Wikipedia:Reference desk/Archives/Miscellaneous/2023 December 11

= December 11 =

No winner in the second round
Under two-round system what if still no winner emerges in the second round? Would there be a third round of elections? Thanks. 212.180.235.46 (talk) 15:26, 11 December 2023 (UTC)
 * Under a two-round system, only the top two candidates from the first round go through to the second. Unless there is a dead heat, one must then achieve a majority.  Are you perhaps thinking of the exhaustive ballot system when you keep voting with the candidate having the least votes eliminated at each stage? Martin of Sheffield (talk) 15:50, 11 December 2023 (UTC)
 * I mean what if both candidates fail to achieve that majority in the second round? Would there be a third one? 212.180.235.46 (talk) 14:13, 12 December 2023 (UTC)
 * If there is a dead heat, the means of tiebreak may be specified in the rules of the particular election. It could be as simple as Coin flipping. However, for example, the French constitution (found as a reference from 1962 French presidential election referendum) states that the President shall be elected by an absolute majority of votes cast and doesn't say what to do in the event of a tie in the second ballot. AlmostReadytoFly (talk) 14:21, 12 December 2023 (UTC)
 * Regarding French Presidentual elections this article quoting a constitutional scholar, explains that: 1) such a case is considered so unlikely that it's not covered in the constitution; 2) but nonetheless were it to happen, the Constitutional Council (the French equivalent of the Supreme Court, but for constitutional matters only) would need to settle the case, likely by deciding that the vote be taken again. And for those who wonder why it's considered so unlikely, a difference of a single vote among some 32 million cast (as was the case in 2022) would be enough to decide in favor of one candidate over the other. Xuxl (talk) 14:42, 12 December 2023 (UTC)
 * the simplest thing would be to call for a recount. Manual recounts rarely produce exactly the same result, and just one vote difference would sort it out. Martin of Sheffield (talk) 14:49, 12 December 2023 (UTC)
 * No, obviously we're talking about the case where there is a tie after the recount that would have happened in any close case. --142.112.220.31 (talk) 17:47, 12 December 2023 (UTC)
 * Yes, while I don't know about the French system in particular, I think most systems have some provision for a recount if the vote is close enough. Sometimes it may even be automatic. But in any case, it's very likely that if the vote was close enough that a tie is possible there is going to be a recount so this would only arise after all that is sorted out. And because as unlikely as an exact tie is, it's even more unlikely you'll get a tie both from the initial full count and the recount, I think we can largely discount the possibility this will happen. I guess theoretically there could be some system which says something like the loser may ask for a recount if the vote is within 0.1% (or whatever) and it isn't automatic in any scenario which means you now have a problem with a tie even before the recount but I wonder if such a system exists. Nil Einne (talk) Nil Einne (talk) 17:13, 16 December 2023 (UTC)
 * List of close election results lists ~twenty notable election ties and their outcomes. Modocc (talk) 17:38, 16 December 2023 (UTC)
 * Assuming 32 million voters cast a vote, each flipping a fair coin to decide the choice, the probability of a tie is less than 1 in 109632956. It is more likely that a blind monkey in front of a typewriter, assiduously but randomly hitting the keys, hammers out the text of Shakespeare's Hamlet without a single typo. --Lambiam 16:27, 12 December 2023 (UTC)
 * No, that number would be 1 in 232,000,000: it's the probability of any one pre-specified sequence occurring if the votes are listed in order. You have to multiply it by the appropriate binom in ial coefficient. In this case the probability is a tie is obviously (2n choose n)/(n!)2 (2n choose n)/22n, which is to say ((2n)! / (n!)2) / 22n, where n = 16,000,000. Using Stirling's approximation for the factorials and simplifying by hand, I make that to be 1/&Sqrt;(&pi;n): perhaps someone can check that with a symbolic algebra package.  It works out to about 1/7,100.  Of course, given that the number of voters is only approximate, the practical probability is only half of that, since we also have to consider the probability that the total number of voters is odd. --142.112.220.31 (talk) 17:47, 12 December 2023 (UTC)
 * I indeed made a stupid mistake, computing $$1/\textstyle\binom{2n}{n}$$ instead of $$\textstyle\binom{2n}{n}/2^{2n}.$$ The formula (2n choose n)/(n!)2 you gave is also incorrect, but the next one is correct. Rather than using Stirling's approximation directly, it is easier to use the formula from, which I linked to above, --Lambiam 07:26, 13 December 2023 (UTC)
 * Sorry, stupid editing error on my part. I wrote the second formula first and then decided to show where I got it from, and blew it. And it seemed easier to me to use Stirling's approximation because it was familiar to me and the other formulation was not. Anyway, I believe my 1/7,100 (or in practical terms 1/14,200) is correct. --142.112.220.136 (talk) 06:38, 15 December 2023 (UTC)

What is this pastel pink/blue building in the article Sawgrass Mills?
If you scroll down until you see a photo in the article Sawgrass Mills, there is a photo taken in “The Oasis” section. There is some pastel pink/blue building behind the back. What is it? Is it a movie theater? Is it an amusement center? Or it is just a outlet?(There is also a woman in the photo) —The Industrial Me 1563 (talk) 18:30, 11 December 2023 (UTC)
 * Regal Cinema https://www.google.com/maps/place/Sawgrass+Mills/@26.1545373,-80.3222978,3a,75y,88.54h,92.92t/data=!3m7!1e1!3m5!1sAF1QipO3nlRdXB2yL_HlPVsbYOb8kaZ4I1Z-UIsaJW8!2e10!3e11!7i13312!8i6656!4m6!3m5!1s0x88d908feeaeded1f:0x29c1bf6101ce3a42!8m2!3d26.151701!4d-80.320787!16zL20vMDk0a2Qw?entry=tts Nanonic (talk) 19:39, 11 December 2023 (UTC)
 * Thanks. —The Industrial Me 1563 (talk) 21:13, 11 December 2023 (UTC)