| 21. | Cumulative voting satisfies the monotonicity criterion, the participation criterion, the consistency criterion, and reversal symmetry.
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| 22. | However, all forms of STV are vulnerable to some degree of tactical voting because they lack monotonicity.
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| 23. | This is classic monotonicity violation : the 321 who voted for the Liberals took part in hurting their own candidate.
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| 24. | In a single-parameter domain, weak monotonicity is also a " sufficient " condition for implementability.
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| 25. | Then, Ax is the i-th standard basis vector, and hence x \ geq 0 by monotonicity.
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| 26. | The monotonicity property ensures that the degree of truth of conjunction does not decrease if the truth values of conjuncts increase.
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| 27. | POOL is a monotonicity-constrained maximum likelihood method for the prediction of properties that depend monotonically on the input features.
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| 28. | E . g ., harming candidate by changing some ballots from to isn't a violation of the monotonicity criterion.
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| 29. | D . Petz also gave another condition when the equality holds in Monotonicity of quantum relative entropy : the first statement below.
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| 30. | If the order \ leq in the definition of monotonicity is replaced by the strict order, then one obtains a stronger requirement.
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