[Election-Methods] Cumulative Approval

[Juho]

On Apr 7, 2008, at 21:01 , Chris Benham wrote:

> Now say we add three ballots that plump for C.
>
> 31: A>B
> 32: B>C
> 36: C     (were 33:C)
> 04: A>C
>
> Now the winner changes from C back to B (C leads, AB compromises, B  
> leads
> and wins), a failure of  Mono-add-Plump.

AC voters can still compromise and there can be one more round, but  
that has no impact. B wins.

So, adding votes to C makes it lose.

I mentioned also the option to use fractional votes for ties. This  
looks like a "promising" place to test that option. There would be  
one more round where the CA voters would compromise.

31: AB>
32: B>C
18: CA>
18: C>B
04: AC>

A has now 53 approvals, but also that is not enough. B wins. (If A  
would have taken the lead then the BC voters would have had to  
compromise and approve C.)

The use of fragmented votes would maybe decrease the risks here, but  
I'm not sure what its full impact would be.

> Methods that fail this very weak criterion (thereby acquiring  
> "ballot-box-stuffing
> resistance")  are in my book unacceptable.

Maybe the new method could be said to somewhere between IRV and  
Condorcet and due to this ambivalent nature sometimes makes weird  
switches from one side to the other. Don't know any cure for this at  
the moment. Just hoping that the weird behaviour would not lead to  
easy application of strategies (e.g. incentive to not vote in this  
case).

> "There seems to be a mixture of strategic voting cases. The new method
> resembles in some aspects the Condorcet methods. The main idea was
> anyway to patch some of the flaws in IRV. Do you have an overall
> estimate on the problems? Better or worse than IRV?"
>
> In my book this is worse than IRV.  IRV meets Later-no-harm, Later- 
> no-Help,
> and mono-add-top (and therfore mono-add-plump).

Note that one design criterion in this case was to seek behaviour  
that would be somewhere between IRV and Condorcet. This could mean  
breaking many criteria but hopefully breaking them in some less  
severe way than the starting point. This may be wishful thinking, but  
a possibility that might make a method that breaks many criteria  
actually quite practical in the end (since we know that some criteria  
will be violated anyway, and violating all just a little bit could be  
a nice option).

Btw, the most notable positive thing in the new method when compared  
to IRV was in my eyes in my first example where one of the most  
common problems of IRV was eliminated (don't know if that was somehow  
final and conclusive though, but in the correct direction).

> I haven't seen or tried to come up with an example, but I gather  
> this method
> fails the Condorcet criterion.

I don't have one either, but there may well be such examples.

> One method that I think dominates your
> suggestion is  Condorcet//Approval  (and Smith//Approval and  
> Schwartz//Approval).
> They meet Condorcet, mono-raise and mono-add-plump.

Ok, possibly. Maybe the Condorcet part at the beginning eliminates  
some risks. Also Condorcet combined with this method might be  
interesting (but maybe already quite complex).

> Interpreting ranking above bottom as approval, they elect the same  
> winners as
> your suggestion in all your  "positive examples".

Ok. The voters would maybe need to control the approval cut-off  
manually if there was e.g. one hopeless candidate D in addition to  
these three.

> http://lists.electorama.com/pipermail/election-methods- 
> electorama.com/2007-December/021282.html

Yes, interesting. Unfortunately I didn't find time to comment when  
this mail was sent. My basic thinking is that I hope that Condorcet  
would be strategy free enough in many/most environments so that it  
could be used as it is. But if there is a risk of widespread burial  
then countermeasures (as studied in the mail) to stop that could be  
useful. For me that should be enough since use of counter-strategies  
would already be too much. That could already make any method  
unusable for public elections.

Juho







		
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