[EM] Range Voting and Cardinal Ratings Runoff

[Brian Olson]

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)

On Dec 16, 2004, at 5:33 PM, Forest Simmons wrote:

>> Date: Wed, 15 Dec 2004 20:30:19 -0800
>> From: Brian Olson <bql at bolson.org>
>> Subject: Re: [EM] Is range voting the panacea we need?
>
>
>>
>> Straight rating summation is vulnerable to strategic voting. Perhaps 
>> in
>> this study people voted honestly because it obviously didn't matter 
>> and
>> so there was no incentive to vote strategically. In a real election 
>> the
>> stakes would be higher.
>>
>> My favorite solution is to run Instant Runoff style disqualification
>> cycles over Normalized Ratings (IRNR). I believe this method is
>> strategy proof and passes a handful of other desirable election method
>> criterion.
>
> In general, methods that proceed by sequential elimination are not 
> strategy proof:
>
> 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.

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.

Did I miss something in my steps or misunderstand the challenge?


I remember that the question of strategy came up before, and I think I 
should reduced my claim. In the zero information case, a single IRNR 
voter maximizes zir expected utility by voting honestly. With partial 
information, a voting bloc may be able to improve the outcome for them 
by artificially deflating the ratings for a close competitor. As usual, 
with faulty partial information and possibly competing strategic voting 
blocs, they may wind up shooting themselves in the foot and making way 
for a third choice.

> 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.
>
> It doesn't suffer from the burying strategy because all candidates are 
> still in the race in the last round.
>
> A candidate with lots of success in previous rounds just gets the 
> approval cutoff moved closer to her as a "reward," so losers of 
> previous rounds (whether favorite or compromise or both) still have 
> chances in the final round.

This sounds like an interesting method that I missed. Is there a 
reference description of it?

Brian Olson
http://bolson.org/