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20% of people vote 'No' for each question, and everyone else votes 'Yes'. Then each question has an 80% agreement of 'Yes', so the repairs go ahead. However, now consider the situation where the community are asked one question: "Are all three conditions (importance, weather and funds) met?" Now 60% of people disagree with one of these conditions, so only 40% agree on a 'Yes' vote. In this case, the repairs do not go ahead. Thus the road repair team gets different feedback depending on how they poll their community.
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This dilemma results because an actual decision-making procedure might be premise-based or conclusion-based. In a premise-based procedure, the judges decide by voting whether the conditions for liability are met. In a conclusion-based procedure, the judges decide directly whether the defendant should
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Each judge could make consistent (non-contradictory) judgments, and the paradox will still emerge. Most judges could think P is true, and most judges could think Q is true. In this example, that means they would vote that the caretaker probably mowed over the roses, and that the contract did indeed
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Consider a community voting on road repairs asked three questions; the repairs go ahead if all three answers are 'Yes'. The questions are: "Are the roads important?", "Is the weather right for road repair?" and "Are there available funds for repairs?" Imagine that three (non-overlapping) groups of
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To see how, imagine that a three-member court must decide whether someone is liable for a breach of contract. For example, a lawn caretaker is accused of violating a contract not to mow over the land-owner's roses. The jurors must decide which of the following propositions are true:
343:, which endeavors to understand and predict group behaviour. Petitt warns that we need to understand groups because they can be very powerful, can effect greater change, and yet the group as a whole may not have a strong conscience (see
358:. List and Pettit argue that the discursive dilemma can be likewise generalized to a sort of "List–Pettit theorem". Their theorem states that the inconsistencies remain for any aggregation method which meets a few natural conditions.
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simply by identifying the majority opinion on multiple questions. This is because contradictory conceptions of a group can emerge depending on the type of questioning that is chosen.
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Pettit believes that the lesson of this paradox is that there is no simple way to aggregate individual opinions into a single, coherent "group entity". These ideas are relevant to
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be liable. In the above formulation, the paradox is that the two procedures do not necessarily lead to the same result; the two procedures can even lead to opposite results.
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At the same time, most judges may think that P and Q are not both true at once. In this example, that means most judges conclude the caretaker is
370:- similar to judgement aggregation in that voters have to decide on several related issues; different in that they vote according to their
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is important to sort out, and Petitt insists that groups should have limited rights, and various obligations and checks on their power.
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270:: the defendant had a contractual obligation not to do that action (i.e. was there a contract not to mow over the roses?);
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In general, any decision that is not unanimous can be logically self-contradictory. The theorem is closely related to the
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The doctrinal paradox shows it is difficult to construct a model of
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Aggregating Sets of
Judgments: Two Impossibility Results Compared
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The discursive dilemma can be seen as a special case of the
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