<html><head></head><body>Anthony,<br>
<br>
Some, but not all issues, are going to have the correlation you are<br>
talking about. Given that there are two issues that are really just<br>
facets of some third issue, we can just let that third issue be<br>
one of the two dimensions in my model. But surely there will be<br>
some fourth issue that doesn't correlate with the first two.<br>
<br>
Nevertheless, it's not a major change. I could make the type of distance<br>
a command-line option so that it will be easy to test the effect of<br>
changing it. Not my first priority, though, since I still have to:<br>
<br>
1. Code more methods. Actually, I've done several already, but in the<br>
Condorcet category I've only done Plain Condorcet. I will probably<br>
add SSD and stop there. The sim will then include Random Choice,<br>
Random Ballot, Plurality, IRV, PC, SSD, Borda, and Approval. I also<br>
have to add tie-breakers for the methods I've implemented.<br>
2. Code front-runner strategies for Approval and Plurality. My chief<br>
interest at this point is to determine how sensitive Approval is to<br>
voter strategy.<br>
3. Code non-uniform distributions. Right now, I've only done uniform<br>
distributions, and all methods except the random ones and Plurality<br>
have about 90% success rate or better at picking the candidate with<br>
highest potential. Plurality is somewhere in the 60-70% range (even<br>
IRV gets around 90%). I expect a lot to change when the distributions<br>
of voters and candidates both have some modality.<br>
<br>
On the front-runner strategy question, I will probably select two<br>
front runners by multiplying each candidate's majority potential<br>
by a random number between 1 and 2. That way, centrist candidates<br>
are favored to be front runners, but the effect of non-issue factors<br>
will be modeled, too.<br>
<br>
Instead of the two non-zero info strategies for Approval that I<br>
previously suggested, I now plan to implement a single strategy,<br>
which will be to adjust the voter's rating of each front runner up<br>
or down (up for the preferred front runner, down for the other)<br>
before applying the above-the-mean strategy. I haven't decided<br>
on the exact algorithm for this adjustment, though.<br>
<br>
Richard<br>
<br>
<br>
Anthony Simmons wrote:<br>
<blockquote type="cite" cite="mid:3.0.5.16.20010521163029.24576c4c@krl.org"><pre wrap="">Usually, if there are a whole lot of factors (as in "factor<br>analysis"), they aren't independent. For example, you'd<br>imagine that if I'm morally opposed to ice cream, I'd most<br>likely be opposed to frozen yogurt as well. If you make one<br>the X coordinate and one the Y coordinate, and plot the<br>positions of actual moral philosophers, you'd expect to find<br>a pretty steady correlation between X and Y, with most of the<br>pack along a straight line through the origin and<br>representing a third factor (a derived one in this case), Z,<br>"moral correctness of frozen confections".<br><br>It's reasonable to consider Z as basic as X and Y, so we'd<br>like to be able to rotate our graph so that this factor is<br>horizontal or vertical and becomes one of the coordinate<br>axes, without changing any of the relationships between the<br>variables or the distances between points on the Z line; we<br>wouldn't want a policy to become more or less extreme on our<br>scale just because we rotated the scales.<br><br>Using the root-sum-of-squares distance makes all of this very<br>clean. Of course, you could preserve distances in other<br>ways. If you were using the the city block distance, and you<br>rotated the coordinates so that (1, 1) ended up on the X<br>axis, you could stretch it to (2, 0). After all, if you're<br>not using Euclidean distance, then there's no requirement<br>that (1, 1) rotates onto (1.414, 0). But when you throw out<br>the way we normally measure distances, you throw out the<br>underlying geometry, and we all know that the most important<br>thing about any measurement is the underlying geometric<br>aesthetics.<br><br>Another consideration: In the illustration above, the data<br>actually lies along one dimension, embedded in a two-<br>dimensional space. If we were to add popsicles to ice cream<br></pre>
</blockquote>
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