[EM] Re: Range Voting and Cardinal Ratings Runoff

[Forest Simmons]

  Kevin Venzke <stepjak at yahoo.fr> wrote ...

> Subject: Re: [EM] Range Voting and Cardinal Ratings Runoff
> To: election-methods at electorama.com
> Message-ID: <20041217031345.61263.qmail at web13811.mail.yahoo.com>
> Content-Type: text/plain; charset=iso-8859-1
>
> --- Forest Simmons <simmonfo at up.edu> a écrit :
>> For this reason Kevin came up with the "Runoff Without Elimination" idea,
>> culminating in his "Gradual Approval," which I believe to be a superior
>> use of Cardinal Ratings style ballots.
>
> I think I'd better note that I didn't come up with "Runoff Without
> Elimination" as a name or idea... I recall old archive messages
> where "RWE" was discussed by Mike Ossipoff and Donald Davison.
>

But you did invent "Gradual Approval."  Right?


Brian Olson <bql at bolson.org> wrote ...

> First, Instant Runoff Normalized Ratings (IRNR) explained -
> in a paragraph:
> http://bolson.org/voting/methods.html#IRNR
> slide show:
> http://bolson.org/voting/IRNR_explaination.pdf   (219KB)
> http://bolson.org/voting/IRNR_explaination.mov  (2.3MB)
>

<snip>

> Forest wrote ...
>> Suppose that there are only three candidates, and you think that your
>> compromise C has a significantly better chance than your favorite F of
>> winning against the candidate D that you dislike the most, and that
>> there is a good chance that D will be one of the finalists.  Suppose
>> further, that F and C both have decent chances of getting into the
>> final round.
>>
>> In this situation, you have an incentive to "bury" your favorite F,
>> i.e. to try and make F lose in the first round.
>

Brian replied ...

> I don't think this can happen with IRNR.
>
> If I truly prefer F>C>D, if I'm right about IRNR then it should be
> impossible to find a configuration of votes for which it's better for
> me to vote C>D>F (or C>F>D ?). In this hypothetical vote configuration,
> if I vote honestly F>C>D, then D will be elected, but if I vote C
> first, C will be elected. But this is not possible with IRNR because of
> the re-normalization process that happens on each round.
>
> If I vote F=1.0, C=0.8, D=0.0 and F is disqualified, then my second
> round re-normalized vote is C=1.0, D=0.0 . In fact, no matter what my
> rating of F and C (holding D constant at 0.0), if either of them is
> eliminated in the first round, my second round vote will be {the
> remaining of F or C}=1.0, D=0.0 . And if that doesn't elect someone I
> want, nothing will.
>

Nothing will only because by then it is too late:

Suppose that F is the one that makes it to the final round and that F 
loses to D, but that C is preferred above D by more voters than not.

Then it would have been to your advantage to rate C at the top and F at 
the bottom, but now it's too late.

"Hindsight is 20/20, buy low, sell high, etc."

But if you were led to believe or strongly suspect (before voting) that C 
could beat D, while F could not, and that one of C or F would be 
eliminated in the first round, then you would be tempted to bury F before 
it was too late.

...

> [Gradual Approval] sounds like an interesting method that I missed. Is 
> there a
> reference description of it?
>


It's easier to describe than to look up:


If there are n candidates, then there are n-1 rounds.

(For k between 1 and n-1) in round number k the approval cutoff for each 
ballot is calculated as the average rating of the top n-k+1 approved 
candidates of the previous round.

The winner of the final round is the method winner.

[When k=1 this makes sense if we agree that all n candidates comprise the 
set of top n winners of round zero.]

Note that the winner is either the head-to-head winner of the top two 
approved candidates of the penultimate round, OR someone who gets more 
approval than either of these when the approval cutoff is placed half way 
between them on each ballot.

If I remember correctly, according to Kevin, when the approval cutoff 
lands right on the rating of some candidate, then all candidates at that 
rating are given half approval.

I prefer the version that just gives them their rating divided by the max 
possible rating, so if they are closer to the top rating, they get more 
than half, closer to zero, less than half, etc.

In this version, then (automatically) if all of the candidates from the 
previous round share the max rating on your ballot, then they still get 
full approval, whereas if they are all at the bottom, they get zero 
approval.

In Kevin's version, this feature is not automatic, but it is put into the 
rules.

Forest