Taking the infinite norm Linf of a vector is equivalent to take the max of the absolute values of its components... > > De: Brian Olson <[EMAIL PROTECTED]> > Date: 2005/10/14 ven. PM 03:03:01 GMT-04:00 > À: [EMAIL PROTECTED] (Warren Smith) > Cc: [email protected] > 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/ > > ---- > election-methods mailing list - see http://electorama.com/em for list info >
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