[EM] IRV vs Plurality

[Juho]

On Jan 26, 2010, at 6:07 AM, Chris Benham wrote:

> Juho  wrote (25 Jan 2010):
>
> "I reply to myself since I want to present one possible simple method
> that combines Condorcet and added weight to first preferences
> (something that IRV offers in its own peculiar way).
>
> Let's add an approval cutoff in the Condorcet ballots. The first
> approach could be to accept only winners that have some agreed amount
> of approvals. But I'll skip that approach and propose something
> softer. A clear approval cutoff sounds too black and white to me
> (unless there is already some agreed level of approval that must be
> met).
>
> The proposal is simply to add some more strength to opinions that
> cross the approval cutoff. Ballot A>B>>C>D would be counted as 1 point
> to pairwise comparisons A>B and C>D but some higher number of points
> (e.g. 1.5) to comparisons A>C, A>D, B>C and B>D. This would introduce
> some approval style strategic opportunities in the method but basic
> ranking would stay as sincere as it was. I don't believe the approval
> related strategic problems would be as bad in this method as in
> Approval itself."
> <snip>
>
> The  "some higher number of points (e.g. 1.5)"  looks arbitrary

Yes it is (with the intention to allow the required amount of core  
support to be adjusted), just like the whole method is (somewhat ad  
hoc). I'd like to have a good definition of what the target of "core  
support" and "weight on first preferences" is. That would make it  
possible to discuss the benefits and problems better. Now the proposed  
method is just simple, it may work well enough in real elections, and  
offers one approach to emphasizing core support.

> and results
> in the method failing Majority Favourite, never mind Condorcet etc.
>
> 51: A>B>>C
> 41: B>>C>A
> 08: C>>A>B
>
> B>A 61.5 - 59,  B>C 112.5 - 12,  A>C 76.5 - 53
>
> 51% voted A as their unique favourite and 59% voted A above B, and  
> yet B wins.

Yes, and I believe there are more criteria that the method fails. We  
should however from some point of view be happy since the method  
elected B that seems to have 92% core support (maybe this is how I  
defined core support in this method).

Those 51% that approved both A and B must be quite happy with electing  
B since they indicated that B is approved (has their "core support").  
If some of them strongly think that A should have won instead of B  
then they applied the Approval strategy poorly (= should have approved  
A only in a situation where A and B are the main competitors).

Those 59% that preferred A over B include also the C supporters. They  
should have approved also A to make the chances of A winning B bigger.  
Thus also the C supporters didn't use the traditional Approval  
strategy properly (assuming that they strongly want A to win B).

The basic assumption thus is that the voter given rankings are mainly  
sincere but large part of the approvals may be strategic. In real life  
the strategic incentives are probably not as strong as in this example.

It may well be that this method can be characterized as "not fully  
Condorcet and Approval strategy added". I'm not quite sure that the  
intended idea of "mostly Condorcet with core support rewarded" (= do  
what the IRV core support idea is supposed to do) works well enough to  
justify this characterization and the use of this method (when core  
support is required). There is however some tendency to reward the  
large parties or other core support (as intended) and the behaviour is  
quite natural with some more common sets of votes. See example below.

45: A>>B>C
10: B>>A=C
45: C>>B>A

This is an example with a centrist Condorcet winner. In Condorcet B  
would win. In the proposed method the core support of B is not  
sufficient. A=C 67.5 - 67.5,  A>B 82.5 - 60,  C>B 82.5 - 60.

If the number of votes would be changed to 42: A>>B>C, 16: B>>A=C, 42:  
C>>B>A that would be enough to make B the winner with the chosen  
factor 1.5 (16 = "sufficient amount of core support").

Juho



>
> Chris Benham
>
>
>       
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