[EM] Auctions
Voting by auction-- morally repugnant but strategy free! The simple, humble Clarke tax method does seem a bituh unfair to me. There are various ways to remedy this problem like having it be based on the log of your income or making it based on how much income you have left as a means of judging how much you have contributed. There is a near endless number of ways to tweak this in order to amount to something useful. Here is my question: Let's say voters have this imaginary currency. It is a multiwinner race and they can distribute as much as they want to each candidate. Let's say you take the (relatively) extreme measure of determining the winners according to (what essentially amounts to...) naive Range voting. Now go back and eliminate any ballot that overvoted.. Or instead of elimination for overvoting, you could use some other method of reallocation, the point is simple: The methods will be based on naive Range. You determine the first set of winners this way. (You could conceivably use naive approval or naive something else, but what is the point...) ; ) auction-type methods rely on weakening overvotes rather than the more traditional elect one candidate and then punish the supporters. As a starting point, let me explain what I mean by Naive Auction Range before before proposing more complicated methods. Here is how it works. 1) Voters fill out a range ballot. An ordinary Range ballot 2) The Naive Range winners are calculated. 3) you go back and eliminate any ballots that have voted more than whatever the individual maximum score was (in this case 99) 4) go to 2 We can make an improvement to this: Naive Reweighted Auction Range instead of eliminating overvoting ballots, change their weight such that they are no longer overvoting. You could make arule that once it gets to one tenth or some arbitrary number it is no longer counted to prevent infinite loops. You could also make an eliinated ballot simply become a Cumulative Vote ballot instead. To my knowledge, acution type iteration hasn't really been discussed. Disclaimer: it is about 1 AM and I ate way too much candy. I also didn't look very hard for previous mentions of a similar topic. Greg Nisbet The Ten Commandments contain 297 words. The Bill of Rights is stated in 463 words. Lincoln's Gettysburg Address contains 266 words. A recent federal directive to regulate the price of cabbage contains 26,911 words. – The Atlanta Journal Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Auction-type Iteration
I think I should explain this a bit further and add more examples and possible methods. For the moment, just focus on the naive Overvote and DIE method Naive Auction Range. I am not quite sure of the time complexity of this, but two conditions would allow it to terminate its loop early: 1) if the result of the post-killing overvoters election is exactly the same or if no overvotes are found --exceeding unlikely, but still a good point to mention. To be perfectly honest, I haven't done much initial testing on this, but I will have a program for it ready by about err some time tomorrow, maybe. I am too tired to program *YAWN* More on this issue: as you can probably guess, many improvements can be made to overvote and die. One of them I suggested was aallowing ballots to be reduced. Another one is falling back to a different type of ballot. ONe decreed to be a non-overvote. Like an SNTV ballot, an STV ballot, a CV ballot, a PBV ballot etc. This type of iteration (I think) achieves relatively good clone immunity. Granted, it isn't perfect. However, the Reweighted Overvote and Die method would allow this to some extent. You could probably do one better by incorporating a cardinal type element in it That way, if you overvote, you can drop candidates such that you are not overvoting anymore. This could also be achieved by having multiple ballots. When one ballot is deemed illegal due to overvoting, you would switch over to the highest ranked working ballot. One could also allow some level of overvote forgiveness... or one could make overvote elimination probabilistic. In a later, more structured email, I will have about a dozen or so variants. Greg Nisbet The Ten Commandments contain 297 words. The Bill of Rights is stated in 463 words. Lincoln's Gettysburg Address contains 266 words. A recent federal directive to regulate the price of cabbage contains 26,911 words. – The Atlanta Journal Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] language/framing quibble
Fred Gohlke wrote: Good Morning, Kristofer There is so much good material in your message that, instead of responding to all of it, I'm going to select bits and pieces and comment on them, one at a time, until I've responded to all of them. I hope this will help us focus on specific parts of the complex topic we're discussing. For today, I'm going to concentrate on two of your comments regarding group (or council) size: 1) Have a council of seven. Use a PR method like STV to pick four or five. These go to the next level. That may exclude opinions held by fewer than two of the seven, but it's better than 50%-1. If you can handle a larger council, have one of size 12 that picks 9; if seven is too many, a group of five that elects two. For small groups like this, it might be possible to make a simpler PR method than STV, but I'm not sure how. 2) It's more like (if we elect three out of nine and it's always the second who wins -- to make the diagram easier) e n wLevel 2 behknqtwz Level 1 b e h k n q t w z Level 1 abcdefghi jklmnopqr stuvwxyzA Level 0 The horizon for all the subsequent members (behknqtwz) is wider than would be the case if they were split up into groups of three. In this example, each person at a level represents three below him, just like what would be the case if you had groups of two, but, and this is the important part, they have input from the entire group of eight