[EM] Voting Theory and Populism clarification

[Raph Frank]

On Tue, Oct 21, 2008 at 12:06 AM, Kevin Venzke <stepjak at yahoo.fr> wrote:
> I can't understand why you left out the possibility that the "top two"
> are considered to be A and C!
>
> This should be quite possible if A and B are considered more similar to
> each other than either is to C.

40 A>B>C
20 B>A>C
40 C>B>A

Assume, the strategy is "Best of top 2 plus all better than expected winner".

Option 3:
expected: C win and A 2nd

40: A+B
20: B+A
40: C

That gives

A: 60
B: 60
C: 40

Thus this becomes: A+B expected winners

Option 4:
expected: A win + C 2nd

40:A
20:B+C
40:C+B

A: 40
B: 60
C: 60

This becomes: B+C expected winners

In both cases, after the poll, the assumptions have to be updated.

Option 3 becomes option 1 from my last post.  Option 4 becomes option
2 from my last post.

Thus the transfers are

1->2 (and B wins)
2->1 (and B wins)
3->1
4->2

Thus no matter which of the 4 are the initial starting assumptions, it
ends up in state 1 or state 2.

Also, it would only oscillate if the support levels are perfectly balanced.

The other possible options should also lead eventually to B wins.

Assume that the strategy is "

a) Approve the best of top 2
b) Approve all you prefer to the expected winner.

Call C the condorcet winner, W the initial expected winner and S the
initial second place.

Poll number 1:

C will get majority approval as he is preferred to W (by rule b) in
the strategy)
Each voter will approve one or other of the top 2 by rule a.  This
means that one of them will get less than 50% approval.

This means that C is promoted to one of the top 2 after poll number 1.

Assume that W is the one who also has majority approval.

Poll number 2

C will again get approved by a majority (by both rule a and rule b)
W will get less than a majority (as he is the other of the top 2)

Nobody else will be approved by a majority (this is a probability).

C is now considered the expected winner.

Poll number 3

C will again get approved by a majority (by both rule a and rule b)
Nobody else will be approved by a majority (by rule b)

The effect is that one the condorcet winner becomes the expected
winner, he will not be displaced.  Also, there is a pretty good chance
that he will end up there.

Even if "poll 2" doesn't result in C ever winning, the fact that he is
always one of the top 2 in polls and his opponent is changing will
likely cause the voters to assume that he is the likely winner, and
then we move to state/poll 3.

Ofc, if there isn't a condorcet winner, then the whole thing goes unstable.