[EM] Instant Runoff Normalized Ratings

[Kevin Venzke]

Brian,

 --- bql at bolson.org a écrit : 
> Every voter casts a rating of each choice on a scale of -1.0 to 1.0 or
> some equivalent scale. Each voter's voting power is normalized, each
> rating is divided by the sum of the absolute values of the ratings so that
> each voter has a voting power of 1.0 . All of the normalized ratings are
> summed. The choice with the lowest rating sum is disqualified. On
> successive iterations votes are re-normalized without disqualified
> choices, redistributing a voter's voting power to the still-active choices
> in proportion to the original vote.

This is the first I've heard someone suggest eliminating based on a vote that you 
have to split into pieces.  It would be better if you let people give whatever ratings 
they want, and then just *rescale* them to 0.0-1.0.

That method would be very similar to Approval-Elimination Runoff.  In AER the
voter specifices either 1.0 or 0.0 for each candidate, although after each elimination
there is no rescaling or renormalization or anything.

> Monotonic: yes. At all stages a change in a vote directly and
> proportionally changes the outcome.

Yikes.  Your method is not monotonic for the same reason IRV isn't monotonic.
Suppose pairwise A beats B, B C, and C A.  C is eliminated and A wins.  In IRV or
your method, giving more support to A can take votes away from B and cause B
to be eliminated instead of C.  Then C beats A.

> Participation: Yes. There's no way for a ballot with a higher X rating
> than Y rating to contribute more to Y's sum than X's. Thus an additional X
> > Y ballot cannot elect Y over X.

You should consider more than individual rounds in isolation.  These arguments
for Monotonicity and Participation are also true for IRV in individual rounds.

AER is monotonic (partly because there is no rescaling), but the only methods I know 
of which meet Participation are FPP, Approval, CR, Borda, and Woodall's Descending 
Coalition methods.

Kevin Venzke
stepjak at yahoo.fr


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