instead of just three. Thus some may represent all the views of less than three, while others represent some of the views of more than three. The latter type would be excluded, or at least heavily attenuated, in the triad case. For convenience, I'll work with a group size of 9 picking 3 by a form of proportional representation: Am I correct in imagining the process would function by having each of the 9 people rank the other 8 in preferential order and then resolve the preferences to select the 3 people that are most preferred by the 9? Yes. In a truly unbiased scenario, each of the 9 people could submit a complete ranking (including himself), but since you've said you don't want voters ranking themselves first, they would rank all but themselves. Either the method would consider them equal-first, or have some sort of special no opinion provision (like Warren's Range). That seems like a really good idea. It is, however, a new idea for me, so it may take me some time to digest all the ramifications of the concept. Even so, the first thoughts that leap to mind are: 1) It would allow voting secrecy. In a group size of 3 selecting 1, secrecy is not possible; a selection can only be made if 2 of the three agree on the selection. Many people say secrecy is important. For my part, I'm not sure. It may be important in the kind of electoral process we have now, but I'm not sure open agreement of free people is not a better option. You could weaken that in two ways. The first would be to simply make the voting public. For instance, each person may need to say my vote is A, then B, then C.., and then that is recorded. The second would be to have a consensus step like I considered in my previous post, where the proportional representation method is just advisory, and what really counts is a supermajority vote for who'll go onwards. The second wouldn't really be PR, though - or rather, it would only be so if the councilmembers are all good negotiators. 2) It reduces the potential for confrontation that would be likely to characterize 3-person groups. We can make the argument that, in the selection of representatives, confrontation is a good thing. Seeing how individuals react in tense situations gives us great insight into their ability to represent our interests. We can also make the argument that a pressure-cooker environment is hard on the participants. This returns us to the subject of optimal council sizes. I already talked about Parkinson's coefficient of inefficiency (that committees degrade significantly above 20 members), but beyond that, I think the only way to really know or to find answers to your questions - such as whether confrontation is too intense at three, or if it's too slack at nine - is to try it. People are people, so not everything can be derived from models. There is one thing I will add, though. If we have a very simple concept of how people negotiate, where each have to know all the others to find a good compromise, then the collective burden increases as the second power of the number of members. (For n members, each has n-1 links, so n*(n-1)). This means, for the simple model at least, that we pay more by increasing the size from 10 to 17 than from 3 to 10. 3) Each participant's opportunity to evaluate each other participant is reduced; they must evaluate 8 people in the allotted time
Re: [EM] Auctions
On Sat, Nov 1, 2008 at 7:53 AM, Greg Nisbet [EMAIL PROTECTED] wrote: Voting by auction-- morally repugnant but strategy free! Why? In any case, the Clarke tax method has serious issues, but in principle, you give each option on honest utility rating. The simple, humble Clarke tax method does seem a bituh unfair to me. There are various ways to remedy this problem like having it be based on the log of your income or making it based on how much income you have left as a means of judging how much you have contributed. There is a near endless number of ways to tweak this in order to amount to something useful. The big issue is that according to economic theory, nobody would vote. If someone is in a polling booth, they have already ignored economic theory and thus there is no way they are going to care about a tiny probability of paying. Or instead of elimination for overvoting, you could use some other method of reallocation, the point is simple: What's an overvote? Do you mean people who bid more than they have? auction-type methods rely on weakening overvotes rather than the more traditional elect one candidate and then punish the supporters. As a starting point, let me explain what I mean by Naive Auction Range before before proposing more complicated methods. Here is how it works. 1) Voters fill out a range ballot. An ordinary Range ballot 2) The Naive Range winners are calculated. 3) you go back and eliminate any ballots that have voted more than whatever the individual maximum score was (in this case 99) 4) go to 2 That is an endless loop, I assume you mean: 1) Voters fill out a range ballot. An ordinary Range ballot 2) eliminate any ballots that have voted more than whatever the individual maximum score was (in this case 99) 3) The Naive Range winners are calculated. instead of eliminating overvoting ballots, change their weight such that they are no longer overvoting. Right, another option is to make it impossible to overvote. If there is space only for 2 digits, then you can't overvote. You could make arule that once it gets to one tenth or some arbitrary number it is no longer counted to prevent infinite loops. Huh? You could also make an eliinated ballot simply become a Cumulative Vote ballot instead. Huh again :). To my knowledge, acution type iteration hasn't really been discussed. Disclaimer: it is about 1 AM and I ate way too much candy. I also didn't look very hard for previous mentions of a similar topic. Election-Methods mailing list - see http://electorama.com/em for list info
