[EM] Proportional Strength Binary Tree Legislature

[Michael Rouse]

was: Unicameral/Polycameral Legislatures

After playing a bit with binary-tree legislatures, I've come to the
conclusion that while it does a good job representing regional interests
(put a dam/interstate highway/government office in my district!), it doesn't
do as good a job reflecting diffuse national interests (peace, the
environment, second-amendment rights) -- though to be fair, neither does our
present form of representation.

(Brief description of binary-tree Legislature: Winner of national election
becomes President-elect and placed at the peak of the tree, his name is
removed, and the country split into two regions of equal population. Winner
of each region is placed under the President-elect, their names are removed,
and each region split in half again. Continue until you have the number of
regions you want. A bill must have at least one string of unbroken "yes"
votes from base to peak of tree in order to become law.)

A solution to this problem might be giving each representative not only a
position on the binary tree, but a relative strength based on how many votes
he or she received in the national election. Not only would a bill require
an unbroken string of "yes" votes from bottom to top, it would require
greater than half the combined strength of all representatives.

As an example, consider the following tree:
10
(8, 5)
(4,3)(2,1)

The numbers are the relative strengths of representatives, and they are
placed in their relative positions. 8 and 6 are two branches coming from the
10; (4.3) is attached to the 8, and (2,1) is attached to the 6. (10,5,1)
would be an unbroken string, but the total value would be only 16 and our
rule requires at least 18. Getting  the representative with the strength of
2 to vote yes would push the bill over the top. On the other hand, simply
having the candidates represented by 10 and by 8 vote for a bill would not
be sufficient even though their strength adds up to 18, because there is no
unbroken line from peak to base (and the bottom "no" votes overrule them
anyway).

If we base representative's pay on their position within the tree (the
higher they are the more they are paid) and their relative strengths (the
more votes they get in relation to other representatives the more they are
paid), then it would be to the candidate's advantage to not only win his
district, but to appeal to the country at large. If a politician voted for
pork-barrel projects in his district to gain local votes, he could easily
lose national votes and find his influence and his pay reduced in the next
election.

Michael Rouse
mrouse at cdsnet.net

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