Dear Juho, I'm not sure what you mean by > How about using STV or some other proportional method to select the > n-1 worst candidates and then elect the remaining one?
Could you give an example or show how this would work out in the situation under consideration? Yours, Jobst > > Juho > > > On Apr 28, 2008, at 20:58 , Jobst Heitzig wrote: > >> Hello folks, >> >> over the last months I have again and again tried to find a >> solution to >> a seemingly simple problem: >> >> The Goal >> --------- >> Find a group decision method which will elect C with near certainty in >> the following situation: >> - There are three options A,B,C >> - There are 51 voters who prefer A to B, and 49 who prefer B to A. >> - All voters prefer C to a lottery in which their favourite has 51% >> probability and the other faction's favourite has 49% probability. >> - Both factions are strategic and may coordinate their voting >> behaviour. >> >> >> Those of you who like cardinal utilities may assume the following: >> 51: A 100 > C 52 > B 0 >> 49: B 100 > C 52 > A 0 >> >> Note that Range Voting would meet the goal if the voters would be >> assumed to vote honestly instead of strategically. With strategic >> voters, however, Range Voting will elect A. >> >> As of now, I know of only one method that will solve the problem (and >> unfortunately that method is not monotonic): it is called AMP and is >> defined below. >> >> >> *** So, I ask everyone to design some *** >> *** method that meets the above goal! *** >> >> >> Have fun, >> Jobst >> >> >> Method AMP (approval-seeded maximal pairings) >> --------------------------------------------- >> >> Ballot: >> >> a) Each voter marks one option as her "favourite" option and may name >> any number of "offers". An "offer" is an (ordered) pair of options >> (y,z). by "offering" (y,z) the voter expresses that she is willing to >> transfer "her" share of the winning probability from her favourite >> x to >> the compromise z if a second voter transfers his share of the winning >> probability from his favourite y to this compromise z. >> (Usually, a voter would agree to this if she prefers z to >> tossing a >> coin between her favourite and y). >> >> b) Alternatively, a voter may specify cardinal ratings for all >> options. >> Then the highest-rated option x is considered the voter's "favourite", >> and each option-pair (y,z) for with z is higher rated that the mean >> rating of x and y is considered an "offer" by this voter. >> >> c) As another, simpler alternative, a voter may name only a >> "favourite" >> option x and any number of "also approved" options. Then each >> option-pair (y,z) for which z but not y is "also approved" is >> considered >> an "offer" by this voter. >> >> >> Tally: >> >> 1. For each option z, the "approval score" of z is the number of >> voters >> who offered (y,z) with any y. >> >> 2. Start with an empty urn and by considering all voters "free for >> cooperation". >> >> 3. For each option z, in order of descending approval score, do the >> following: >> >> 3.1. Find the largest set of voters that can be divvied up into >> disjoint >> voter-pairs {v,w} such that v and w are still free for cooperation, v >> offered (y,z), and w offered (x,z), where x is v's favourite and y is >> w's favourite. >> >> 3.2. For each voter v in this largest set, put a ball labelled with >> the >> compromise option z in the urn and consider v no longer free for >> cooperation. >> >> 4. For each voter who still remains free for cooperation after this >> was >> done for all options, put a ball labelled with the favourite option of >> that voter in the urn. >> >> 5. Finally, the winning option is determined by drawing a ball from >> the >> urn. >> >> (In rare cases, some tiebreaker may be needed in step 3 or 3.1.) >> >> >> Why this meets the goal: In the described situation, the only >> strategic >> equilibrium is when all B-voters offer (A,C) and at least 49 of the >> A-voters "offer" (B,C). As a result, AMP will elect C with 98% >> probability, and A with 2% probability. >> >> >> >> ---- >> Election-Methods mailing list - see http://electorama.com/em for >> list info > > > > > > ___________________________________________________________ > All new Yahoo! Mail "The new Interface is stunning in its simplicity and ease > of use." - PC Magazine > http://uk.docs.yahoo.com/nowyoucan.html > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > ---- Election-Methods mailing list - see http://electorama.com/em for list info