> I would say that > the "majority" criterion in other systems (plurality > w/ run-off, IRV, Majority Choice Approval) is a shade > arbitrary.
> Stepjak I can make two arguments about MCA's arbitrariness. A one candidate Approval vote is like saying yes or no to choosing the candidate. However, there is a region between the no (0% = 0) and the yes (100% = 1). You either vote the candidate in (1) or not (0). In other words, it's a like an analogue to digital system. The analogue signal needs to converted to a 1 bit number. For such a A-to-D system, where should the cut off point be? Right in between the 0 and 1. 0.5, that is. Now back a bit to MCA. MCA has Favored, Compromise and Unapproved. If the Compromise level were removed, all that would remain is Favored and Unapproved. In other words, just ordinary Approval. There is the argument that only the candidate(s) that get a yes from the "A-to-D" system should win. That means only candidate(s) with more than 50% Favored should win. Obviously, there would need to be more steps if none of the candidates got more than 50% of the Favored votes and a candidate had to be chosen. However, I've been wondering whether one candidate 'trumps' all of the other candidates if the candidate was the only one that got greater than 50% of the Favored votes. Suppose there is a three candidate MCA race, where all voters submit the following sincere votes: 51 ABC 49 BCA Using 50% as the percentage Favored votes required for a win, A would win with MCA. However, it would be natural to assume that the opposite of Favored is Unapproved. That is, MCA has levels that are like a 3-level Cardinal Ratings system with each Favored vote getting +1 and each Unapproved vote getting -1. Therefore, each Compromise vote should get 0. Using this, B would be the winner. For A, the 49 Unapproved votes cancels out virtually all of the 51 Favored votes. For B, none of the 49 Favored votes is cancelled out. (Interestingly, A is the Condorcet Winner in this race.) So, what is the Favored win percentage that is required to "trump" the other candidates? 67 ABC 33 BCA Nett favored votes: A: 67 - 33 = 34 B: 33 - 0 = 33 C: 0 - 67 = -67 In other words, 2/3 of the votes must be Favored votes. It seems to me that 2/3 could be a hard target to reach. After all, it is only 10% (a tenth) away from 75% (3/4). Therefore, voters and possibly candidates might not think too much about Favored votes. Admittedly, these two examples are only three candidate cases. With more candidates, candidates would be given joint "levels." The likelihood of more than one candidate getting 2/3 of the Favored votes would increase. However, in an MCA race with more than three candidates, how would voters vote? How should voters vote given that each voter would have their own utilities for each candidate? In other words, quantitatively, where is the cut off point between Favored and Compromise? Where is the cut off point between Compromise and Unapproved? Could these cut off points be positioned fairly by choosing the correct Favored vote percentage/cut off point? Thanks, Gervase. ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
