[EM] information content, game theory, cooperation

[Árpád Magosányi]

Hi!

I am sorry for igniting such a flamewar.

1. information content
I propose that this topic should be discussed only after understanding
Shannon's information theory.
A good introductory material is on Wikipedia:
http://en.wikipedia.org/wiki/Information_entropy
If we consider all variations of votes equally possible, we end up  that for
n candidates
- approval voting have 2^n possibilities (hence log2(2^n)=n bits)
- preferential voting have n! possibilities (hence log2(n!) bits) (not
counting the cases wherre not all candidates are ranked)

I have made a mistake stating that it is clear that prefeerential voting
have more information.
It is true only for n>=4. Fortunately I am too young, didn't vote in
communist times, so I have only encountered situations where n>=4. So now I
consider that while my statement wasn't correct mathematically, it is true
in real life situations.

Now you can discuss how information content is different in real life
because all votes not being equally possible, but please do not challenge
well established theoretical facts.

2. game theory

The discussion about how Nash equilibrium is reached with different voting
methods had been very enlightening to me. It shown how to tackle my
country's current situation from a mathematical standpoint.
Maybe assumption about full information, no cooperation or logical voters
should be changed, and changes of opinion of voters between election should
be accounted for to have a better model. But there is the brief explanation
of how I could understand the situation:
We have a voting system which is converging fast, and the convergence point
(I do not use notion of Nash equilibrium here) is far from the least
unacceptable situation considering voters' preferences.

3. cooperation

Since I have asked, I have found the answer to my question: what is the
distinctive feature of Schulze?
(The page has been on rangevoting.org, but I cannot find it now.)
Shulze prefers the candidate which beatpath is weak (as far I can remember
Schulze's description). Which means something like it is the least
unacceptable candidate. I have the feeling that this is connected with
cooperativeness of the candidate.
Formal description or refusal of this effect is welcome.
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