[EM] Improved Generalised Bucklin

[Eric Gorr]

At 2:40 AM +0930 8/26/03, Chris Benham wrote:
>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.

This assumes that they would even be seen when going in both 
directions and that obviously may not be the case.

As such, the middle preferences are, but the very nature of the 
method, considered to be less important then the top and bottom 
preferences, which will always be seen by the method.

>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.

You have yet to provide any specifics showing this.

At a minimum, it would seem to be necessary to list the problems you 
consider to be serious and then show that your method would not 
suffer from them while another method would, while also defending the 
problem as being a truly serious one.

>But having said that,didn't James Green-Armytage recently raise the alarm ?

Yes, an alarm was raised, but I can see no reason to consider the 
problem serious with respect to RP and perhaps every other method as 
well.

>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."

And if the A voters were to do the same thing, since they cannot know 
they are going to win in such a close race, C would win.

It *MAY* be reasonable to assume both groups would know that C is not 
going to win, but there is no guarantee of even that.

Since neither the A or the B voters can know what the other group 
will do and since both do not want C to win, the only rational choice 
they can make is to vote sincerely.

As such, I fail to see the seriousness of this problem.

At best, it would seem to be only interesting from a strictly 
academic point of view.

>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.

I am actually starting to consider it to be something that a method 
does not want to have...i.e. it is a serious problem if it passes 
participation.

Why?

Because it would seem to place far to much emphasis on the individual 
voter, when the goal of these methods is to find the group preference.

No single person should ever expect their top choice to win.

Instead, they should desire to help the group determine who is the 
most preferred candidate....this is what RP does to the best of it's 
ability.

>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",

In other words, they did not vote because they wanted to choose to 
won. Dictatorships are something to avoid.