Thanks for your reply, lets see what I can grasp on this pass, shall we? ;)
From: Jameson Quinn [mailto:[email protected]] Sent: Sunday, June 16, 2013 10:36 PM Subject: Re: [EM] Voting Criteria 101, Four Criteria 2013/6/16 Benjamin Grant <[email protected] <mailto:[email protected]> > Re: Majority Criteria: To be honest, I am worried that some (or all) of your history lesson regarding Arrow might not have landed as well as it should in my brain. Sorry. Sometimes I tend to try to say things too succinctly, and end up leaving my meaning a bit locked up in jargon or terminology. If you have any specific questions about the "history lesson" I'd be happy to expand. No problem, I may return to that. freely assign a score of 0 to the maximum amount to each candidate (say 100), the candidate with the greatest aggregate score wins) let me see how this might fail. Lets say out of 1000 people 550 give candidate A scores of 100. Then lets say that 700 people give candidate B scores of 80 each. Lets also say that everyone else falls short of either of those totals. A gets 55,000 total, B gets 56,000. B wins. Right. On the one hand, one could say in one sense this violates Majority, but in another sense one could perhaps with even more justification claim that B actually has the larger majority. Or maybe to put another way, Majority criteria only applies to voters when the system is one person, 1 vote others perhaps Majority criteria applies to *votes*, not voters. In other words, maybe Majority criteria should be worded thusly: If one candidate is preferred by an absolute majority of *votes*, then that candidate must win. That would be stretching the criterion to the point of meaninglessness. The majority criterion speaks of voters, and Range doesn't pass, but Bucklin systems do. The more controversial case for this criterion is approval. Some try to define the criterion so that an internal preference which doesn't fit on the ballot is enough to constitute a "majority"; others prefer to define it so that a "majority" only means anything in terms of the ballots themselves. I tend to side with the latter as a matter of definition, but I certainly understand that as a practical matter approval's passing of the majority criterion leaves much to be desired. So my takeaway I think is that vis-à-vis voting systems, there are 3 kinds of voting systems with regard to the Majority criterion: systems that fulfil the criterion, systems that fail it, and systems in which majority makes no sense. I would say that First Past the Post would be an example of the 1st it is easy to see that FPTP fulfils Majority, as if over 50% of the votes cast are for A, then A wins, always. An (admittedly lame) example of the 2nd a system that fails the Majority Criterion, is the following: Of all candidates on the ballot, the one that gets the least votes, wins. Call this LPTP (Last Past the Post) However, lets look at Score Voting again which I *think* can work like this: each voter gives each candidate a score from 0 to 9 on their ballot, with empty spots being treated as 0. Then add up all the scores for each candidate, the one with the highest total score wins. Now lets look at the following election being run that way: 45 votes give Candidate A a score of 9, Candidate B a score of 6, Candidate C a score of 0, and Candidate D a score of 3 20 votes give A:0, B:6, C:9, and D:3 20 votes give A:0 B:6 C:3 D:9 15 votes give A:6 B:9 C:3 D:0 The totals are A:495 B:645 C:285 D:375 so B wins. My thought is that perhaps in the context of this vote, the concept of majority as applied in the first two example (FPTP and LPTP) doesnt work here. I also think that changing the definition of majority so that it is intelligible here will make it less understandable in the context of FPTP/LPTP. Maybe what I am wondering is, is the context of some of these voting system so different that *some* concepts like majority do not make sense in all contexts, and that trying to alter the definition to make it fit better in one context makes it fit worse in others? As originally written, I think, the Majority criterion states that: if one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win Well, in the above Score Voting system context, the concept of preference as an all or nothing trait makes no sense. You could has scores of A:9 B:6 C:3 D:1 and be said to in some sense express some amount of preference for each of them. The only way in which the criterion would make sense is if we mutated the criterion somewhat like this: if one candidate is preferred (at the highest score or ranking, where such exists) by a majority (more than 50%) of voters, then that candidate must win OK, lets create a new Score Voting election, four candidates, 100 voters, 0-9 scores: 51 votes: A:9 B:7 C:4 D:0 29 votes: A:0 B:5 C:6 D:9 11 votes: A:1 B:7 C:4 D:0 9 votes: A:2 B:0 C:9 D:2 Results: A:488 B:555 C:515 D:255 Well, in this case over half of the group ranked A the highest, but ranked B just a little lower. I guess we could say that in one sense A did not win even though he got the highest vote from over half. And yet I dont feel bad about B winning since the 51 percent likes B almost as much, and B had much more support than A with both the 29% and the 11%. It seems intuitive to say that B had more support than A in that election. And yet, it also seems intuitive to me to say that the Last Past the Post (LPTP) election system is a bad one. Whats bad about LPTP that is simultaneously not bad about B winning the above election? Maybe we ought to toss out the Majority criterion altogether, and replace it with something more on point? (I know, who the heck am I to suggest such a thing, I am not sure I am suggesting it seriously as much as following the thought process to its conclusion.) Maybe the underlying idea is behind the desire for the Majority Criterion is two-fold: 1) We dont want to see losers win. We dont want someone winning who is obviously (in some sense) received less support than someone they beat. For example, LPTP: in a single vote system, where each person votes for only a single candidate on the ballot, and then all votes are added, and the one with the least votes wins we do not want to see that outcome, assuming that the intent of the ballot is presented as voting for your favorite candidate. 2) We also dont want to see a FPTP election where five people run for office, one candidate gets 26 percent of the vote and wins, but 74% of the voters got their preferences overruled by the 26% - minority rule. So perhaps thats another criteria dealing with something like the greatest good for the greatest number or something? The first one can probably be worded something like A more preferred candidate should not lose to a less preferred candidate, and then if needed people can argue over what it means to be more preferred or less preferred in different contexts. However, in the ones where it matters, ie, LPTP it should be obvious. As to the second I think that is what the Majority criterion is trying to encapsulate. At any rate, it is the only piece that I *personally* need from a system. I am not sure how to word it it. Perhaps something like this: If, as quantified by the voting system, the preference that a candidate be elected is less than the preference that they NOT be elected, then they must not win. Or more strongly, perhaps, If, as quantified by the voting system, a candidate cannot muster more support for their election than against it, they must not win. OK, so now we have two criterion: Losers Cant Win: A more preferred candidate must not lose to a less preferred candidate. (This one may be so trivially obvious that no one ever bothered to name it or worry about it.) No Minority Rule: If, as quantified by the voting system, a candidate cannot muster more support for their election than against it, they must not win. Now for all I know, either or both of the above already exist as a criterion that I just havent bumped into yet if so, please tell me what their proper name is so I can use it. Heres my main question though: As understood, under what circumstances can a voting system FAIL the Majority Criterion, but NOT fail either Losers Cant Win or No Minority Rule, as defined above? Or to put another way, if we retain LCW and NMR, do we really need the seemingly more vague Majority Criterion? Thoughts? Anyone? Beuler? Will respond to points on the other Criteria in a following post, this is I am sure quite long enough on its own. -Benn Grant eFix Computer Consulting <mailto:[email protected]> [email protected] 603.283.6601
---- Election-Methods mailing list - see http://electorama.com/em for list info
