Probability Scenario

#1
Here’s the scenario:

A committee of 9 people is deciding which 5 people of 14 candidates should be hired for a job.
In order to be hired, a candidate must receive 5 votes.
Each of the 9 people on the committee has 5 votes to give (i.e., each of the 9 can each only vote for five people).

While it’s possible that more than five of the candidates could receive 5 votes (right?) it seems pretty improbable. That’s my question: how probable/improbable is it that more than 5 of the 14 would receive
5 votes?
 

rogojel

TS Contributor
#2
hi,
I am sure there is a nice and fancy way to calculate this, but in case you are interested in the actual numbers running a quick simulation wirh 100000 voting runs gives: 0 candidates with more then 5 votes - 37%, 1 candidate 45%, 2 candidates 16%, 3 candidates 2%, 4 candidates 0,1% , 5 candidates 0.001%.

regards
 

ArtK

New Member
#5
Here’s the scenario:

A committee of 9 people is deciding which 5 people of 14 candidates should be hired for a job.
In order to be hired, a candidate must receive 5 votes.
Each of the 9 people on the committee has 5 votes to give (i.e., each of the 9 can each only vote for five people).

While it’s possible that more than five of the candidates could receive 5 votes (right?) it seems pretty improbable. That’s my question: how probable/improbable is it that more than 5 of the 14 would receive
5 votes?
Well, assuming random selections by the judges, you're right that the probability of 6 candidates getting 5 votes from each of 9 judges is small (about 0.0003). But so is the probability of 5 candidates getting 5 votes rather small (about 0.005). It strikes me that if all of the 14 candidates are judged to be on a par, and all well qualified, that the resulting random selections by the judges would lead to similar low probabilities ...and none of the qualified candidates would be selected.

Seems to me the process is geared to work fairly well only when a small handfull of candidates stand head-and-shoulders above the rest.

Art