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 -- Omm (0)-(0) http://www.mathematik.uni-kl.de/~wwwstoch/voss/index.html
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