[EM] Introduction (cont.)

Richard Moore rmoore4 at home.com
Fri Aug 10 19:18:08 PDT 2001

Roy One wrote:
> Richard Moore wrote:
>>We weren't really thinking much about low-quality 
>>information cases. It's always good to have someone come 
>>along with fresh insight on these matters, so thanks!
> Thanks for putting all the effort into bringing me up to speed. You
> do make good arguments for the applicability of strategy, even when
> the probabilities are poorly known.

I did make one significant mistake, however: In the 
zero-info case, it is *still* the best strategy to vote full 
scale, using the above-the-mean strategy (same as Approval). 
The reason is that the deltaP matrix still exists for 
zero-info; it's just highly symmetric in that case. It looks 
like this (example for four candidates, with scaling since 
only relative values are important):


You multiply this matrix by the vector of your utilities, 
and that gives you your strategic values. All 
strategically-positive candidates get a full approval vote 
and all strategically-negative candidates get a full 
disapproval, to maximize the total strategic value.

(An example of a method where zero-info results in sincere 
votes is Borda.)

The addition of (high-quality) information only shifts the 
threshold, so you approve more or fewer candidates.

But I agree it's possible that with low-quality information 
there might be candidates you won't be able to decide what 
to do with. So there will sometimes be a transition region 
containing candidates that can't easily be assigned a 
full-scale vote. These are the ones we would vote sincere 
ratings for.

> In my mind, the feedback loop should be similarly self-defeating. Of
> course, it's possible that chaos theory isn't as neat and tidy as I
> want it to be (or that it isn't even the right buzzword).

I imagine in some cases the feedback will be negative and 
therefore stabilizing. In others, it will be positive but 
drive the system into saturation, which will then cause the 
system to stabilize with saturated values. In others, 
feedback will be positive but cause instability (oscillation).


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