[EM] Some brief campaign argument (Approval)

Martin Harper mcnh2 at cam.ac.uk
Sat Apr 21 04:13:27 PDT 2001

Richard Moore wrote:

> By the way, for the mathematically inclined, I think I was mistaken --
> I believe the term I meant is Linfinity-normalized. In case I'm still wrong
> (it's getting late) I'll clarify this: I mean that the utilities in each 
> set are
> shifted to center on the origin and then scaled by a factor equal to the
> maximum utility in the set. So instead of (100, 40, 40, 0) we would have
> (1, -1/5, -1/5, -1). The point is that each set of utilities should have the
> same minimum and maximum.

This post makes me wonder if there's a better normalisation to use... 
L-infinity is obviouly the simplest, but L-1 {sum of deviations from 
mean} and L-2 {standard deviation} might be equally valid.

Here's an example:

vote 1&2: A 100%, B 50%, C 50%, D 0%

vote 3: A 0%, B 0%, C 100%, D 100%

vote 4: A 0%, B 100%, C 0%, D 100%

L-infinity methods would aim to declare this election a 4-way draw, 
whereas L-1 and L-2 methods would aim to declare candidate A as the 
winner. Which is right?

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