[Election-Methods] RE : Re: Is the Condorcet winner always the best?

Jonathan Lundell jlundell at pobox.com
Tue Dec 11 12:20:49 PST 2007

On Dec 11, 2007, at 6:05 AM, Kevin Venzke wrote:

> Jonathan,
> --- Jonathan Lundell <jlundell at pobox.com> a écrit :
>> ...should choose B as a good compromise, with the A voters saying A  
>> is
>> good, B OK, C very bad. But Diego's profile suggests to me that the A
>> voters are saying something like A is good, B is bad, C is very bad.
>> Not that they can express it in a normal linear ballot, just that
>> we're being told a little more about their opinions.
> In my opinion, to the extent that the effect of a ">>bad>verybad"  
> vote is
> disregarded, the point of letting voters indicate such preferences is
> undermined anyway.

I'm not advocating it as a ballot option, only as a meta-notation  
shorthand to give us kibitzers a little more information about the  
voters' utility functions.

>> In my example, the effect of a later-no-harm voting rule is evident.
>> In Diego's, a rule (such as STV) that elects A doesn't seem
>> unreasonable to me.
>> The problem is that with an ordinary linear ballot (no '>>'), we  
>> can't
>> distinguish between the cases. Not that I'm arguing that we should
>> employ '>>'; offhand, that strikes me as a complication to be  
>> avoided.
> In one sense I don't agree. If >> is allowed then apparently it's  
> safe to
> vote ">>bad>verybad." If >> isn't allowed then voters will probably  
> be more
> cautious, since the method could very well take them as serious if  
> they say
> that bad is better than verybad.
> I tend to think that if B doesn't win in Diego's scenario, the  
> method is
> second-guessing the voters. It either disbelieves the C voters'  
> preference
> for B over A, or finds that there's something more important than  
> majority
> rule.

There's a reasonable argument to be made (hardly originally by me) on  
either side of the question of whether a compromise candidate is  
sometimes (or always) better to the candidate of one faction in a  
close election.

If the vote were:

53 A
47 C

...we'd shrug and call it a fairly close election, or at least no  
landslide, and forget about it, even if all 100 voters strongly  
disapproved of the opposing candidate. If we introduce a third  
candidate whom the A and C voters despise only slightly less than C  
and A respectively, and end up with something like Diego's profile, we  
have 100 (or 90 in that profile) unhappy voters instead of 47.

I'm not saying that it's unarguable, nor that the voting system should  
somehow anticipate the situation (through the use of '>>', for  
example). I think it's a fuzzy case with no perfect answer, and that  
we don't really want to make the ballot more complex, or add to the  
possibilities for manipulation that such a rule would entail. I'm just  
saying that it's not obvious that, in all cases, the best rule is the  
one that lets B win.

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