[EM] Finding the probable best candidate?

[Forest Simmons]

On Tue, 12 Feb 2002, Richard Moore wrote:

> Forest Simmons wrote:
> 
> > That still leaves open at least two important questions.
> > 
> > (1) How do we ascertain voter utilities accurately? The uncertainty
> > principle operates here; the measurement process inevitably introduces
> > uncertainties.  How do we minimize this uncertainty to the extent
> > possible?
> > 
> > (2) Voter utility is a vector valued function.  Which scalar combination
> > of components of that function are we trying to maximize?  Their sum? 
> > Their median value?  Their mode? Their sum of squares?  Their minimum? 
> > Their lowest quartile value?  The distance from 100 percent utility in all
> > components as measured by some metric or another? 
> > 
> > There are infinitely many possible choices for (2), and they all affect
> > (1).
> > 
> > How many methods have actually been designed with these considerations at
> > the forefront?
> > 
> > How many methods, by sheer luck or the good intuition of the inventor,
> > stand up reasonably well under the light of these questions?
> > 
> > Not many.
> > 
> > Forest
> 
> 
> L2-normalized CR, under zero information situations, gives no incentive
> to the voter to exaggerate or distort ratings. Of course, the presence
> of information about outcome probabilities will introduce such incentives,
> and may even cause inversion of preferences. Which Approval avoids, but
> only by sacrificing resolution. Approval might be thought of as the best
> first-order approximation. It seems to me that, in non-zero-information
> situations, any higher-order approximation will introduce errors that
> could be even more significant than the quantization error in Approval.
> Since it only introduces quantization noise, I suspect that Approval
> does a good job of averaging out the influence of information-influenced
> strategies, given a diverse electorate. (Perhaps a good electronics
> analogy would be a delta-sigma converter -- think of the 1-bit D/A
> converters found in many CD players.)
> 
>   -- Richard
> 

Perhaps using an L_n norm with n somewhere between 2 and infinity (which
corresponds to the max norm that yields regular CR which is strategically
equivalent to Approval) would be a good compromise. The n could be
adjusted to take into account the relative importance of quantization
error and potential for manipulation in the application. 

Forest