Prefer Accept Reject voting: Difference between revisions

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Line 5: # Out of the candidates (if any) with no more than 50% "Reject", find the one with the most points. '''For every ballot which doesn't "Prefer" this frontrunner, add 1 point for each "Accept".''' # If the frontrunner still has the most points, they win. Otherwise, the winner is the candidate with fewest "Reject" ratings. To express it in a single sentence: if the most-preferred non-majority-rejected candidate, X, has more non-reject votes than any other candidate has non-reject votes that aren't below X, then X wins; otherwise, the least-rejected candidate wins. Note that the procedure above will always elect a candidate with no more than 50% "Reject", if any exist. This is because, if any exist, one of them will be the frontrunner, and they will thus score points equal to at least 50% of the voters. Line 24 ⟶ 26: * It fails [[Independence of irrelevant alternatives]], but passes [[Local independence of irrelevant alternatives]]. * It fails the [[Condorcet criterion]], but if there is a voted majority Condorcet winner X, then any faction (defined as the set of voters who prefer X>Y,Z, or alternately as the set who prefer Y>X>Z, for some Y and Z) can ensure that ZX ~~doesn't~~beats ~~win~~Z, using semi-honest ballots (X>>Z or YX>>Z, respectively). * It fails the [[participation criterion]] but passes the [[semi-honest participation criterion]]. Line 43 ⟶ 45: * 40: C>B None are majority-rejected, and C is the frontrunner. Points are: A, 60; B, 55; C, 55; X, 35. A wins. However, if 611 of the last group of voters strategically betrayed their true favorite C, the situation would be as follows: * 30: AX>B (That is, on 35 ballots, A and X are preferred, B is accepted, and C is rejected) Line 49 ⟶ 51: * 15: B>A * 10: B>AC * 3429: C>B * 611: B Now, C is not viable with 51% rejection; so B is the leader. Since C is no longer the leader, B gets the 34 points from C voters, and wins. The strategy succeeded; the strategic voters are better off. Line 120 ⟶ 122: === Logic for 25%-preferred threshold (step 2) === The 25%-preferred threshold in step 21 is not purely arbitrary; it is exactly enough so that, in a 3-candidate election where all voters give all three grades, there will always be at least 1 candidate who passes the thresholds to not be disqualified. In other words: if a minority supports a rejected candidate, while a majority divides preferences between two candidates while accepting the other, then at least one of those two will not be disqualified. This does not hold for an election with 4 or more candidates, because the majority could split its preferences more than two ways; but even in those cases, it is usually reasonable to hope that the top 3 candidates combined will get enough preferences to ensure that at least one of them is above the 25% threshold. [[Category:Graded Bucklin ~~systems~~methods]]