If a "rating" is based off of the last 100 yes/no answers, looking to see how my rating would be affected based on a number of factors outlined below.

Question

My rating is based off of the previous 100 ratings, which consists simply of of "Yes" or "No". It is calculated as such so that when you receive the 101th rating, the 1st rating falls off, 102nd rating the 2nd falls off, and so on.

I am currently at a 65%, so that would mean 65 yes and 35 no. The order in which the 65 yes's and 35 no's is unknown.

Over the course of the next 27 ratings, I provide 25 yes's and 2 no's in any order you wish (1 no, 23 yes, 1 no, 2 yes is okay. 24 yes, 2 no, 1 yes is okay, and so on). However my rating after these 27 answers has just moved up to 67%.

How many more times can continue to answer "yes" while keeping the rating at 67%? Meaning - at what point must the rating go up to 68% if every answer from this point is "yes".

What does this have to do with statistical mechanics? None of these tags seems appropriate. — saulspatz, Dec 02 '19 at 06:22
Please remove them then and let me know more appropriate tags. thank you. — wardr, Dec 02 '19 at 06:26

saulspatz · Accepted Answer · 2019-12-02T14:33:40.363

1

You can add the most "yes" votes without without changing your rating if all the "yes" votes are at the front. Since there we only two "no" votes in the last $27$ and the rating only went up $2$, there must have been $27$ "yes" votes dropped from the front. If all $65$ "yes" votes were at the front to start with, there are $38$ left, and there cannot be more. So, you can vote "yes" at most $38$ times before your rating increases.

edited Dec 02 '19 at 14:33

answered Dec 02 '19 at 06:31

saulspatz

53,131

1

if they're all no votes and you vote yes repeatedly that'll make the vote go up, won't it ? since the no votes are replaced with yes votes up – Saketh Malyala Dec 02 '19 at 08:10
1

@SakethMalyala I don't know what I was thinking. Must have been past my bedtime. – saulspatz Dec 02 '19 at 14:18
I do believe this is the correct answer, thank you so much. good job! – wardr Dec 03 '19 at 08:48

If a "rating" is based off of the last 100 yes/no answers, looking to see how my rating would be affected based on a number of factors outlined below.

1 Answers1