[EM] Fixing Range Voting

[Diego Santos]

2008/10/16 Brian Olson <bql at bolson.org>

> 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?
>

A few months ago I thought a Condocret variation of INRN:

1. Calculate the Smith set using range ballots.
2. Eliminate candidates outside the Smith set
3. Rescale the votes. For example, if some vote was: A:100, B: 70, C:30, D:
10, E:0, and Smith = {D, C, D}, the rescaled vote would be: B: 100, C: 33.3,
D: 0
4. Elect the candidate with the highest sum.

Because Smith implies local IIA, this problem would be arguably reduced.


>
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-- 
________________________________
Diego Renato dos Santos
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