[EM] bug in electowiki

[stephane.rouillon at sympatico.ca]

Taking the infinite norm Linf of a vector is
equivalent to take the max of the absolute values of its components...
> 
> De: Brian Olson <bql at bolson.org>
> Date: 2005/10/14 ven. PM 03:03:01 GMT-04:00
> À: wds at math.temple.edu (Warren Smith)
> Cc: election-methods at electorama.com
> Objet: Re: [EM] bug in electowiki
> 
> On Oct 14, 2005, at 8:38 AM, Warren Smith wrote:
> 
> > I edited the http://wiki.electorama.com/wiki/ 
> > Instant_Runoff_Normalized_Ratings
> > page
> 
> The edit added some mathy stuff about normalization, and this:
> 
> > If it were not for the "runoff," then generally the best strategy  
> > in IRNR[p] is simply to (strategically) plurality-vote, i.e. giving  
> > all candidates except one a rating of zero. This is true whenever  
> > there are two "frontrunner" candidates judged to be far more likely  
> > to win than the others and p is finite (then vote for the best  
> > among these two), and its truth is unaffected by the runoff by  
> > induction on rounds.
> >
> > If p is infinite, IRNR without the runoff would just become  
> > equivalent to range voting in the range [-1, 1] with an extra rule  
> > demanding that the best- or worst-rated candidate must have a  
> > rating with absolute value 1. The best strategy is then the same as  
> > for approval voting and again this statement's validity is  
> > unaffected by adding the runoff.
> 
> I'm kinda confused about this commentary. I think it doesn't directly  
> pertain to IRNR, but rather IRNR if you break it.
> 
> I'll accept for now that all-on-one is the correct strategy for a  
> normalized ratings vote. I think I demonstrated that to myself once.  
> But still, why comment on IRNR without the IR on this page?
> 
> Is the L-infinity normal interesting or useful? Divide the ratings by  
> the infinity-root of the sum of the ratings raised to the infinity?  
> It's been too long since I studied such things and I can't tell what  
> that operation would practically _do_ to some data.
> 
> I think practically L1 and L2 are all we need.
> 
> So, your commentary may be correct, but, um, so what?
> 
> Brian Olson
> http://bolson.org/
> 
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