Puzzle Time - Election Edition
-
You can treat the votes as a weighted random walk, right?. I studies this many years ago, but can't remember a damn thing about the analysis. I Wiki'd it briefly, and then closed the page in horror at how much I've forgotten.
I was only joking
-
I was thinking you could model it as a lattice path of n=94, but only after the first two votes come in. But I haven’t figured out how to work the probabilities in.
-
You can treat the votes as a weighted random walk, right?. I studies this many years ago, but can't remember a damn thing about the analysis. I Wiki'd it briefly, and then closed the page in horror at how much I've forgotten.
@Doctor-Phibes said in Puzzle Time - Election Edition:
You can treat the votes as a weighted random walk, right?. I studies this many years ago, but can't remember a damn thing about the analysis. I Wiki'd it briefly, and then closed the page in horror at how much I've forgotten.
Yep, thought about that, too. What makes this problem difficult is that it's not a Markov chain: the probabilities change based on previous outcomes.
A standard example in stochastic processes is that of a drunkard who either takes steps towards a cliff with probability p or the other way with probability 1-p, and then to compute the probability that he will eventually fall over the cliff. But that's simpler because it is a Markov chain, I think.
-
Here's why:
||
Let's call a sequence of votes a path.There's a one-to-one correspondence between the paths that start with H and the paths that start with K but lead to a tie.
Meaning there are just as many of the former as of the latter.
The "successful" paths are the remaining ones.
So the probability of being on a successful path is
1 - 2*(probability of starting with H).
The probability of starting with H is 95/200. Hence
1-2*95/200 = (105-95)/(105-95) = 0.05.
||
That was way easier than I thought. Which probably means I screwed up
-
Here's how to construct the 1:1 correspondence.
Assume a path that leads to a tie, say
KKHH...
which yields a tie after 4 votes.
Now take every vote until the tie and flip K with H and vice versa.
The remainder stays the same.HHKK...
That's the corresponding path starting with H.
That correspondence works both ways because every path starting with H must eventually be tied at some point (because K has more votes).
-
No, there are plenty of cases where K has the lead, loses the lead for a while, and gains it back.
@jon-nyc said in Puzzle Time - Election Edition:
No, there are plenty of cases where K has the lead, loses the lead for a while, and gains it back.
Exactly. Those cases shouldn't count as successful. And I don't count them, since they are among the paths where there is at least one tie in between.
Hello! It looks like you're interested in this conversation, but you don't have an account yet.
Getting fed up of having to scroll through the same posts each visit? When you register for an account, you'll always come back to exactly where you were before, and choose to be notified of new replies (either via email, or push notification). You'll also be able to save bookmarks and upvote posts to show your appreciation to other community members.
With your input, this post could be even better 💗
Register Login