[EM] Improved Generalised Bucklin

[Chris Benham]

  On Sat.23-8-03 Eric Gorr wrote:

Why do you believe the middle preferences of a voter should matter 
less then the highest or lowest preferences?

CB:I don't believe that (and never said I did). You may have discovered an unintended effect. I admit that it is maybe a bit odd that the same middle preferences can count both for a candidate in one finalist sub-election, and against the candidate in the other.

What are these serious strategy problems? Do you believe solutions to 
them cannot be found outside of the voting method? If so, why?

CB:I didn't exactly mean that RP neccessarily has serious strategy problems. I meant that my suggested method would have srategy problems fewer in number and also not as ("less")serious.
But having said that,didn't James Green-Armytage recently raise the alarm ?
 
On Sun.Aug 17,03 he wrote:
"Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B

It is extremely clear here that C seriously does not deserve to win, as he
is ranked last by 90% of the voters. Also, it is clear that A deserves to
win, albeit by a narrow margin.
Now, if the method is Condorcet (minimax, Schwartz / minimax, ranked
pairs, or beatpath), and if everyone voted sincerely, A would win.
However, if the 44 B>A voters strategically vote B>C (offensive order
reversal), a cycle is formed, in which the defeat of B is now the defeat
of least magnitude, and so B wins.

46: A>B
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 90:10

This is already very unfair, and a clear subversion of the democratic
process."

CB: The strategic problem is that the sincere CW can be vulnerable to simple Burial strategy.
In the example James gives, nothing very clever or sophisticated is needed by the B voters. B voters who know nothing about the voting method, can just perceive that the A is the main threat to their favourite and that it is highly unlikely that C will win, and then gamble that insincerely down-ranking A will pay off (or not hurt). Of course this will be more tempting/rational if the gap in their preferences between A and C is small compared to the gap between B and A.
My proposed method succeeds in this example(as I showed in my original post), and I am still blushing from all the applause.
Also I am surprised that you don't regard failing Participation (aka Generalised Monotonicity) is itself serious. If someone says "I didn't bother voting because it has been mathematically proved that by voting I could have caused my favourite candidate to lose", we want to be able to say "Ha!Ha!, what ridiculous rubbish, that person is insane" and not "S/he is right".

Chris Benham


























 


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