Timeline for Is there a truly general voting impossibility theorem that applies to real elections?
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13 events
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| Jul 17, 2014 at 6:59 | comment | added | Waldemar | @Tom Leinster One solution to this problem is to apply a modified version of the range voting system. Candidates are not individuals but cardinality-$n$ subsets. One subset is a winner. We get an unordered $n$-element set. | |
| Jul 17, 2014 at 1:03 | comment | added | Timothy Chow | @NeilStrickland: See the edit to my answer for a fuller explanation of what I meant. | |
| Jul 16, 2014 at 17:08 | comment | added | Tom Leinster | @Waldemar: it's true that if you pick a single winner $n$ times, you get a list of $n$ candidates. But it gives $n$ candidates in order, whereas I was asking for an unordered $n$-element set (because that's what's often wanted in practice). | |
| Jul 16, 2014 at 15:53 | comment | added | Neil Strickland | @TimothyChow: "After all, if the preference is not expressed, why postulate that it exists at all?" This whole subject area starts with the issue that voters have strong preferences beyond what they can express by ticking a single candidate, and this is perceived to be a serious problem in practice. If you assume that away, then there is not much left to talk about. Certainly, you cannot formulate anything like the Gibbard-Satterthwaite axioms without assuming that voters have a preference preorder on the possible outcomes. | |
| Jul 16, 2014 at 15:45 | comment | added | Neil Strickland | @TimothyChow: Tom does not want to force voters to provide more information, but he wants to allow it (or at least, consider allowing it); see his yellow vs brown comments. Any system that allows rich preferences must cover the case where all voters happen to have rich preferences, and that special case is equivalent to a system where voters are forced to specify rich preferences. | |
| Jul 16, 2014 at 15:22 | comment | added | Timothy Chow | @NeilStrickland: As Tom himself said, he doesn't want to increase the information content. He just wants to allow more general voter preferences. I'd recommend not thinking in terms of "information content"; that presupposes that voters have all kinds of complicated preferences in their heads and we're just sampling those preferences with a ballot. For the kind of generalization that the OP wants, I think it's better to picture the voters as not having any preferences at all beyond what appears on the ballot. After all, if the preference is not expressed, why postulate that it exists at all? | |
| Jul 16, 2014 at 15:06 | comment | added | Waldemar | @Tom Leinster I’m not sure if the approval voting (or rather its generalized variant – range voting) does not answer your question. First, you were not looking for a solution but for an impossibility theorem. It seems to me that an existence of a solution can be interpreted as the impossibility of the impossibility theorem. Second, if you repeat a procedure $n$ times then you can get a cardinality-$n$ subset and not just a single winner. | |
| Jul 16, 2014 at 12:48 | comment | added | Tom Leinster | @NeilStrickland: it's not accurate to say that I "want to increase the information content". I'm completely open as to what the voters do inside the booth. | |
| Jul 16, 2014 at 12:45 | comment | added | Tom Leinster | I'm glad to learn the phrase "approval voting"; I'd mentioned marking out of 10 in my question, and this is marking out of 1. But again, this isn't an answer to my question. (I can only apologize that it seems to have been unclear, but I don't see how to make it any clearer.) First, I wasn't looking for any "solution": I was looking for a general impossibility theorem. Second, you're talking about selecting a single winner, and although that's an interesting special case, I was asking about electing a cardinality-$n$ subset of the set of candidates, where perhaps $n > 1$. | |
| Jul 16, 2014 at 9:22 | comment | added | Neil Strickland | Note that this is compatible with Timothy Chow's answer: approval voting avoids strategic voting by reducing the information content of each voter's input (relative to the situation envisaged by Arrow), whereas the OP seemed to want to increase the information content. It seems clear that some voters will be unhappy that they have to group awesome candidates together with barely acceptable ones, and one could probably produce formal criteria to reflect that kind of unhappiness, but I do not know whether that has been done. | |
| Jul 16, 2014 at 6:13 | comment | added | Gerry Myerson | en.wikipedia.org/wiki/Approval_voting has a table of system desiderata and the extent to which approval voting meets them under various assumptions about voter preferences, also a discussion of vulnerabilities to strategic voting. | |
| Jul 16, 2014 at 3:41 | review | First posts | |||
| Jul 16, 2014 at 4:49 | |||||
| Jul 16, 2014 at 3:40 | history | answered | DLH | CC BY-SA 3.0 |