Statistics Question?

Question

How can I figure this out: I am in a pool of 550 people voting 10 votes each for 550 candidates. You can't vote for a candidate more than once. 100 Candidates win. How many votes do I need to win?

Answer 1

If the person can vote for himself,
first 10 persons can vote for 100 candidates and
each candidate can get 1 vote from first 10 persons.

for 550 persons to vote for 100 candidates,
100 candidates can get 55 votes each to win.

You need at least 55 votes to win

Answer 2

Assuming that everyone votes, and that everyone votes 10 times, giving 1-10 votes (and never using the same number twice), this is what it comes down to. The first thing we know is that there are 550 * 10 * 11 / 2 = 30,250 available votes (550 voters times the total number of vote score per voter).

Since there are 100 winners, and assuming that all the votes went to the winners (i.e. those who did not win received zero votes), the average vote score for the winners is 30,250 / 100 = 302.5

The best case scenario is that you can vote for yourself and that you get all the votes - in that case, you have 550 * 10 = 5,500 vote score and you get the first place.

On the other hand, you could get in the 100 group by winning a single vote, and if the rest 450 voters (who did not win) did not vote for themselves. It might be highly unlikely, but not impossible. Here's how (just one possibility):
1. One man gets all the 10 point votes
2. Another man gets all the 9 point votes
3. Third one gets all the 8 point votes
...
9. One man gets all the 2 point votes

So far, 29,700 votes used and 9 people elected, which leaves us with 550 votes (comprised of 1 point votes) and 91 more to be elected.

10. You get 1 vote (1 point), and 89 people get 6 votes each (1 point votes). The last man gets 15 votes (in total: 1+ 6 * 89 + 15 = 550 1-point votes).

So, in total, it's:
550 * 10 + 550 * 9 + ... + 550 * 2 + 1 + 89 * 6 + 15 = 30,250 vote points, and

9 + 1 + 89 + 1 = 100 elected
(9 with the most points plus YOU plus 89 with 6 points each plus the last one with 15 points)

In the end, everything depends on the voters / those who are candidates, and in real life things are not that random or simple. Or perfect, for that matter.