20201202, 03:18  #12  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,143 Posts 
Quote:
There are solutions to give both higher percentages and lower percentages, so those can be eliminated quickly. Indeed the given percentage is very specific, and that is why it was easy to find the answers. It could also be done by hand if one were so inclined, it wouldn't take very long at all. Last fiddled with by retina on 20201202 at 03:21 

20201202, 04:47  #13 
Romulan Interpreter
Jun 2011
Thailand
3·47·67 Posts 
Agree from this part of the world, if you limit your pi's to [100,150], there are about 350 millions (51^5) possibilities in the whole search space, so a brute force is quite fast, without any "intelligence" behind. Write a pari line with 5 for or while loops one inside the other and forget it for a while (pun intended).
(Edit: I considered that the "odd pi" trick is there only to ensure there is no "tie" in voting, but as long as there is no tie, the even numbers work as well, that is why I said 51, and not 25). Last fiddled with by LaurV on 20201202 at 04:54 
20201202, 06:28  #14  
Jul 2015
2×13 Posts 
Quote:


20201202, 07:09  #15  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,143 Posts 
Quote:
And I find 1336 results. Also, I now find 104 results for the original puzzle, after seeing that I did indeed have a mistake. And curiously these results are the same for both 1000 and 1001 electors, so the error in the definition statement makes no difference. 

20201202, 12:51  #16  
Feb 2017
Nowhere
2^{6}·71 Posts 
Quote:
Quote:
One of the presentday complications in the US presidential election system is that Maine and Nebraska do not assign electors by "winner take all." Possibly the most undemocratic US presidential election was that of 1824. According to History.com, Quote:
Then there was the election of 1876... 

20201203, 02:07  #17 
Romulan Interpreter
Jun 2011
Thailand
3×47×67 Posts 
Because that's trivial. 74.5424292845258 for odds, and 74.6268656716418 when evens are included too, due to the fact that you can make the "won" electorates 150, while in the first case you can only make them 149, so you got a bit higher percentage
You only need pencil, paper, and 3 minutes to find that out. Last fiddled with by LaurV on 20201203 at 04:13 
20201203, 02:24  #18  
Romulan Interpreter
Jun 2011
Thailand
3·47·67 Posts 
Quote:
Last fiddled with by LaurV on 20201203 at 04:23 

20201203, 14:17  #19 
Oct 2017
1110010_{2} Posts 
Has anyone a link to a list of the number of eligible voters for each state of the USA and to the realworld nonsimplified formula, how the electors are computed?
I found a list, how many voters voted in each state, but I guess that we shall use the number of eligible voters. Or is that the real task? 
20201203, 15:22  #20  
Feb 2017
Nowhere
1000111000000_{2} Posts 
Quote:
Quote:
Each State's electors are assigned according to State law. In all but Nebraska and Maine, the rule is "winner take all." Nebraska and Maine divide the electors to reflect the popular vote, but I don't know the formula. As to eligible voters, the basic requirement is citizenship, and the age requirement is at least 18, by the TwentySixth Amendment. Some (naturalborn or naturalized) US citizens who are old enough to vote are ineligible because e.g. they are convicted felons. In order to cast a ballot, an otherwise eligible voter has to register to vote. This part of the process allows States to prevent otherwise eligible people from voting because they are not rich enough, not white enough, or not Republican enough. The number of registered voters in each State is probably available on line. You might try the US Census or ballotpedia,org EDIT: This Ballotpedia page has a table of registered voters by state as of 2018. Last fiddled with by Dr Sardonicus on 20201203 at 17:14 Reason: xifgin posty; and as indicated 

20201203, 18:51  #21 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10010101101001_{2} Posts 
Nebraska and Maine allot 1 elector per congressional district (most votes in that district determines who gets that elector) and then the 2 remaining electors "atlarge" are assigned based on who got the most votes in the state.

20210110, 15:35  #22 
Jan 2017
5A_{16} Posts 
Adding my solution here since the month is over:
This was quite an easy problem, with a straightforward solution that requires no programming either. That each state is between 100 and 150 population means that the candidate that wins 3 states is always the overall winner (wins states with at least 303 votes, opponent at most 298  the details of the elector stuff can never matter). Maximal loss in this setup means getting every vote in the 2 biggest states, and maximum nonwinning amount in the 3 smallest. The only possible ratio within the given population sizes that is close to 71.781305% is 405/567 (as you can see with standard rational approximation, or just an exhaustive search). So the total population is 567, and the loser gets 405 votes. The winning candidate gets 567407=160 votes. In a minimal win, he gets (population+1)/2 votes in each of the smallest 3 states. So (p1+p2+p3+3)/2=160, and p1+p2+p3=317. Any state sizes where the sum of the 3 smallest is 317 and total population is 567 are a valid solution. 
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