[EM] Instant Runoff Normalized Ratings

[bql at bolson.org]

Hi, I've been reading the list for a couple weeks. I got into voting
theory a couple years ago after reading a Science News article. It
described IRV and I thought "Gee that's convoluted. I could do better with
a simpler procedure."

I wrote a simulator and ran a few million elections. The results are at
http://bolson.org/voting/

If your favorite system isn't in there, tell me about it and maybe I'll
add it to the next round.

I'm writing today to tell about my new favorite system:

Instant Runoff Normalized Ratings
(IRNR)

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.

The handiest checklist of qualities I could find is:
http://electionmethods.org/evaluation.htm

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

Condorcet: yes-ish. I believe that IRNR is more powerful than Condorcet
because it also addresses the degree of preference and not just the order.
Otherwise, IRNR and Condorcet both address the whole votes of the whole
electorate at once, and if the ratings contain no more information than
rankings, IRNR should find the same winner as Condorcet.

Generalized Condorcet: "yes". I wave my hand and say, yes, of course it
will do the right thing.

"Strategy Free": maybe not. A 51% majority could rate candidate A at 0.02
and B at 0.01, 49% could vote B 1.0 and A -1.0 . B would win. Does this
violate SFC? Is it a just system anyway? If IRNR were modified to expand
votes out to a 1.0 to -1.0 scale before normalizing them the 51% vote
would translate to A=1.0 and B=-1.0; A would win.

GSFC: no comment at this time. See Strategy Free.

Strong Defense Strategy: Yes. A majority casting votes can win without
mis-ordering any votes. Rating their favorite at 1.0 would achieve this.
BUT, there might be a compromise choice that the majority and some of the
minority rate at 0.8 which could win. Perhaps this is an imprecision in
the wording of SDS. The compromise choice is backed by a super-majority.
Does SDS actually mean that the winner should be picked by the largest
majority?

Weak Defense Strategy: Yes. A majority casting ratings of -1.0 for their
least favorite choice would prevent the election of that choice. On the
first round of disqualification this choice would have the lowest summary
rating and be disqualified. UNLESS, there was a more widely but less
vociferously disliked choice, comparable to the positive case in SDS. Are
we talking largest majorities here?

Favorite Betrayal Criterion: Yes. This is the most important criterion to
me. I believe IRNR provides no incentive to vote other than honestly. The
decision made by IRNR is always in proportion to the ratings cast by a
voter, so the voter is best served by ratings which are in line with their
true desires. Because of the proportional nature of IRNR, there are not
the singularities that IRV suffers.

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.

Summability: No. Because this is an instant runoff method, all votes must
be centrally collected and run together. Computationally inconvenient, I
know. It is not even representable as a candidates-factorial size array as
IRV could be.


Brian Olson
http://bolson.org/