Many results of modern physics--those of quantum mechanics, for instance--come in a probabilistic... more Many results of modern physics--those of quantum mechanics, for instance--come in a probabilistic guise. But what do probabilistic statements in physics mean? Are probabilities matters of objective fact and part of the furniture of the world, as objectivists think? Or do they only express ignorance or belief, as Bayesians suggest? And how are probabilistic hypotheses justified and supported by empirical evidence? Finally, what does the probabilistic nature of physics imply for our understanding of the world? This volume is the ...
Colorado’s Amendment 36 proposed to switch Colorado’s representation in the Electoral College fro... more Colorado’s Amendment 36 proposed to switch Colorado’s representation in the Electoral College from winner-takes-all to proportionality. We evaluate unilateral and uniform switches to proportionality both from Colorado’s perspective and from an impartial perspective on the basis of a priori and a posteriori voting power measures. The present system is to be preferred to a unilateral switch from any perspective on any measure. A uniform switch is to be preferred to the present system from Colorado’s perspective on an a priori measure, and from an impartial perspective on an a posteriori measure. The present system is to be preferred to a uniform switch from Colorado’s perspective on an a posteriori measure (with some qualifications), and from an impartial perspective on an a priori measure. We conclude with a discussion of the appropriateness of these measures.
We consider a decision board with representatives who vote on proposals on behalf of their consti... more We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We set up a simple model and obtain roughly the following results. If the interests of people from the same constituency are uncorrelated, then a weighted rule with square root weights does best in terms of both ideals. If there are perfect correlations, then the utilitarian ideal requires proportional weights, whereas the egalitarian ideal requires equal weights. We investigate correlations that are in between these extremes and provide analytic arguments to connect our results to Barberà and Jackson (J Polit Econ 114(2):317–339, 2006) and to Banzhaf voting power.
In decision-theory, the notion of regret enters into the minimax decision-rule and has a determin... more In decision-theory, the notion of regret enters into the minimax decision-rule and has a determinate usage in this context. However, there are many alternative ways of conceiving of regret. The chapter constructs the einmal-ist- nicht-keinmal ('once is not never') game, in which a single sampling radically changes the expected value of the game in a way that is quite counterintuitive, as the basis for studying regret after a loss following the choice of an uncertain action. Crucially, the very loss affects the posterior expectation of the game and the posterior credence about the objective chances of a win. Our taxonomy of regret contains regret over the action chosen and regret over the outcome obtained as its main categories, and is mirrored by a taxonomy of joy after a win following the choice of an uncertain action,It is used to criticize Krähmer and Stone's analysis of risk aversion for uncertain actions.
The mean majority deficit in a two-tier voting system is a function of the partition of the popul... more The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.
Belgium has recently extended its euthanasia legislation to minors, making it the first legislati... more Belgium has recently extended its euthanasia legislation to minors, making it the first legislation in the world that does not specify any age limit. I consider two strands in the opposition to this legislation. First, I identify five arguments in the public debate to the effect that euthanasia for minors is somehow worse than euthanasia for adults-viz, arguments from weightiness, capability of discernment, pressure, sensitivity and sufficient palliative care-and show that these arguments are wanting. Second, there is another position in the public debate that wishes to keep the current age restriction on the books and have ethics boards exercise discretion in euthanasia decisions for minors. I interpret this position on the background of Velleman's 'Against the Right to Die' and show that, although costs remain substantial, it actually can provide some qualified support against extending euthanasia legislation to minors.
Many results of modern physics--those of quantum mechanics, for instance--come in a probabilistic... more Many results of modern physics--those of quantum mechanics, for instance--come in a probabilistic guise. But what do probabilistic statements in physics mean? Are probabilities matters of objective fact and part of the furniture of the world, as objectivists think? Or do they only express ignorance or belief, as Bayesians suggest? And how are probabilistic hypotheses justified and supported by empirical evidence? Finally, what does the probabilistic nature of physics imply for our understanding of the world? This volume is the ...
Colorado’s Amendment 36 proposed to switch Colorado’s representation in the Electoral College fro... more Colorado’s Amendment 36 proposed to switch Colorado’s representation in the Electoral College from winner-takes-all to proportionality. We evaluate unilateral and uniform switches to proportionality both from Colorado’s perspective and from an impartial perspective on the basis of a priori and a posteriori voting power measures. The present system is to be preferred to a unilateral switch from any perspective on any measure. A uniform switch is to be preferred to the present system from Colorado’s perspective on an a priori measure, and from an impartial perspective on an a posteriori measure. The present system is to be preferred to a uniform switch from Colorado’s perspective on an a posteriori measure (with some qualifications), and from an impartial perspective on an a priori measure. We conclude with a discussion of the appropriateness of these measures.
We consider a decision board with representatives who vote on proposals on behalf of their consti... more We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We set up a simple model and obtain roughly the following results. If the interests of people from the same constituency are uncorrelated, then a weighted rule with square root weights does best in terms of both ideals. If there are perfect correlations, then the utilitarian ideal requires proportional weights, whereas the egalitarian ideal requires equal weights. We investigate correlations that are in between these extremes and provide analytic arguments to connect our results to Barberà and Jackson (J Polit Econ 114(2):317–339, 2006) and to Banzhaf voting power.
In decision-theory, the notion of regret enters into the minimax decision-rule and has a determin... more In decision-theory, the notion of regret enters into the minimax decision-rule and has a determinate usage in this context. However, there are many alternative ways of conceiving of regret. The chapter constructs the einmal-ist- nicht-keinmal ('once is not never') game, in which a single sampling radically changes the expected value of the game in a way that is quite counterintuitive, as the basis for studying regret after a loss following the choice of an uncertain action. Crucially, the very loss affects the posterior expectation of the game and the posterior credence about the objective chances of a win. Our taxonomy of regret contains regret over the action chosen and regret over the outcome obtained as its main categories, and is mirrored by a taxonomy of joy after a win following the choice of an uncertain action,It is used to criticize Krähmer and Stone's analysis of risk aversion for uncertain actions.
The mean majority deficit in a two-tier voting system is a function of the partition of the popul... more The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.
Belgium has recently extended its euthanasia legislation to minors, making it the first legislati... more Belgium has recently extended its euthanasia legislation to minors, making it the first legislation in the world that does not specify any age limit. I consider two strands in the opposition to this legislation. First, I identify five arguments in the public debate to the effect that euthanasia for minors is somehow worse than euthanasia for adults-viz, arguments from weightiness, capability of discernment, pressure, sensitivity and sufficient palliative care-and show that these arguments are wanting. Second, there is another position in the public debate that wishes to keep the current age restriction on the books and have ethics boards exercise discretion in euthanasia decisions for minors. I interpret this position on the background of Velleman's 'Against the Right to Die' and show that, although costs remain substantial, it actually can provide some qualified support against extending euthanasia legislation to minors.
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