I need expert help on the math behind the following voting mechanism, any comment towards solutions are greatly appreciated!
A country is holding a poll to determine the top 100 restaurants out of its 100 thousand domestic restaurants.
Assuming each restaurant is unique, no chains or franchises, all of them share equal and fair chance of exposure to all customers nationwide.
In the end there were 1 million valid voters, with each voter named 5 restaurants. Say each voter entered 5 non-repeat and valid entries.
Is there a way to estimate: 1. the minimum votes a restaurant needs to be in top 100; 2. how many votes does #1 get?
I'm not a math expert so my educated guess is each restaurant has a probability of 0.1% chance to be voted but that's as far as I could go, I have absolutely 0 idea how to proceed next…
Look forward to your help, thanks!
Thank you guys for all the insightful inputs! I’m confident that we’re on the right track to finding out the best answer and we’re close.
If we are to put our solutions to test in a real world scenario however, I think it’s highly unlikely that a mere 2 digit votes will render a lucky restaurant Top 100. I assume we can all agree on this?
So now the question is: how can we apply common sense to the equation? How do we identify the distribution model in real world?
The Gaussian distribution seems to be an adequate one to describe the world we live in, where heavenly restaurants and unholy ones are extremely rare, and passable/half-decent ones constitute the majority.
Let's add more conditions to define the scenario:
- Each restaurant has a Twitter account
- The voting result is positively correlated with Twitter follower counts
- The #1 restaurant has 10,000,000 followers whereas #100 has 100K
Does this make more sense?