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*To*: membership@icann.org*Subject*: [Membership] Voting systems: Approval voting*From*: Joop Teernstra <terastra@terabytz.co.nz>*Date*: Tue, 02 Feb 1999 20:10:16 +1200*Sender*: owner-membership@zephyr.isi.edu

Diane, I looked at your report.htm I think there are better options than the voting systems proposed so far. May I contribute this as an alternative and possibly superior voting system? (Mike Saari's paper) Discussion invited. RATIONAL GROUP DECISION-MAKING (by saari@aol.com) Suppose a group of rational, intelligent people is trying to make a choice amongst several alternatives. Will their voting system give them a consistent (and good) outcome? For virtually every voting system in use today, the answer is, sadly, NO. This paper demonstrates this simple but startling conclusion. Fortunately there is a solution (which I will also describe). Let's construct a simple voting scenario. Suppose the choice is between two viable candidates/propositions/flavors "A" and "B". Using a particular voting system and assuming only A and B are on the ballot, suppose that A consistently wins each election. Now let's repeat the very same vote, but with additional alternatives "X, Y, Z, etc." on the ballot as well. If a case can be demonstrated where B wins over A, then I assert that that voting system is fatally flawed, because it is not accurately recording the preferences of the voters. [Two classes of additional candidates that easily stress any voting system are any numbers of "Bozos" and/or "Twins". A "Bozo" is any mediocre candidate. A "Twin" is a candidate which is identical and indistinguishable from another particular candidate. Given a choice between two Twins, assume that voters will choose randomly, since either "Twin" outcome is equally good.] To demonstrate a typical flawed voting system, take the common "simple plurality" method (vote for one candidate, and the highest total wins). For the simple A vs. B case, assume that A consistently wins (A=60%, B=40%). Now we add an indistinguishable, identical twin (A') to the ballot and re-vote. The likely outcome is that B wins (A=30%, A'=30%, B=40%). Thus, this system is flawed. Adding a "runoff" stage to the previous "vote for one candidate" system (the other common "solution") doesn't work either! The proof, you say? For the same scenario as before (A wins 60%- 40%), let's add nine "A" Twins and one "B" Twin. Each version of A will get 6% of the vote, and each B twin will get 20%. The runoff will be between B and B', and the result is again flawed. Various more complex schemes are often proposed, and most have been tried. But the same flaw can be demonstrated with every other "ranked"-type voting system. I invite the reader to try out the "Twin/Bozo" stress test against their favorite "other voting system". Here is an excellent "Litmus test" example to work with: Suppose that all voters in the group rate (subjectively, but honestly) candidate B as "Very, Very Good". 60% of the group rate candidate A as "Excellent", but a large 40% minority rate candidate A as "Awful". (Which candidate is really "best" is ambiguous but that's not the issue here; only whether adding choices could alter the outcome under a given voting system.) For the simple one-vote system (with or without runoff), the flaw is demonstrated as described above. Take ranked "Borda Voting" as another popular suggestion. (Borda Voting means that, with 5 candidates, everybody ranks their choices first, second, third, fourth, fifth. Each "first" vote earns 5 points for that candidate; each "second" vote earns 4 points, etc.) A wins in the simple case, but adding several Bozos to the ballot will shift the result to B. Borda is therefore flawed. Every other proposed system of ranked voting (such as successive- elimination and other even-more-hopelessly-complex schemes) can also be shown to be flawed in a similar manner. THE ONLY VOTING SYSTEMS WHICH DO NOT HAVE THIS BASIC FLAW ARE "RATED" (not "ranked") systems. "Approval Voting" (vote yes or no for each candidate, then a simple tally) is the simplest voting system which is not fundamentally flawed. My personal favorites are "Offset Approval (vote each candidate with a number between +10 and -50)" and "Rational Approval (vote yes or no for each candidate, and divide the yes count by the no count)". Let's see how basic "Approval Voting" holds up against the "Litmus Test". Clearly, the 40% minority that hates A will probably vote A=NO/B=YES for the simple A-B case. The other 60% will vote either A=YES/B=YES ("They're both quite qualified.") or A=YES/B=NO ("B isn't good enough for me.") Depending on the overall distribution of these votes (which depends on the sense of the group as to whether or not "Very Good" is good enough for the task at hand), either A or B could win this contest. However, seeing lots of Bozos is unlikely to change any particular voter's vote, whatever it was! And if the voter used to vote yes for A and now there are five indistinguishable "A" Twins on the ballot, they will simply vote yes for all of them. Result: NO FLAW. CONCLUSION: "Approval Voting" (or its variations) will produce consistent, rational results for any situation of group decision- making. ANY OTHER "RANKED" VOTING SYSTEM IS SUBJECT TO MANIPULATION (by the "nominating committee") AND/OR IS SUBJECT TO RANDOM DISTORTIONS (depending on the chance distributions of candidates). --Joop-- http://www.democracy.org.nz/

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