Electing Chief Residents

[lowbudget]

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At an 20-20-20 program, with 2 resident-elected Chief Residents, what is the minimum number of votes a candidate needs if 5 people are running office? Top 2 vote getters win the office. Each resident gets 2 votes.

 

[Apollyon]

You're asking a math question. If you can calculate drug doses or drip rates, you can do it!

Even if you can't, the internet has wide-ranging resources to help you.

When you say "each resident gets two votes", can one person cast both votes for the same person? Or is it a "pick two of five", and, if a person only votes for one person, the second vote is null?

 

[lowbudget]

Meh, I'm not as smart as some of you (although I have a number already in mind). And yes, this is a math problem.

One person cannot cast both votes to the same person. You must pick 2 of five. I don't know what happens if only one vote is casted. I imagine the vote is still counted, however, let's assume that all residents pick 3 chiefs on their ballots.

 

[NotAProgDirector]

Meh, I'm not as smart as some of you (although I have a number already in mind). And yes, this is a math problem.

One person cannot cast both votes to the same person. You must pick 2 of five. I don't know what happens if only one vote is casted. I imagine the vote is still counted, however, let's assume that all residents pick 3 chiefs on their ballots.

60 residents in the program total. Each gets 2 votes (per your original post, this one suggests everyone gets 3 votes). So, there are 120 total votes.

There are 2 chief spots.

Worst case scenario is that 3 people split all the votes (let's call them A, B, and C). In that case 20 people vote for A + B, 20 people vote for B + C, and 20 people vote for A + C. You can see that in this case, each candidate gets 40 votes.

Hence, if you get 41 votes, you must mathematically win.

You can actually build an excel table that will tell you, based on the number of votes that you get, what your chances of winning are -- you simply calculate the chances of two other people getting enough votes to beat your vote total, assuming everyone votes randomly (which is a big and invalid assumption, but an interesting math challenge indeed).

 

[Pilot]

First question I would ask is "do the residents votes really count towards anything"? At the residency I completed, the residents votes were "taken under consideration", but the faculty made the ultimate decision as to who the Chief Residents were.

 

[gutonc]

Is there a way to vote against getting co-opted into that miserable job?

 

[michaelrack]

At an 20-20-20 program, with 2 resident-elected Chief Residents, what is the minimum number of votes a candidate needs if 5 people are running office? Top 2 vote getters win the office. Each resident gets 2 votes.

I think the answer is 16-

everyone gives one vote to candidate A - 60 votes

then if the remaining votes are split 16 for B, 15 C, 15 D, and 14 for candidate E , 16 would be the minimum number of votes.

 

[NotAProgDirector]

I think the answer is 16-

everyone gives one vote to candidate A - 60 votes

then if the remaining votes are split 16 for B, 15 C, 15 D, and 14 for candidate E , 16 would be the minimum number of votes.

What if the vote tallies are:
A - 16
B - 20
C - 20
D - 32
E - 32

Person with 16 comes in last, and D & E win with 32.

 

[michaelrack]

What if the vote tallies are:
A - 16
B - 20
C - 20
D - 32
E - 32

Person with 16 comes in last, and D & E win with 32.

It is very unlikely that someone could become chief with only 16 votes, but it is mathematically possible. I think that is the question the OP was asking- the minimum # of votes that would make it possible to become chief.

 

[NotAProgDirector]

It is very unlikely that someone could become chief with only 16 votes, but it is mathematically possible. I think that is the question the OP was asking- the minimum # of votes that would make it possible to become chief.

Yes - logged in early this AM to correct my post but you've already beat me to the punch. We answered different questions. If you get 41 votes you must win, no matter what else happens with the other votes. If you get 15 votes, you must lose, no matter what else happens with the rest of the votes (I am assuming that a four-way-tie is a "loss"). Not clear which question the OP was asking, although re-reading it I think your answer is the one they wanted. In any case, now he/she has both answers.

Turns out that figuring the exact likelihood of winning based upon the number of votes you get is more complicated than I first thought. I'm still thinking about it, but a Monte Carlo simulation might be the best way to answer that question.