[EM] Fixing Range Voting

[Brian Olson]

On Oct 15, 2008, at 1:59 PM, Peter Barath wrote:

> I'm not sure I would vote honestly in such circumstance.
>
> Let my "honest" rangings be:
>
> 100 percent for my favourite but almost chanceless Robin Hood
> 20 percent for the frontrunner Cinderella
> 0 percent for the other frontrunner Ugly Duckling
>
> I think I would vote: 100 Robin Hood;  99 Cinderella;  0 Ugly Duckling
>
> If I'm really sure that the race decides between Cinderella and
> Ugly Duckling, why care too much for poor Robin Hood?
>
> And what, if I'm not really sure, because that's the situation which
> multi-candidate voting is really about?
>
> If I lower Cinderella's 99 to her honest 20, I make Robin Hood a
> little bit more hopeful not to drop first. But more hopeful against
> whom? Cinderella, of course, because I didn't change Robin and Ugly's
> obvious rangings. So I made more probable a situation in which more
> than 50 percent is the probability that the worst candidate wins.
> This is a doubtful advantage.
>
> On the other side, there is the effect that by rising Cinderella's
> points from the honest 20 to 99 I made more probable the similarly
> unlikely but positively desirable effect of Ugly dropping first
> instead of her.
>
> So, which does have more weigh? The doubtful little hope for
> Robin Hood, or the clear little hope against Ugly Duckling?
> I think the latter. Maybe at some point, let's say Cinderella's
> 5 percent, I like Robin so much more that I chose the first one.
>
> In that case I probably would vote 100-1-0
>
> These voting are not the "honest" although by one percent "honer"
> than the simple Approval voting.
>
> But I would be open for persuasion.

If you vote (100,20,0), (100,99,0) or (100,1,0), if your 100 hero  
loses in the first round, your vote in the second round is (x,100,0).  
So, what are the various consequences in the first round vote, in case  
it makes a difference there?
I think the normalization comes into why you want to vote differently.
(100,20,0) => (98.1,19.6,0)
(100,99,0) => (71.1,70.4,0)
(100,1,0) => (99.995,0.99995,0)

I think the tradeoff is that in a many-candidate race your lower  
preferences might contribute to runoff-disqualification order. You can  
put the vast majority of your vote on your favorite, and that's ok and  
your vote will get transferred to the remaining candidates if you  
don't get that favorite, but your lower rated choices might still be  
affecting which choices are disqualified or remaining at that time.
The 100,99 vote looks tempting because it normalizes to a lot of  
absolute value, but that does come at the price of losing some weight  
on your favorite and making your 2nd choice a bunch more likely to win.
I think it's this tradeoff that will squeeze people towards voting  
honest ratings.
I could see honest voting want any of these three votes. Wanting A or  
B vastly more than C, wanting A vastly more than B or C, or some more  
gradual falloff. Does IRNR not do the right thing for those three  
voters?