Timeline for Is there a truly general voting impossibility theorem that applies to real elections?
Current License: CC BY-SA 3.0
29 events
| when toggle format | what | by | license | comment | |
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| Jan 7, 2021 at 17:24 | history | protected | CommunityBot | ||
| Nov 30, 2016 at 10:35 | answer | added | Thomas Klimpel | timeline score: 0 | |
| Jul 9, 2016 at 9:52 | answer | added | Marcus Pivato | timeline score: 7 | |
| Jul 18, 2014 at 19:53 | answer | added | Qiaochu Yuan | timeline score: 2 | |
| Jul 18, 2014 at 18:55 | answer | added | Will Sawin | timeline score: 6 | |
| Jul 16, 2014 at 14:15 | comment | added | Waldemar | @Neil Strickland Moreover, tactical voting is not necessarily equivalent to insincere voting – see en.wikipedia.org/wiki/Approval_voting#Sincere_voting. If in approval voting I’m voting only for A while I’m preferring A to B to C to D I’m voting sincerely but strategically (tactically). My reported preferences are that I’m indifferent between B, C and D. | |
| Jul 16, 2014 at 13:31 | comment | added | Neil Strickland | Let's explore further what you might mean by "reasonable conditions ... such as ... tactical voting unhelpful". In G-S, "tactical voting" means that one voter, who knows what all other voters have done, can sometimes get an outcome that they prefer by voting insincerely. I don't see any way to formulate any condition like this unless each voter has at least a preference preorder on the set of possible outcomes. Any general theory would need to cope with the special case where $n=1$ and each voter's preorder is actually a total order on the set of candidates. | |
| Jul 16, 2014 at 3:40 | answer | added | DLH | timeline score: 6 | |
| Jul 15, 2014 at 20:03 | answer | added | Timothy Chow | timeline score: 19 | |
| Jul 15, 2014 at 15:56 | answer | added | usul | timeline score: 2 | |
| Jul 15, 2014 at 12:38 | answer | added | Neil Strickland | timeline score: 6 | |
| Jul 15, 2014 at 12:28 | comment | added | Tom Leinster | @Douglas: thanks, I see your point. But still, I'm asking a more general question than the one you're answering. I'm not merely asking about the case where the input type is derivable from a total order (i.e. where if each voter has chosen a total order on the set of candidates, they do not need to think any further in order to perform the required task in the polling booth). I want a theorem that makes no assumptions at all on what the voters might be required to do. | |
| Jul 15, 2014 at 12:20 | history | edited | Tom Leinster | CC BY-SA 3.0 |
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| Jul 15, 2014 at 12:14 | comment | added | Tom Leinster | @Neil (in response to your "Also, any..." comment): you're still not thinking generally enough! A total order on the set of candidates doesn't answer every conceivable question. E.g. maybe I prefer the yellow party to the brown party, so I'd put the yellow candidates at the top of any total order I was asked to construct; on the other hand, I think it's unhealthy for the committee to be all-yellow, so I want to express the preference that at least one elected member is brown. You can't encode that in a total order, can you? | |
| Jul 15, 2014 at 12:12 | comment | added | Douglas Zare | Yes, G-S shows that there is no good voting system when you allow voters to state partial orders or preorders instead of total orders. You are adding possibilities to a set over which there is no good voting system, and this can't create a good voting system. The incoherent social choices guaranteed by G-S still exist in the enlarged set. | |
| Jul 15, 2014 at 12:08 | comment | added | Tom Leinster | @Douglas: I don't see that the G-S theorem covers it. E.g. can you deduce from it that if each voter puts a preorder (i.e. a reflexive transitive relation) on a set of 25 candidates, there is no good way of choosing the top 3? | |
| Jul 15, 2014 at 12:06 | comment | added | Tom Leinster | @Neil: but what the voters are asked to do might depend on $n$. | |
| Jul 15, 2014 at 12:05 | comment | added | Neil Strickland | Also, one possible "reasonable condition" is that if we ask the system to produce an optimal set $C_n$ with $|C_n|=n$, and then repeat for $n+1$, then we should have $C_n\subset C_{n+1}$. With that condition, we get a total order out at the end. | |
| Jul 15, 2014 at 12:05 | comment | added | Tom Leinster | @Neil: I deliberately left "reasonable conditions" flexible, because I'm simply looking for any theorem of this form. | |
| Jul 15, 2014 at 12:03 | history | edited | Tom Leinster | CC BY-SA 3.0 |
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| Jul 15, 2014 at 12:03 | comment | added | Neil Strickland | Also, any "good system" must be able to handle the case where each elector does in fact have a total preference order (with equally spaced preferences, say) and answers whatever question they are asked in accordance with that. | |
| Jul 15, 2014 at 12:01 | comment | added | Douglas Zare | The Gibbard-Satterthwaite Theorem covers anything that could be constructed from voters who do state a complete set of preferences. As far as I can tell, it covers the things you mention in the last paragraph. | |
| Jul 15, 2014 at 11:59 | comment | added | Neil Strickland | I don't think it's at all clear what "reasonable conditions" would mean in this generality. | |
| Jul 15, 2014 at 11:54 | comment | added | Tom Leinster | @Douglas: for exactly the same reason as in my first comment to Waldemar. The G-S theorem only applies to the situation where each voter is asked to put a total order on the set of candidates. | |
| Jul 15, 2014 at 11:51 | comment | added | Douglas Zare | Please clarify why the Gibbard-Satterthwaite Theorem doesn't answer your question. | |
| Jul 15, 2014 at 11:48 | comment | added | Tom Leinster | Also, that Wikipedia page says the Duggan-Schwartz theorem is about electing a nonempty set of candidates whose cardinality is not predetermined. I'm asking about the (usual) situation where it is predetermined. | |
| Jul 15, 2014 at 11:45 | comment | added | Tom Leinster | Not according to its Wikipedia page, which says the D-S theorem only applies to the situation "where each individual ranks all candidates in order of preference". I want a theorem that says that no matter what voters are asked to do, a good system is impossible. | |
| Jul 15, 2014 at 11:43 | comment | added | Waldemar | Isn't the Duggan–Schwartz theorem (en.wikipedia.org/wiki/Duggan%E2%80%93Schwartz_theorem) the answer? | |
| Jul 15, 2014 at 11:33 | history | asked | Tom Leinster | CC BY-SA 3.0 |