Hello, I want to inject some facts into the discussion. You can also find the following analysis on my Debian voting system web page at
http://www.mathematik.uni-kl.de/~wwwstoch/voss/comp/vote.html
I want to examine the following voting system:
Let N(a,b) be the number of votes which prefer options a
over options b. Let Q be some positive number (the quorum).
step 1: remove each option x, where N(x,default) < Q
(per-option quorum)
step 2: Use Condorcet voting with Cloneproof Schwartz Sequential
Dropping on the remaining options.
step 3: In case of a tie after CpSSD the elector with a casting
vote chooses the winner from the Schwartz set
Which of the criterions from http://electionmethods.org/evaluation.htm
does this voting system preserve? In the following examples D denotes
the default option and a vote like ABD means "A is prefered to both B
and D and B is prefered to D".
Monotonicity Criterion (MC):
Still holds. An option option which was previously removed in
step 1 can be added if a vote ranks it higher. Everything else is
as in Condorcet voting.
Condorcet Criterion (CC),
Generalised Condorcet Criterion (GCC),
Strategy-Free Criterion (SFC),
Generalised Strategy-Free Criterion (GSFC):
These do NOT hold.
Example: Q=1, only vote: AD
A is the "Ideal Democratic Winner" and the only member of the
Smith set. It is also prefered by a majority to D.
But the default option D wins.
Strong Defensive Strategy Criterion (SDSC),
Weak Defensive Strategy Criterion (WDSC):
These do hold. If a majority prefers A over B then it can vote
ADB to ensure that B cannot win. Either B fails at the quota
criterion or the SDSC condition of the Condorcet method ensures
that B looses.
Result: with the introduction of an per-option quorum we loose CC,
GCC, SFC, GSFC. We still have MC, SDSC and WDSC.
If nobody else volunteers, I will try to do the same analysis for the
global quorum tomorrow. Let's see.
Jochen
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Omm
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http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html
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