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#1 Re: Help Me ! » Elections Winning Odds problem » 2009-05-18 03:45:08

If we collected all the votes and picked one random vote then the probability that this vote goes to a specific candidate:

P1 (one Rank1Candidate) = 3 / (3*8+2*12+1*30)
P2 (one Rank2 Candidate) = 2 / (3*8+2*12+1*30)
P3 (one Rank3 Candidate) = 1 / (3*8+2*12+1*30)

Thus all candidates in the same rank has equal chances.

Since each voter has 8 votes then the probability of RankX candidate to be voted for:

P_vote = 1 - P_novote

The probability of candidate from RankX not being voted for from 1 voter is:

P_novote = (1 - PX)^8 bcasue there are 8 votes total and not being voted for can be described as:

[(1-Px) for vote1] And [(1-Px) for Vote2] And....... And [(1-Px) for vote8)   =  (1-Px)^8

P_vote = 1 - (1-Px)^8


For each candidate in ranks group:

P1_Vote = 1 - (1 - P1)^8
P2_Vote = 1 - (1 - P2)^8
P3_Vote = 1 - (1 - P3)^8

#2 Re: Help Me ! » Elections Winning Odds problem » 2009-05-17 10:23:33

Yes,

There was and error in the oppenning post where I said Rank1 has twice Rank2, I have edited it.

The ratios are taken directly from score so:

R1:R2 = 3:2
R1:R3 = 3:1
R2:R3 = 2:1

#3 Help Me ! » Elections Winning Odds problem » 2009-05-17 08:59:46

deep_blue
Replies: 4

I have a probability problem that puzzles me:

There are elections for a city council, total of 50 candidates and 1000 voters. There are 8 seats available in the city council and each voter has 8 votes so that a voter must select 8 different names from 50 candidates with any order. To win the election a candidate must get votes of 40% of voters.

Candidates = 50
Voters = 1000
seats = 8
Vmin = Votes required to win = 0.4*1000 = 400

Assume that polls results were taken and that candidates were ranked according to this poll into the following ranks:
Rank1: 8 candidates  , score = 3
Rank2: 12 candidates , score = 2
Rank3: 30 candidates , score = 1

Rank1 has 3 times the chances of Rank3 and 1.5 the chances of Rank2 .. and so on.

What is the probability of a candidate from Rank1 to win the elections?
What is the probability of a candidate from Rank2 to win the elections?
What is the probability of a candidate from Rank3 to win the elections?

I tried solving the problem but didn't get convincing results, I will not show the procedure that I used to avoid affecting any received answers.

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