[EM] Finding the probable best candidate?

[Richard Moore]

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