[Election-Methods] Clone related problems in Range/Approval Juho

[Juho]

On Apr 22, 2008, at 7:12 , Kevin Venzke wrote:

>>> If the method fails (picks a bad winner) when the field
>>> can't be narrowed to three viable candidates in time for the
>>> election, or
>>> when the candidates can't be interpreted to fit on a 1D spectrum,
>>> I'd say
>>> that's ok. The first problem is self-correcting, and the second one
>>> shouldn't be all that common.
>>
>> The next common candidate opinion space could be one with two
>> dimensions. One dimension may be enough to cover most basic cases but
>> there may be also other quite common patters that may resemble having
>> two dimensions, having two centrists with somewhat different profiles
>> etc.
>
> However, it shouldn't matter too much even when there is more than one
> dimension. With three candidates one can always draw a triangle at  
> worst.
> Hopefully the candidate opposite the longest edge can be identified  
> as the
> center candidate, with voter strategies responding to this perception
> appropriately.

Yes, if the distribution of voter opinions in the space follows  
roughly the distribution of the candidate opinions then the triangle  
method is quite accurate. I was actually thinking already having e.g.  
four candidates. Then the figure could be e.g. a diamond. And the  
best winner might be the candidate (of the two centrist ones) that is  
closer to the longest diagonal.

(The reason why I came to think about the "two centrists" example is  
that then the "median voter" could prefer either of them.)

Four candidates can also make some other patterns than the diamond.  
And the voter opinions may in all cases be more complex than evenly  
distributed around the set of candidate opinions.

I however agree that studying the three candidate cases and giving  
solutions to all of them may already solve majority of the problem  
situations that are typically encountered in real life elections, so  
it is the best place to start and fix first. Four candidates may add  
some interesting scenarios to this (e.g. the diamond case above,  
smith set + 1, impact of two clones within a party, two loops).  
Having more than four might already typically mean studies of  
multiple clones or situations with lots of uncertainty (and also  
realistic examples of less predictable situations where strategies  
are not as easy to apply as with a more limited set of candidates).

Juho






	
	
		
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