first preferences who does not have a full majority pairwise<br>
loss to the very next candidate in first-preference order.<br>
<br>
There is also CdlA (Conditional Approval) which is a method where voters<br>
gradually add more of their preferences as a result of disliked options<br>
being the vote leader in a "round."<br>
<div class="im"><br>
> 5. some conclusions, like RangeNS is better than IRV and<br>
> IRV-tr and C//A, look<br>
> fairly solid (happen in all your sims*); others, like<br>
> Bucklin is<br>
> better than RangeNS,<br>
> look inconclusive (happen in some of your sims, but reverse<br>
> happens in<br>
> other sims)<br>
><br>
> *There was one exception, but it had very small regret for<br>
> all methods<br>
> other than MMPO and ApprZIS.<br>
<br>
</div>I don't try to draw many conclusions at this point simply because not<br>
many scenarios have been analyzed. I mean four of the scenarios I posted<br>
were only 1D. And most of the utility differences were very small.<br>
<font color="#888888"><br>
Kevin Venzke<br>
</font><div><div></div><div class="h5"><br>
<br>
<br>
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</div></div></blockquote></div><br>