[EM] IRNR

[bql at bolson.org]

On Mon, 17 May 2004, Curt Siffert wrote:

> Brian - it sounds like zero is meaningless in IRNR, correct?

On the "like ... dislike" scale of ratings, 0.0 is "no opinion".

> If you
> normalized between 1 and 0 rather than 1 and -1, the results would be
> identical?

I'm not sure of that, but I think adding the negative sign range does
change the expressiveness of the system and the results that can be gotten
from it. Running several thousand simulated elections, I tried both a
-1..1 IRNR (the native format of the sim) and a 0..1 shifted version, and
they were almost identical but the 0..1 shifted version was slightly
different, slightly less efficient.

> Or, if I vote 0, -0.25, -0.5, -1; that's the same as if I
> vote 1, 0.5, 0, -1.  Even though the first time I'm basically saying
> "none of the above", where the second time I'm saying I hate only one
> of them.

Right, as a practical matter it's always open to debate whether we should
be able to junk-vote an election and force a new one, or whether the
system should always just grab the 'best' even if that best isn't actually
positive. My implementation declares any 'best' to be the winner.

Elsewhere in my post I described explicitly doing scaling like you
describe to optimize a voter's vote for them when they don't know how to
vote best to use the system. Your vote is different if your ratings are on
both sides of 0.0 than if they are all positive or all negative.

*49 -1,1
*51 1,-.01

A wins

*49 -1,1
*51 1,.01

B wins, although a majority prefers A.

> I haven't looked at this closely but wonder if there's a way to keep
> zero meaningful.  Maybe you'd also sum up all the raw votes and
> immediately dump all candidates with sums below zero, before doing the
> normalized sums and IRV stuff.  That probably brings in more strategy
> problems. though.

If votes are expanded to the full range, then 0 is just another rating in
between the others. If votes are just normalized then 0 is a "no-vote" or
"don't care" value. If votes are signed then it can matter whether you
vote positively or negatively for a specific choice. You may not be able
to defeat a choice you vote positively for. If votes are positive-only
then 0.0 is the "no-vote/don't-care" value, adding nothing to a choice's
talley, and it is equivalently a minimum level of preference rating.

*49 0,1
*51 1,0

A wins. If some or all of the 51% raise their rating of B, then they
indicate some acceptance of that choice and B may become a legitimate
compromise choice. (But this isn't an interesting example.  Interesting
examples include nuanced ratings between 3 or more choices.)

Brian Olson
http://bolson.org/