[Election-Methods] Re: Cumulative Approval

[Chris Benham]

Juho juho4880 at yahoo.co.uk 
Sun Apr 6 14:45:29 PDT 2008 

> Like  IRV it fails Mono-raise and so is vulnerable to the Pushover
> strategy.
>
> 49: A
> 27: B>A
> 24: C>B
>
> Your suggested method elects B.
>
>
> 45: A
> 04: C>A  (was A)
> 27: B>A
> 24: C>B
>
> Now your method elects A.

I think here it should elect B.
- A leads, CB compromises
- B leads, CA compromises
- B leads and wins

Juho,
Yes, sorry, I overlooked your clause 4:

> (4) take from that set only those voters who still have not approved
> all the candidates that they prefer to the leader

31: A>B
32: B>C
37: C

My earlier example, where B wins (as in IRV).

31: A>B
32: B>C
33: C
04: A>C  (insincerely changed from C)

Now C wins (as in IRV) due to four of the sincere C supporters pulling off the 
Pushover strategy. 

(A leads, BC compromises, C leads, AB compomises, C still leads and wins.) 

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.

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

"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).

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

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

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


Chris  Benham



> (1) all voters approve their favourite candidate(s)
> (2) find the candidate that has most approvals (leader) (use tie
> breaker if needed)
> (3) find those voters that have not yet approved the leader
> (4) take from that set only those voters who still have not approved
> all the candidates that they prefer to the leader
> (5)
> (6) take from that set only those voters whose best approval result
> among the approved candidates is lowest
> (7) these voters will change their vote to approve also the next
> candidate(s) (in their order of preference)
> (8) if there were still such voters jump back to point (2)
> (9) elect the candidate with highest number of approvals (use tie
> breaker if needed)


      Get the name you always wanted with the new y7mail email address.
www.yahoo7.com.au/y7mail