Elections and Happiness
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I feel like Im getting lost in my rabbit hole trying to solve this.
So the idea is we have 3 rounds of voting, 1 to find the top 2 candidate, 2 to find the winner of the 2 and 3 to find who made everyone happy
The part I'm getting stuck on is why there is a need to have the 2 rounds of votes, if the winner is who has the most votes anyways.
The example given 1973 7 4 0.945 0.731 1 0.542; 0.272 0.11 0.042 1; 0.335 1 0.045 0; 1 0.005 0.783 0.323; 0.247 0.014 0.664 1; 1 0.005 0.018 0.071; 0.022 0.058 0.294 1
Candidate 4 has the most votes at 3 total votes as well as the most happiness 3.936 Candidate 1 has the second most votes (2 votes) as well as the second most happiness 3.821
In this example, the people voted for the right person no?
Hi, this problem aims to illustrate that voting systems can be perceived as skewed or unfair. Your are absolutely right that candidate 4 gets 3 votes in round 1, candidate 1 gets 2 votes, and the others get 1 vote each. Note that nobody gets the absolute majority of votes in round 1; that would require at least 4 of the 7 total votes. In this problem, we therefore always go to a head-to-head of the top two candidates in a second round. In a vote of candidate 1 versus candidate 4, candidate 1 gets 4 votes and candidate 4 gets 3 votes. Therefore candidate 1 wins. If voting was based on total happiness instead, candidate 4 would win.
Hi, thank you for writting back.
Going off of the second part of your response, how did candidate 1 get 4 votes?
I'm sure this is where i get lost at. Is it where we compare the votes, and they recieve the "vote"?
Round 1:
Cand1 Cand2 Cand3 Cand4
Voter1: 0.945 0.731 1.000 0.542
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Voter2: 0.272 0.110 0.042 1.000
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Voter3: 0.335 1.000 0.045 0.000
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Voter4: 1.000 0.005 0.783 0.323
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Voter5: 0.247 0.014 0.664 1.000
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Voter6: 1.000 0.005 0.018 0.071
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Voter7: 0.022 0.058 0.294 1.000
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Round 2:
Cand1 Cand4
Voter1: 0.945 0.542
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Voter2: 0.272 1.000
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Voter3: 0.335 0.000
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Voter4: 1.000 0.323
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Voter5: 0.247 1.000
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Voter6: 1.000 0.071
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Voter7: 0.022 1.000
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