Optimal Bounds for the Change-Making Problem

The change-making problem is the problem of representing a given value with the fewest coins possible. We investigate the problem of determining whether the greedy algorithm produces an optimal representation of all amounts for a given set of coin denominations 1 = c_1 < c_2 < ... < c_m. Chang and Gill show that if the greedy algorithm is not always optimal, then there exists a counterexample x in the rangec_3 <= x < (c_m(c_m c_m-1 + c_m - 3c_m-1)) \ (c_m - c_m-1).To test for the existence of such a counterexample, Chang and Gill propose computing and comparing the greedy and optimal representations of all x in this range. In this paper we show that if a counterexample exists, then the smallest one lies in the range c_3 + 1 < x < c_m + c_m-1, and these bounds are tight. Moreover, we give a simple test for the existence of a counterexample that does not require the calculation of optimal representations.In addition, we give a complete characterization of three-coin systems and an efficient algorithm for all systems with a fixed number of coins. Finally, we show that a related problem is coNP-complete

Complexity, Climate Change and the Precautionary Principle

The precautionary principle has been proposed as a basis making decisions about environmental health under conditions of uncertainty, but remains controversial. This paper shows how the precautionary principle may be interpreted as a guide to decision making in complex systems characterised by unfavorable surprises. The application of the precautionary principle to the problem of climate change is discussed.

This Paper Might Change your Mind

Rational decision change can happen without information change. This is a problem for standard views of decision theory, on which linguistic intervention in rational decision-making is captured in terms of information change. But the standard view gives us no way to model interventions involving expressions that only have an attentional effects on conversational contexts. How are expressions with non-informational content - like epistemic modals - used to intervene in rational decision making? We show how to model rational decision change without information change: replace a standard conception of value (on which the value of a set of worlds reduces to values of individual worlds in the set) with one on which the value of a set of worlds is determined by a selection function that picks out a generic member world. We discuss some upshots of this view for theorizing in philosophy and formal semantics

Climate Change and the Limits of the Possible

Climate change looks to be more than just another environmental problem. It threatens to test the limits of our dominant ways of understanding and solving, not just environmental problems, but problems of political economy generally. Climate change has distinctive temporal and spatial features – how long it takes to unfold and the ways in which its effects are distributed across the globe – which may outstrip the capacity of our basic principles of economic and political decision-making. If so, then understanding the issue in a static way may ensure that we expect to fail in addressing it and are inarticulate about our prospects for success. That is, if we assume that economic and political decisions reflect the present distribution of self-interest within the existing structure of rules and institutions, we may be unable to see our way beyond the problem, because it so neatly frustrates the problem-solving power of our current arrangements. We may need, instead, to adopt a dynamic view of political econom

Moral disengagement and the motivational gap in climate change

Although climate change jeopardizes the fundamental human rights of current as well as future people, current actions and ambitions to tackle it are inadequate. There are two prominent explanations for this motivational gap in the climate ethics literature. The first maintains that our conventional moral judgement system is not well equipped to identify a complex problem such as climate change as an important moral problem. The second explanation refers to people’s reluctance to change their behaviour and the temptation to shirk responsibility. We argue that both factors are at play in the motivational gap and that they are complemented by crucial moral psychological insights regarding moral disengagement, which enables emitters to dissociate self-condemnation from harmful conduct. In this way, emitters are able to maintain their profligate, consumptive lifestyle, even though this conflicts with their moral standards with respect to climate change. We provide some illustrations of how strategies of moral disengagement are deployed in climate change and discuss the relationship between the explanations for the motivational gap and moral disengagement. On the basis of this explanatory framework, we submit that there are three pathways to tackle the motivational gap and moral disengagement in climate change: making climate change more salient to emitters and affirming their self-efficacy; reconsidering the self-interested motives that necessitate moral disengagement; and tackling moral disengagement directly

No Harm Done? An Experimental Approach to the Nonidentity Problem

Discussions of the non-identity problem presuppose a widely shared intuition that actions or policies that change who comes into existence don't, thereby, become morally unproblematic. We hypothesize that this intuition isn’t generally shared by the public, which could have widespread implications concerning how to generate support for large-scale, identity-affecting policies relating to matters like climate change. To test this, we ran a version of the well-known dictator game designed to mimic the public's behavior over identity-affecting choices. We found the public does seem to behave more selfishly when making identity-affecting choices, which should be concerning. We further hypothesized that one possible mechanism is the notion of harm the public uses in their decision-making and find that substantial portions of the population seem to each employ distinct notions of harm in their normative thinking. These findings raise puzzling features about the public’s normative thinking that call out for further empirical examination

Path integral solution for an angle-dependent anharmonic oscillator

We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we were able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.Comment: Corrected typos and mistakes, To appear in Communications in Theoretical Physic

Neural correlates of cognitive dissonance and choice-induced preference change

According to many modern economic theories, actions simply reflect an individual's preferences, whereas a psychological phenomenon called “cognitive dissonance” claims that actions can also create preference. Cognitive dissonance theory states that after making a difficult choice between two equally preferred items, the act of rejecting a favorite item induces an uncomfortable feeling (cognitive dissonance), which in turn motivates individuals to change their preferences to match their prior decision (i.e., reducing preference for rejected items). Recently, however, Chen and Risen [Chen K, Risen J (2010) J Pers Soc Psychol 99:573–594] pointed out a serious methodological problem, which casts a doubt on the very existence of this choice-induced preference change as studied over the past 50 y. Here, using a proper control condition and two measures of preferences (self-report and brain activity), we found that the mere act of making a choice can change self-report preference as well as its neural representation (i.e., striatum activity), thus providing strong evidence for choice-induced preference change. Furthermore, our data indicate that the anterior cingulate cortex and dorsolateral prefrontal cortex tracked the degree of cognitive dissonance on a trial-by-trial basis. Our findings provide important insights into the neural basis of how actions can alter an individual's preferences