[EM] More easily hand-counting three-slot Condorcet

[Kevin Venzke]

Dear Jobst,

 --- Jobst Heitzig <heitzig-j at web.de> a écrit : 
> > (The scenario I have in mind is: Approval ranking: A>B>C.  Pairwise:
> > B>A>C>B.  B wins. If B's approval is simply reduced somehow, with no
> > other changes: Approval ranking: A>C>B.  Now A wins.)
> 
> Isn't that very strange? We have a cycle A>C>B>A and the one with the
> *second* largest approval (B) should win? If you like to put more weight
> on approval, it would only seem natural to me to require that in a
> 3-cycle, the most approved one should win.

Well, I'm not trying to "put more weight" on approval, but to
imitate the results of WV methods with the information available.

Also, the rule of course is not that the second-most-approved candidate
prevails in a cycle.  The rule is that the least-approved's win is the
one that is discarded.  My intended strategy is to discard "noise"
candidates.  For example, again:

9 A>B>C
8 B>C>A
7 C>A>B

I don't want to see B win here.  Nine A voters will kick themselves
if B wins.  The best resolution seems to be to pretend the (clearly)
weakest candidate, C, didn't run.

Especially with three-ranks, lower approval seems to coincide with
weaker WV victories.

One thing I notice unhappily is that with my rule, the B>C>A voters
can't make C win without ranking C above B.  That's something to
think about.

> Second, it counts some
> voters prefering the defeated candidate over the defeating one.
> 
> The latter fault seems very bad to me when using approval of the
> defeating option since it means that when trying to convince people to
> go voting, you will have to admit that when they put A in slot 1 and B
> in slot 2, they can actually strengthen the reverse defeat B>A!

The conditions needed for this to take victory from A seem too
specific to me:
1. Approval order A>B>C (C being some third candidate)
2. Pairwise cycle A>C>B>A
3. Downranking B has to change the approval order to A>C>B.

It seems to me that the voter would need some extremely good
information in order to get anxious about this possibility.  Dropping
B to the last slot without such information would be very risky;
not only does it reduce the strength of B's victories, it can
change them into losses.

> So, in situations in which it seems really important to have a counting
> procedure as easy as you demand, I suggest to use the above variant
> instead of your original one.

I would certainly use it if the voters considered the results easier
to understand.

However, I'm having trouble thinking of a way to define the method
using your new defeat strength without reference to "cycles."  Maybe
it can be done, but I drew a picture and it seemed unlikely.

Yours,
Kevin Venzke


	

	
		
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