Dear Abd ulRahman! Welcome to the list from me, too.
What do you think about the following story (leading to a group decision method somewhat similar to DMC): Consider a group of people having to decide for one out of a number of options. At first, they may think that deciding by a "simple vote" would be both easy and efficient. So they come together and let each one raise her hand for her favourite option. After a number of these "first past the post"-decisions they realize some problems. Sometimes some individuals have not enough information to decide for a single favourite or are undecided for other reasons, so the group changes the system and allows for abstention. But they realize also that sometimes two very similar options both lose but would have won if only one of the two would have been suggested (the "spoiler" effect). And they realize that moderate compromise options often lose because the group tends to be polarized between two extremes one of which will win instead of the compromise. Finally, there may be rare occasions where some member of the group tries to "cheat" and vote for a second option as soon as he realizes that his favourite has no chance of winning. For all of these reasons someone suggests that they simplify the voting procedure slightly by letting everyone vote for as few or as many options as they like. Although some object that this would violate "one man one vote" and would therefore give some voters more power, they give it a try and soon find out that it's not true that the more options you vote for the more weight your vote has. So they switch to the new system, and at first it seems to work much better and avoid the problems they had. But after a number of these "approval voting"-decision they realize a strange effect: sometimes only few voters actually make use of the possibility and most still only vote for one option, although often it is clear that they in reality also approve of another option. After some analysis they find out that this insincere "bullet voting" has various strategic reasons. Someone suggests to get back to the old system, but upon closer inspection they find also evidence of strategic voting in the old system. Now someone makes a somewhat "unorthodox" suggestion: In order to avoid choosing a bad option only because of strategic voting, they treat the first voting round only as a kind of poll to base the real decision upon. The real decision would go like this: one of the group is declared the "moderator" by lot. The moderator's duty is to pick what seems to be the best compromise option in view of the information from the first round. If s/he picks the option with the most votes, that options is indeed declared the winner. But if she picks a different option, this choice is then checked by the group like this: because each option which got more votes than the moderator's option seems to be a better choice at first glance, the moderator asks the group to affirm by simple majority vote that her picked option is actually a better compromise than the other option. If the picked option wins all these pairwise comparisons, it is declared the winner, otherwise the moderator must pick a new option until a winner is found. Although this seems to be more complicated than the other two systems, and even introduces some randomness because the moderator is chosen by lot, over the time they find a number of advantages of the third system: First of all, it is much harder to mess up the result by voting strategically, because of the additional check and because that check is lead by a randomly chosen person. Second of all, it turns out that sometimes there is an option which beats all others in direct pairwise contests but would not have won in either of the first two systems; whereas the new system gives such "Beats-all-winners" a fair chance of winning because the moderator need only pick this option and it will win. Also, minorities will not so easily get the impression of being oppressed by a majority since they still often have the chance to improve the result by providing the moderator. The chance to become the moderator also encourages thinking about compromises instead of only thinking of one's favourite, and this can finally lead to suggesting getter compromises in the first place. Finally, the additional "check" gives everyone the feeling that the system is safer and uses more of the available information than the other two; obviously wrong decisions are much less probable. Now, although I used many words to introduce this group decision method to you, I still think it is very easy to understand the procedure and the reasons for it, do you agree? Yours, Jobst PS: The above method makes use of Forest Simmons' idea to combine pairwise preference defeats and approval defeats. I call it "Democratic Fair Choice" (DFC). The set of possible winners (= those options which would win if the moderator picks them = those options which beat all more-approved ones in pairwise comparisons) always includes the Approval winner, the DMC winner, and the Condorcet winner, if one exists. The random component can be interpreted as using the well-known method "Random Ballot" to choose from a set of "good" options. Hence the method can be considered a compromise between three classical approaches, namely Random Ballot (good because of perfect strategy proofness), Approval Voting (good because of simplicity and efficiency when voters are honest), and Condorcet (gives great stability against a-posteriori-complaints). A version of DFC designed for public elections is in the wiki: http://wiki.electorama.com/wiki/Imagine_Democratic_Fair_Choice ---- Election-methods mailing list - see http://electorama.com/em for list info