Timeline for Is there a truly general voting impossibility theorem that applies to real elections?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 17, 2014 at 11:51 | comment | added | Tom Leinster | Tim: yes, the empty ballot is certainly included among the "anything" that the voters could do. | |
| Jul 17, 2014 at 1:02 | comment | added | Timothy Chow | @SamHopkins: My understanding is that the counterexamples you mention involve an infinite population, not an infinite ballot. | |
| Jul 16, 2014 at 16:00 | comment | added | Sam Hopkins | Aren't there counterexamples to Arrow's theorem when we have an 'infinite ballot', though?: en.wikipedia.org/wiki/… | |
| Jul 16, 2014 at 15:56 | history | edited | Timothy Chow | CC BY-SA 3.0 |
Added a long clarification
|
| Jul 16, 2014 at 15:01 | comment | added | Timothy Chow | Tom, I have not actually changed your question, just the way of thinking about your question. Nothing I said relies on total orders or partial orders. For any thing that you want the voters to do, just think of it as capturing every desire that that voter has and nothing more. Let me turn your comment back on yourself and suggest that you're not thinking generally enough. Is the empty ballot, where every voter submits nothing at all, included among the "anything" that the voters could do? It should be, if you're truly thinking generally. | |
| Jul 16, 2014 at 1:14 | comment | added | Tom Leinster | That's an interesting set of thoughts, Tim, and I've learned from it. However, you're changing my question into a different (also interesting) question. I asked what I wanted to ask! Conceivably, there's something voters could do that bears no resemblance to any kind of order (partial or total) but would result in a fair way of picking a cardinality-$n$ subset of the candidates. I'm looking for theorems that say this is impossible, avoiding the assumption that imposing a total order is the most sophisticated thing a voter might do. (E.g. see my brown/yellow comment above.) | |
| Jul 15, 2014 at 20:03 | history | answered | Timothy Chow | CC BY-SA 3.0 |