Sorry if the thing already has a name. Let's suppose there is a vote, where the voters are to chose from a number of numbers. For example, the membership fee of the club, the minimum age of application, the size of the office, anything.
Something where we can suppose: If a person prefers number a over number b, and a > b > c then she will prefer b over c (because c is even further from a). Also, if she prefers a over b and a < b < c then she will prefer b over c (because c is even further from a). Scenario one. They vote by everyone giving her first preference then they search the median value. For example: Let the membership fee be: 200$ 7 votes ------------------------------- (-) 180$ 16 votes ------------------------------- (-) 150$ 23 votes ------------------------------- (+) 140$ 9 votes ------------------------------- (+) 100$ 32 votes ------------------------------- (+) 70$ 2 votes In this ladder-like scheme I put a sign at the end of each separating line: the sign is - if there are more votes under the line, and is + if there are mor votes above the line. The winner is the 150$ because there is the change, so more than half of the voters wants the fee be 150$ or higher, and more than half wants it to be 150$ or lower. Scenario two. They vote Condorcet, while they keep the above mentioned convention: if somebody sees 180$ as the best option she must prefer 140$ over 70$ etc. The convention says nothing about the preference between, say, 200$ and 70$ in this case. Theorem 1: If in scenario one there is a winner (no ties) then in scenario two there is a Condorcet-winner and is the same as the "ladder" winner in scenario one. Theorem 2: The ladder voting is strategy-free. I don't waste the space with proofs, they seem pretty obvious. The theoretical (well, maybe sometimes practical, yes, we used sometimes to vote about numbers) significance I see mainly in the second theorem. We don't have many strategy- free voting methods, only this, the Clarke-tax and the random methods mentioned usually with the Gibbard-Satterthwaite theorem: (random vote and runoff between two random candidates) for more than 2 choseable possibilities. Peter Barath ____________________________________________________________________ Tavaszig, most minden féláron! ADSL Internet már 1 745 Ft/hó -tól. Keresse ajánlatunkat a http://www.freestart.hu oldalon! ---- Election-Methods mailing list - see http://electorama.com/em for list info
