User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
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Find the Smith set. Whoever has the most approvals in it wins.
Some examples of finding the Condorcet winner faster:
Take this example: http://web.math.princeton.edu/math_alive/6/Lab1/Condorcet.html
First, it can be observed that there are 55 voters, with all but 18 of them ranking Molson 5th (last), so [[ISDA]] allows us to say that Molson can be eliminated because a (mutual) majority prefer anyone but him. So the simplified preferences are:<blockquote>18 S>MB>G>K
12: K>MB>S>G
10: G>K>MB>S
9: S>G>MB>K
4: MB>K>S>G
2: MB>G>S>K</blockquote>It should be noted that Samuel Adams has 27 out of 55 1st choice votes, almost a majority, so it'd be prudent to check his matchups first.
S vs. MB: 27 vs. 28, a loss for Samuel Adams. So now it might be best to check MB's matchups.
MB vs. G: 30 in the top 2 lines alone, a majority, so MB is known to win just with that information alone.
MB vs. K: 18 + 9 + 4 = 31, a majority, so MB beats K. So Meister Braum is the Condorcet winner in this example.
A quick note: It can be seen that the top two lines rank only S or K above MB, and the top two lines are a majority. So one way to quickly figure out who won would've been to compare S and K to MB, and if MB pairwise beats them, then it is guaranteed that MB won, because when ignoring S and K, a majority prefer MB over all others. This is a demonstration of how Condorcet methods' attempts to make majority rule maximally comply with [[IIA]] helps in analyzing election scenarios.
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